{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0001","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push0\",\"pop0\",\"accept0\"],\"input_alphabet\":[\"a0\",\"b0\"],\"stack_alphabet\":[\"Z0\",\"A0\"],\"start_state\":\"push0\",\"bottom_symbol\":\"Z0\",\"final_states\":[\"accept0\"],\"transitions\":[[\"push0\",\"a0\",\"Z0\",\"push0\",[\"Z0\",\"A0\"]],[\"push0\",\"a0\",\"A0\",\"push0\",[\"A0\",\"A0\"]],[\"push0\",\"b0\",\"A0\",\"pop0\",[]],[\"pop0\",\"b0\",\"A0\",\"pop0\",[]],[\"push0\",null,\"Z0\",\"accept0\",[\"Z0\"]],[\"pop0\",null,\"Z0\",\"accept0\",[\"Z0\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push0, pop0, accept0], [a0, b0], [Z0, A0], push0, Z0, [accept0], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push0, pop0, accept0], [a0, b0], [Z0, A0], push0, Z0, [accept0], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107001,"parameters":{"states":["push0","pop0","accept0"],"input_alphabet":["a0","b0"],"stack_alphabet":["Z0","A0"],"start_state":"push0","bottom_symbol":"Z0","final_states":["accept0"],"transitions":[["push0","a0","Z0","push0",["Z0","A0"]],["push0","a0","A0","push0",["A0","A0"]],["push0","b0","A0","pop0",[]],["pop0","b0","A0","pop0",[]],["push0",null,"Z0","accept0",["Z0"]],["pop0",null,"Z0","accept0",["Z0"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z0\",\"final_states\":[\"accept0\"],\"input_alphabet\":[\"a0\",\"b0\"],\"stack_alphabet\":[\"A0\",\"Z0\"],\"start_state\":\"push0\",\"states\":[\"accept0\",\"pop0\",\"push0\"],\"transitions\":[[\"pop0\",\"b0\",\"A0\",\"pop0\",[]],[\"pop0\",null,\"Z0\",\"accept0\",[\"Z0\"]],[\"push0\",\"a0\",\"A0\",\"push0\",[\"A0\",\"A0\"]],[\"push0\",\"a0\",\"Z0\",\"push0\",[\"Z0\",\"A0\"]],[\"push0\",\"b0\",\"A0\",\"pop0\",[]],[\"push0\",null,\"Z0\",\"accept0\",[\"Z0\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0002","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push1\",\"pop1\",\"accept1\"],\"input_alphabet\":[\"a1\",\"b1\"],\"stack_alphabet\":[\"Z1\",\"A1\"],\"start_state\":\"push1\",\"bottom_symbol\":\"Z1\",\"final_states\":[\"accept1\"],\"transitions\":[[\"push1\",\"a1\",\"Z1\",\"push1\",[\"Z1\",\"A1\"]],[\"push1\",\"a1\",\"A1\",\"push1\",[\"A1\",\"A1\"]],[\"push1\",\"b1\",\"A1\",\"pop1\",[]],[\"pop1\",\"b1\",\"A1\",\"pop1\",[]],[\"push1\",null,\"Z1\",\"accept1\",[\"Z1\"]],[\"pop1\",null,\"Z1\",\"accept1\",[\"Z1\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push1, pop1, accept1], [a1, b1], [Z1, A1], push1, Z1, [accept1], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push1, pop1, accept1], [a1, b1], [Z1, A1], push1, Z1, [accept1], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107002,"parameters":{"states":["push1","pop1","accept1"],"input_alphabet":["a1","b1"],"stack_alphabet":["Z1","A1"],"start_state":"push1","bottom_symbol":"Z1","final_states":["accept1"],"transitions":[["push1","a1","Z1","push1",["Z1","A1"]],["push1","a1","A1","push1",["A1","A1"]],["push1","b1","A1","pop1",[]],["pop1","b1","A1","pop1",[]],["push1",null,"Z1","accept1",["Z1"]],["pop1",null,"Z1","accept1",["Z1"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z1\",\"final_states\":[\"accept1\"],\"input_alphabet\":[\"a1\",\"b1\"],\"stack_alphabet\":[\"A1\",\"Z1\"],\"start_state\":\"push1\",\"states\":[\"accept1\",\"pop1\",\"push1\"],\"transitions\":[[\"pop1\",\"b1\",\"A1\",\"pop1\",[]],[\"pop1\",null,\"Z1\",\"accept1\",[\"Z1\"]],[\"push1\",\"a1\",\"A1\",\"push1\",[\"A1\",\"A1\"]],[\"push1\",\"a1\",\"Z1\",\"push1\",[\"Z1\",\"A1\"]],[\"push1\",\"b1\",\"A1\",\"pop1\",[]],[\"push1\",null,\"Z1\",\"accept1\",[\"Z1\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0003","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push2\",\"pop2\",\"accept2\"],\"input_alphabet\":[\"a2\",\"b2\"],\"stack_alphabet\":[\"Z2\",\"A2\"],\"start_state\":\"push2\",\"bottom_symbol\":\"Z2\",\"final_states\":[\"accept2\"],\"transitions\":[[\"push2\",\"a2\",\"Z2\",\"push2\",[\"Z2\",\"A2\"]],[\"push2\",\"a2\",\"A2\",\"push2\",[\"A2\",\"A2\"]],[\"push2\",\"b2\",\"A2\",\"pop2\",[]],[\"pop2\",\"b2\",\"A2\",\"pop2\",[]],[\"push2\",null,\"Z2\",\"accept2\",[\"Z2\"]],[\"pop2\",null,\"Z2\",\"accept2\",[\"Z2\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push2, pop2, accept2], [a2, b2], [Z2, A2], push2, Z2, [accept2], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push2, pop2, accept2], [a2, b2], [Z2, A2], push2, Z2, [accept2], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107003,"parameters":{"states":["push2","pop2","accept2"],"input_alphabet":["a2","b2"],"stack_alphabet":["Z2","A2"],"start_state":"push2","bottom_symbol":"Z2","final_states":["accept2"],"transitions":[["push2","a2","Z2","push2",["Z2","A2"]],["push2","a2","A2","push2",["A2","A2"]],["push2","b2","A2","pop2",[]],["pop2","b2","A2","pop2",[]],["push2",null,"Z2","accept2",["Z2"]],["pop2",null,"Z2","accept2",["Z2"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z2\",\"final_states\":[\"accept2\"],\"input_alphabet\":[\"a2\",\"b2\"],\"stack_alphabet\":[\"A2\",\"Z2\"],\"start_state\":\"push2\",\"states\":[\"accept2\",\"pop2\",\"push2\"],\"transitions\":[[\"pop2\",\"b2\",\"A2\",\"pop2\",[]],[\"pop2\",null,\"Z2\",\"accept2\",[\"Z2\"]],[\"push2\",\"a2\",\"A2\",\"push2\",[\"A2\",\"A2\"]],[\"push2\",\"a2\",\"Z2\",\"push2\",[\"Z2\",\"A2\"]],[\"push2\",\"b2\",\"A2\",\"pop2\",[]],[\"push2\",null,\"Z2\",\"accept2\",[\"Z2\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0004","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push3\",\"pop3\",\"accept3\"],\"input_alphabet\":[\"a3\",\"b3\"],\"stack_alphabet\":[\"Z3\",\"A3\"],\"start_state\":\"push3\",\"bottom_symbol\":\"Z3\",\"final_states\":[\"accept3\"],\"transitions\":[[\"push3\",\"a3\",\"Z3\",\"push3\",[\"Z3\",\"A3\"]],[\"push3\",\"a3\",\"A3\",\"push3\",[\"A3\",\"A3\"]],[\"push3\",\"b3\",\"A3\",\"pop3\",[]],[\"pop3\",\"b3\",\"A3\",\"pop3\",[]],[\"push3\",null,\"Z3\",\"accept3\",[\"Z3\"]],[\"pop3\",null,\"Z3\",\"accept3\",[\"Z3\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push3, pop3, accept3], [a3, b3], [Z3, A3], push3, Z3, [accept3], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push3, pop3, accept3], [a3, b3], [Z3, A3], push3, Z3, [accept3], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107004,"parameters":{"states":["push3","pop3","accept3"],"input_alphabet":["a3","b3"],"stack_alphabet":["Z3","A3"],"start_state":"push3","bottom_symbol":"Z3","final_states":["accept3"],"transitions":[["push3","a3","Z3","push3",["Z3","A3"]],["push3","a3","A3","push3",["A3","A3"]],["push3","b3","A3","pop3",[]],["pop3","b3","A3","pop3",[]],["push3",null,"Z3","accept3",["Z3"]],["pop3",null,"Z3","accept3",["Z3"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z3\",\"final_states\":[\"accept3\"],\"input_alphabet\":[\"a3\",\"b3\"],\"stack_alphabet\":[\"A3\",\"Z3\"],\"start_state\":\"push3\",\"states\":[\"accept3\",\"pop3\",\"push3\"],\"transitions\":[[\"pop3\",\"b3\",\"A3\",\"pop3\",[]],[\"pop3\",null,\"Z3\",\"accept3\",[\"Z3\"]],[\"push3\",\"a3\",\"A3\",\"push3\",[\"A3\",\"A3\"]],[\"push3\",\"a3\",\"Z3\",\"push3\",[\"Z3\",\"A3\"]],[\"push3\",\"b3\",\"A3\",\"pop3\",[]],[\"push3\",null,\"Z3\",\"accept3\",[\"Z3\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0005","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push4\",\"pop4\",\"accept4\"],\"input_alphabet\":[\"a4\",\"b4\"],\"stack_alphabet\":[\"Z4\",\"A4\"],\"start_state\":\"push4\",\"bottom_symbol\":\"Z4\",\"final_states\":[\"accept4\"],\"transitions\":[[\"push4\",\"a4\",\"Z4\",\"push4\",[\"Z4\",\"A4\"]],[\"push4\",\"a4\",\"A4\",\"push4\",[\"A4\",\"A4\"]],[\"push4\",\"b4\",\"A4\",\"pop4\",[]],[\"pop4\",\"b4\",\"A4\",\"pop4\",[]],[\"push4\",null,\"Z4\",\"accept4\",[\"Z4\"]],[\"pop4\",null,\"Z4\",\"accept4\",[\"Z4\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push4, pop4, accept4], [a4, b4], [Z4, A4], push4, Z4, [accept4], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push4, pop4, accept4], [a4, b4], [Z4, A4], push4, Z4, [accept4], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107005,"parameters":{"states":["push4","pop4","accept4"],"input_alphabet":["a4","b4"],"stack_alphabet":["Z4","A4"],"start_state":"push4","bottom_symbol":"Z4","final_states":["accept4"],"transitions":[["push4","a4","Z4","push4",["Z4","A4"]],["push4","a4","A4","push4",["A4","A4"]],["push4","b4","A4","pop4",[]],["pop4","b4","A4","pop4",[]],["push4",null,"Z4","accept4",["Z4"]],["pop4",null,"Z4","accept4",["Z4"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z4\",\"final_states\":[\"accept4\"],\"input_alphabet\":[\"a4\",\"b4\"],\"stack_alphabet\":[\"A4\",\"Z4\"],\"start_state\":\"push4\",\"states\":[\"accept4\",\"pop4\",\"push4\"],\"transitions\":[[\"pop4\",\"b4\",\"A4\",\"pop4\",[]],[\"pop4\",null,\"Z4\",\"accept4\",[\"Z4\"]],[\"push4\",\"a4\",\"A4\",\"push4\",[\"A4\",\"A4\"]],[\"push4\",\"a4\",\"Z4\",\"push4\",[\"Z4\",\"A4\"]],[\"push4\",\"b4\",\"A4\",\"pop4\",[]],[\"push4\",null,\"Z4\",\"accept4\",[\"Z4\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0006","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push5\",\"pop5\",\"accept5\"],\"input_alphabet\":[\"a5\",\"b5\"],\"stack_alphabet\":[\"Z5\",\"A5\"],\"start_state\":\"push5\",\"bottom_symbol\":\"Z5\",\"final_states\":[\"accept5\"],\"transitions\":[[\"push5\",\"a5\",\"Z5\",\"push5\",[\"Z5\",\"A5\"]],[\"push5\",\"a5\",\"A5\",\"push5\",[\"A5\",\"A5\"]],[\"push5\",\"b5\",\"A5\",\"pop5\",[]],[\"pop5\",\"b5\",\"A5\",\"pop5\",[]],[\"push5\",null,\"Z5\",\"accept5\",[\"Z5\"]],[\"pop5\",null,\"Z5\",\"accept5\",[\"Z5\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push5, pop5, accept5], [a5, b5], [Z5, A5], push5, Z5, [accept5], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push5, pop5, accept5], [a5, b5], [Z5, A5], push5, Z5, [accept5], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107006,"parameters":{"states":["push5","pop5","accept5"],"input_alphabet":["a5","b5"],"stack_alphabet":["Z5","A5"],"start_state":"push5","bottom_symbol":"Z5","final_states":["accept5"],"transitions":[["push5","a5","Z5","push5",["Z5","A5"]],["push5","a5","A5","push5",["A5","A5"]],["push5","b5","A5","pop5",[]],["pop5","b5","A5","pop5",[]],["push5",null,"Z5","accept5",["Z5"]],["pop5",null,"Z5","accept5",["Z5"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z5\",\"final_states\":[\"accept5\"],\"input_alphabet\":[\"a5\",\"b5\"],\"stack_alphabet\":[\"A5\",\"Z5\"],\"start_state\":\"push5\",\"states\":[\"accept5\",\"pop5\",\"push5\"],\"transitions\":[[\"pop5\",\"b5\",\"A5\",\"pop5\",[]],[\"pop5\",null,\"Z5\",\"accept5\",[\"Z5\"]],[\"push5\",\"a5\",\"A5\",\"push5\",[\"A5\",\"A5\"]],[\"push5\",\"a5\",\"Z5\",\"push5\",[\"Z5\",\"A5\"]],[\"push5\",\"b5\",\"A5\",\"pop5\",[]],[\"push5\",null,\"Z5\",\"accept5\",[\"Z5\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0007","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push6\",\"pop6\",\"accept6\"],\"input_alphabet\":[\"a6\",\"b6\"],\"stack_alphabet\":[\"Z6\",\"A6\"],\"start_state\":\"push6\",\"bottom_symbol\":\"Z6\",\"final_states\":[\"accept6\"],\"transitions\":[[\"push6\",\"a6\",\"Z6\",\"push6\",[\"Z6\",\"A6\"]],[\"push6\",\"a6\",\"A6\",\"push6\",[\"A6\",\"A6\"]],[\"push6\",\"b6\",\"A6\",\"pop6\",[]],[\"pop6\",\"b6\",\"A6\",\"pop6\",[]],[\"push6\",null,\"Z6\",\"accept6\",[\"Z6\"]],[\"pop6\",null,\"Z6\",\"accept6\",[\"Z6\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push6, pop6, accept6], [a6, b6], [Z6, A6], push6, Z6, [accept6], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push6, pop6, accept6], [a6, b6], [Z6, A6], push6, Z6, [accept6], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107007,"parameters":{"states":["push6","pop6","accept6"],"input_alphabet":["a6","b6"],"stack_alphabet":["Z6","A6"],"start_state":"push6","bottom_symbol":"Z6","final_states":["accept6"],"transitions":[["push6","a6","Z6","push6",["Z6","A6"]],["push6","a6","A6","push6",["A6","A6"]],["push6","b6","A6","pop6",[]],["pop6","b6","A6","pop6",[]],["push6",null,"Z6","accept6",["Z6"]],["pop6",null,"Z6","accept6",["Z6"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z6\",\"final_states\":[\"accept6\"],\"input_alphabet\":[\"a6\",\"b6\"],\"stack_alphabet\":[\"A6\",\"Z6\"],\"start_state\":\"push6\",\"states\":[\"accept6\",\"pop6\",\"push6\"],\"transitions\":[[\"pop6\",\"b6\",\"A6\",\"pop6\",[]],[\"pop6\",null,\"Z6\",\"accept6\",[\"Z6\"]],[\"push6\",\"a6\",\"A6\",\"push6\",[\"A6\",\"A6\"]],[\"push6\",\"a6\",\"Z6\",\"push6\",[\"Z6\",\"A6\"]],[\"push6\",\"b6\",\"A6\",\"pop6\",[]],[\"push6\",null,\"Z6\",\"accept6\",[\"Z6\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0008","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push7\",\"pop7\",\"accept7\"],\"input_alphabet\":[\"a7\",\"b7\"],\"stack_alphabet\":[\"Z7\",\"A7\"],\"start_state\":\"push7\",\"bottom_symbol\":\"Z7\",\"final_states\":[\"accept7\"],\"transitions\":[[\"push7\",\"a7\",\"Z7\",\"push7\",[\"Z7\",\"A7\"]],[\"push7\",\"a7\",\"A7\",\"push7\",[\"A7\",\"A7\"]],[\"push7\",\"b7\",\"A7\",\"pop7\",[]],[\"pop7\",\"b7\",\"A7\",\"pop7\",[]],[\"push7\",null,\"Z7\",\"accept7\",[\"Z7\"]],[\"pop7\",null,\"Z7\",\"accept7\",[\"Z7\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push7, pop7, accept7], [a7, b7], [Z7, A7], push7, Z7, [accept7], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push7, pop7, accept7], [a7, b7], [Z7, A7], push7, Z7, [accept7], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107008,"parameters":{"states":["push7","pop7","accept7"],"input_alphabet":["a7","b7"],"stack_alphabet":["Z7","A7"],"start_state":"push7","bottom_symbol":"Z7","final_states":["accept7"],"transitions":[["push7","a7","Z7","push7",["Z7","A7"]],["push7","a7","A7","push7",["A7","A7"]],["push7","b7","A7","pop7",[]],["pop7","b7","A7","pop7",[]],["push7",null,"Z7","accept7",["Z7"]],["pop7",null,"Z7","accept7",["Z7"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z7\",\"final_states\":[\"accept7\"],\"input_alphabet\":[\"a7\",\"b7\"],\"stack_alphabet\":[\"A7\",\"Z7\"],\"start_state\":\"push7\",\"states\":[\"accept7\",\"pop7\",\"push7\"],\"transitions\":[[\"pop7\",\"b7\",\"A7\",\"pop7\",[]],[\"pop7\",null,\"Z7\",\"accept7\",[\"Z7\"]],[\"push7\",\"a7\",\"A7\",\"push7\",[\"A7\",\"A7\"]],[\"push7\",\"a7\",\"Z7\",\"push7\",[\"Z7\",\"A7\"]],[\"push7\",\"b7\",\"A7\",\"pop7\",[]],[\"push7\",null,\"Z7\",\"accept7\",[\"Z7\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0009","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push8\",\"pop8\",\"accept8\"],\"input_alphabet\":[\"a8\",\"b8\"],\"stack_alphabet\":[\"Z8\",\"A8\"],\"start_state\":\"push8\",\"bottom_symbol\":\"Z8\",\"final_states\":[\"accept8\"],\"transitions\":[[\"push8\",\"a8\",\"Z8\",\"push8\",[\"Z8\",\"A8\"]],[\"push8\",\"a8\",\"A8\",\"push8\",[\"A8\",\"A8\"]],[\"push8\",\"b8\",\"A8\",\"pop8\",[]],[\"pop8\",\"b8\",\"A8\",\"pop8\",[]],[\"push8\",null,\"Z8\",\"accept8\",[\"Z8\"]],[\"pop8\",null,\"Z8\",\"accept8\",[\"Z8\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push8, pop8, accept8], [a8, b8], [Z8, A8], push8, Z8, [accept8], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push8, pop8, accept8], [a8, b8], [Z8, A8], push8, Z8, [accept8], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107009,"parameters":{"states":["push8","pop8","accept8"],"input_alphabet":["a8","b8"],"stack_alphabet":["Z8","A8"],"start_state":"push8","bottom_symbol":"Z8","final_states":["accept8"],"transitions":[["push8","a8","Z8","push8",["Z8","A8"]],["push8","a8","A8","push8",["A8","A8"]],["push8","b8","A8","pop8",[]],["pop8","b8","A8","pop8",[]],["push8",null,"Z8","accept8",["Z8"]],["pop8",null,"Z8","accept8",["Z8"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z8\",\"final_states\":[\"accept8\"],\"input_alphabet\":[\"a8\",\"b8\"],\"stack_alphabet\":[\"A8\",\"Z8\"],\"start_state\":\"push8\",\"states\":[\"accept8\",\"pop8\",\"push8\"],\"transitions\":[[\"pop8\",\"b8\",\"A8\",\"pop8\",[]],[\"pop8\",null,\"Z8\",\"accept8\",[\"Z8\"]],[\"push8\",\"a8\",\"A8\",\"push8\",[\"A8\",\"A8\"]],[\"push8\",\"a8\",\"Z8\",\"push8\",[\"Z8\",\"A8\"]],[\"push8\",\"b8\",\"A8\",\"pop8\",[]],[\"push8\",null,\"Z8\",\"accept8\",[\"Z8\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0010","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push9\",\"pop9\",\"accept9\"],\"input_alphabet\":[\"a9\",\"b9\"],\"stack_alphabet\":[\"Z9\",\"A9\"],\"start_state\":\"push9\",\"bottom_symbol\":\"Z9\",\"final_states\":[\"accept9\"],\"transitions\":[[\"push9\",\"a9\",\"Z9\",\"push9\",[\"Z9\",\"A9\"]],[\"push9\",\"a9\",\"A9\",\"push9\",[\"A9\",\"A9\"]],[\"push9\",\"b9\",\"A9\",\"pop9\",[]],[\"pop9\",\"b9\",\"A9\",\"pop9\",[]],[\"push9\",null,\"Z9\",\"accept9\",[\"Z9\"]],[\"pop9\",null,\"Z9\",\"accept9\",[\"Z9\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push9, pop9, accept9], [a9, b9], [Z9, A9], push9, Z9, [accept9], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push9, pop9, accept9], [a9, b9], [Z9, A9], push9, Z9, [accept9], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107010,"parameters":{"states":["push9","pop9","accept9"],"input_alphabet":["a9","b9"],"stack_alphabet":["Z9","A9"],"start_state":"push9","bottom_symbol":"Z9","final_states":["accept9"],"transitions":[["push9","a9","Z9","push9",["Z9","A9"]],["push9","a9","A9","push9",["A9","A9"]],["push9","b9","A9","pop9",[]],["pop9","b9","A9","pop9",[]],["push9",null,"Z9","accept9",["Z9"]],["pop9",null,"Z9","accept9",["Z9"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z9\",\"final_states\":[\"accept9\"],\"input_alphabet\":[\"a9\",\"b9\"],\"stack_alphabet\":[\"A9\",\"Z9\"],\"start_state\":\"push9\",\"states\":[\"accept9\",\"pop9\",\"push9\"],\"transitions\":[[\"pop9\",\"b9\",\"A9\",\"pop9\",[]],[\"pop9\",null,\"Z9\",\"accept9\",[\"Z9\"]],[\"push9\",\"a9\",\"A9\",\"push9\",[\"A9\",\"A9\"]],[\"push9\",\"a9\",\"Z9\",\"push9\",[\"Z9\",\"A9\"]],[\"push9\",\"b9\",\"A9\",\"pop9\",[]],[\"push9\",null,\"Z9\",\"accept9\",[\"Z9\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0011","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push10\",\"pop10\",\"accept10\"],\"input_alphabet\":[\"a10\",\"b10\"],\"stack_alphabet\":[\"Z10\",\"A10\"],\"start_state\":\"push10\",\"bottom_symbol\":\"Z10\",\"final_states\":[\"accept10\"],\"transitions\":[[\"push10\",\"a10\",\"Z10\",\"push10\",[\"Z10\",\"A10\"]],[\"push10\",\"a10\",\"A10\",\"push10\",[\"A10\",\"A10\"]],[\"push10\",\"b10\",\"A10\",\"pop10\",[]],[\"pop10\",\"b10\",\"A10\",\"pop10\",[]],[\"push10\",null,\"Z10\",\"accept10\",[\"Z10\"]],[\"pop10\",null,\"Z10\",\"accept10\",[\"Z10\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push10, pop10, accept10], [a10, b10], [Z10, A10], push10, Z10, [accept10], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push10, pop10, accept10], [a10, b10], [Z10, A10], push10, Z10, [accept10], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107011,"parameters":{"states":["push10","pop10","accept10"],"input_alphabet":["a10","b10"],"stack_alphabet":["Z10","A10"],"start_state":"push10","bottom_symbol":"Z10","final_states":["accept10"],"transitions":[["push10","a10","Z10","push10",["Z10","A10"]],["push10","a10","A10","push10",["A10","A10"]],["push10","b10","A10","pop10",[]],["pop10","b10","A10","pop10",[]],["push10",null,"Z10","accept10",["Z10"]],["pop10",null,"Z10","accept10",["Z10"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z10\",\"final_states\":[\"accept10\"],\"input_alphabet\":[\"a10\",\"b10\"],\"stack_alphabet\":[\"A10\",\"Z10\"],\"start_state\":\"push10\",\"states\":[\"accept10\",\"pop10\",\"push10\"],\"transitions\":[[\"pop10\",\"b10\",\"A10\",\"pop10\",[]],[\"pop10\",null,\"Z10\",\"accept10\",[\"Z10\"]],[\"push10\",\"a10\",\"A10\",\"push10\",[\"A10\",\"A10\"]],[\"push10\",\"a10\",\"Z10\",\"push10\",[\"Z10\",\"A10\"]],[\"push10\",\"b10\",\"A10\",\"pop10\",[]],[\"push10\",null,\"Z10\",\"accept10\",[\"Z10\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0012","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push11\",\"pop11\",\"accept11\"],\"input_alphabet\":[\"a11\",\"b11\"],\"stack_alphabet\":[\"Z11\",\"A11\"],\"start_state\":\"push11\",\"bottom_symbol\":\"Z11\",\"final_states\":[\"accept11\"],\"transitions\":[[\"push11\",\"a11\",\"Z11\",\"push11\",[\"Z11\",\"A11\"]],[\"push11\",\"a11\",\"A11\",\"push11\",[\"A11\",\"A11\"]],[\"push11\",\"b11\",\"A11\",\"pop11\",[]],[\"pop11\",\"b11\",\"A11\",\"pop11\",[]],[\"push11\",null,\"Z11\",\"accept11\",[\"Z11\"]],[\"pop11\",null,\"Z11\",\"accept11\",[\"Z11\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push11, pop11, accept11], [a11, b11], [Z11, A11], push11, Z11, [accept11], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push11, pop11, accept11], [a11, b11], [Z11, A11], push11, Z11, [accept11], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107012,"parameters":{"states":["push11","pop11","accept11"],"input_alphabet":["a11","b11"],"stack_alphabet":["Z11","A11"],"start_state":"push11","bottom_symbol":"Z11","final_states":["accept11"],"transitions":[["push11","a11","Z11","push11",["Z11","A11"]],["push11","a11","A11","push11",["A11","A11"]],["push11","b11","A11","pop11",[]],["pop11","b11","A11","pop11",[]],["push11",null,"Z11","accept11",["Z11"]],["pop11",null,"Z11","accept11",["Z11"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z11\",\"final_states\":[\"accept11\"],\"input_alphabet\":[\"a11\",\"b11\"],\"stack_alphabet\":[\"A11\",\"Z11\"],\"start_state\":\"push11\",\"states\":[\"accept11\",\"pop11\",\"push11\"],\"transitions\":[[\"pop11\",\"b11\",\"A11\",\"pop11\",[]],[\"pop11\",null,\"Z11\",\"accept11\",[\"Z11\"]],[\"push11\",\"a11\",\"A11\",\"push11\",[\"A11\",\"A11\"]],[\"push11\",\"a11\",\"Z11\",\"push11\",[\"Z11\",\"A11\"]],[\"push11\",\"b11\",\"A11\",\"pop11\",[]],[\"push11\",null,\"Z11\",\"accept11\",[\"Z11\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0013","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push12\",\"pop12\",\"accept12\"],\"input_alphabet\":[\"a12\",\"b12\"],\"stack_alphabet\":[\"Z12\",\"A12\"],\"start_state\":\"push12\",\"bottom_symbol\":\"Z12\",\"final_states\":[\"accept12\"],\"transitions\":[[\"push12\",\"a12\",\"Z12\",\"push12\",[\"Z12\",\"A12\"]],[\"push12\",\"a12\",\"A12\",\"push12\",[\"A12\",\"A12\"]],[\"push12\",\"b12\",\"A12\",\"pop12\",[]],[\"pop12\",\"b12\",\"A12\",\"pop12\",[]],[\"push12\",null,\"Z12\",\"accept12\",[\"Z12\"]],[\"pop12\",null,\"Z12\",\"accept12\",[\"Z12\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push12, pop12, accept12], [a12, b12], [Z12, A12], push12, Z12, [accept12], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push12, pop12, accept12], [a12, b12], [Z12, A12], push12, Z12, [accept12], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107013,"parameters":{"states":["push12","pop12","accept12"],"input_alphabet":["a12","b12"],"stack_alphabet":["Z12","A12"],"start_state":"push12","bottom_symbol":"Z12","final_states":["accept12"],"transitions":[["push12","a12","Z12","push12",["Z12","A12"]],["push12","a12","A12","push12",["A12","A12"]],["push12","b12","A12","pop12",[]],["pop12","b12","A12","pop12",[]],["push12",null,"Z12","accept12",["Z12"]],["pop12",null,"Z12","accept12",["Z12"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z12\",\"final_states\":[\"accept12\"],\"input_alphabet\":[\"a12\",\"b12\"],\"stack_alphabet\":[\"A12\",\"Z12\"],\"start_state\":\"push12\",\"states\":[\"accept12\",\"pop12\",\"push12\"],\"transitions\":[[\"pop12\",\"b12\",\"A12\",\"pop12\",[]],[\"pop12\",null,\"Z12\",\"accept12\",[\"Z12\"]],[\"push12\",\"a12\",\"A12\",\"push12\",[\"A12\",\"A12\"]],[\"push12\",\"a12\",\"Z12\",\"push12\",[\"Z12\",\"A12\"]],[\"push12\",\"b12\",\"A12\",\"pop12\",[]],[\"push12\",null,\"Z12\",\"accept12\",[\"Z12\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0014","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push13\",\"pop13\",\"accept13\"],\"input_alphabet\":[\"a13\",\"b13\"],\"stack_alphabet\":[\"Z13\",\"A13\"],\"start_state\":\"push13\",\"bottom_symbol\":\"Z13\",\"final_states\":[\"accept13\"],\"transitions\":[[\"push13\",\"a13\",\"Z13\",\"push13\",[\"Z13\",\"A13\"]],[\"push13\",\"a13\",\"A13\",\"push13\",[\"A13\",\"A13\"]],[\"push13\",\"b13\",\"A13\",\"pop13\",[]],[\"pop13\",\"b13\",\"A13\",\"pop13\",[]],[\"push13\",null,\"Z13\",\"accept13\",[\"Z13\"]],[\"pop13\",null,\"Z13\",\"accept13\",[\"Z13\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push13, pop13, accept13], [a13, b13], [Z13, A13], push13, Z13, [accept13], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push13, pop13, accept13], [a13, b13], [Z13, A13], push13, Z13, [accept13], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107014,"parameters":{"states":["push13","pop13","accept13"],"input_alphabet":["a13","b13"],"stack_alphabet":["Z13","A13"],"start_state":"push13","bottom_symbol":"Z13","final_states":["accept13"],"transitions":[["push13","a13","Z13","push13",["Z13","A13"]],["push13","a13","A13","push13",["A13","A13"]],["push13","b13","A13","pop13",[]],["pop13","b13","A13","pop13",[]],["push13",null,"Z13","accept13",["Z13"]],["pop13",null,"Z13","accept13",["Z13"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z13\",\"final_states\":[\"accept13\"],\"input_alphabet\":[\"a13\",\"b13\"],\"stack_alphabet\":[\"A13\",\"Z13\"],\"start_state\":\"push13\",\"states\":[\"accept13\",\"pop13\",\"push13\"],\"transitions\":[[\"pop13\",\"b13\",\"A13\",\"pop13\",[]],[\"pop13\",null,\"Z13\",\"accept13\",[\"Z13\"]],[\"push13\",\"a13\",\"A13\",\"push13\",[\"A13\",\"A13\"]],[\"push13\",\"a13\",\"Z13\",\"push13\",[\"Z13\",\"A13\"]],[\"push13\",\"b13\",\"A13\",\"pop13\",[]],[\"push13\",null,\"Z13\",\"accept13\",[\"Z13\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0015","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push14\",\"pop14\",\"accept14\"],\"input_alphabet\":[\"a14\",\"b14\"],\"stack_alphabet\":[\"Z14\",\"A14\"],\"start_state\":\"push14\",\"bottom_symbol\":\"Z14\",\"final_states\":[\"accept14\"],\"transitions\":[[\"push14\",\"a14\",\"Z14\",\"push14\",[\"Z14\",\"A14\"]],[\"push14\",\"a14\",\"A14\",\"push14\",[\"A14\",\"A14\"]],[\"push14\",\"b14\",\"A14\",\"pop14\",[]],[\"pop14\",\"b14\",\"A14\",\"pop14\",[]],[\"push14\",null,\"Z14\",\"accept14\",[\"Z14\"]],[\"pop14\",null,\"Z14\",\"accept14\",[\"Z14\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push14, pop14, accept14], [a14, b14], [Z14, A14], push14, Z14, [accept14], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push14, pop14, accept14], [a14, b14], [Z14, A14], push14, Z14, [accept14], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107015,"parameters":{"states":["push14","pop14","accept14"],"input_alphabet":["a14","b14"],"stack_alphabet":["Z14","A14"],"start_state":"push14","bottom_symbol":"Z14","final_states":["accept14"],"transitions":[["push14","a14","Z14","push14",["Z14","A14"]],["push14","a14","A14","push14",["A14","A14"]],["push14","b14","A14","pop14",[]],["pop14","b14","A14","pop14",[]],["push14",null,"Z14","accept14",["Z14"]],["pop14",null,"Z14","accept14",["Z14"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z14\",\"final_states\":[\"accept14\"],\"input_alphabet\":[\"a14\",\"b14\"],\"stack_alphabet\":[\"A14\",\"Z14\"],\"start_state\":\"push14\",\"states\":[\"accept14\",\"pop14\",\"push14\"],\"transitions\":[[\"pop14\",\"b14\",\"A14\",\"pop14\",[]],[\"pop14\",null,\"Z14\",\"accept14\",[\"Z14\"]],[\"push14\",\"a14\",\"A14\",\"push14\",[\"A14\",\"A14\"]],[\"push14\",\"a14\",\"Z14\",\"push14\",[\"Z14\",\"A14\"]],[\"push14\",\"b14\",\"A14\",\"pop14\",[]],[\"push14\",null,\"Z14\",\"accept14\",[\"Z14\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0016","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push15\",\"pop15\",\"accept15\"],\"input_alphabet\":[\"a15\",\"b15\"],\"stack_alphabet\":[\"Z15\",\"A15\"],\"start_state\":\"push15\",\"bottom_symbol\":\"Z15\",\"final_states\":[\"accept15\"],\"transitions\":[[\"push15\",\"a15\",\"Z15\",\"push15\",[\"Z15\",\"A15\"]],[\"push15\",\"a15\",\"A15\",\"push15\",[\"A15\",\"A15\"]],[\"push15\",\"b15\",\"A15\",\"pop15\",[]],[\"pop15\",\"b15\",\"A15\",\"pop15\",[]],[\"push15\",null,\"Z15\",\"accept15\",[\"Z15\"]],[\"pop15\",null,\"Z15\",\"accept15\",[\"Z15\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push15, pop15, accept15], [a15, b15], [Z15, A15], push15, Z15, [accept15], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push15, pop15, accept15], [a15, b15], [Z15, A15], push15, Z15, [accept15], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107016,"parameters":{"states":["push15","pop15","accept15"],"input_alphabet":["a15","b15"],"stack_alphabet":["Z15","A15"],"start_state":"push15","bottom_symbol":"Z15","final_states":["accept15"],"transitions":[["push15","a15","Z15","push15",["Z15","A15"]],["push15","a15","A15","push15",["A15","A15"]],["push15","b15","A15","pop15",[]],["pop15","b15","A15","pop15",[]],["push15",null,"Z15","accept15",["Z15"]],["pop15",null,"Z15","accept15",["Z15"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z15\",\"final_states\":[\"accept15\"],\"input_alphabet\":[\"a15\",\"b15\"],\"stack_alphabet\":[\"A15\",\"Z15\"],\"start_state\":\"push15\",\"states\":[\"accept15\",\"pop15\",\"push15\"],\"transitions\":[[\"pop15\",\"b15\",\"A15\",\"pop15\",[]],[\"pop15\",null,\"Z15\",\"accept15\",[\"Z15\"]],[\"push15\",\"a15\",\"A15\",\"push15\",[\"A15\",\"A15\"]],[\"push15\",\"a15\",\"Z15\",\"push15\",[\"Z15\",\"A15\"]],[\"push15\",\"b15\",\"A15\",\"pop15\",[]],[\"push15\",null,\"Z15\",\"accept15\",[\"Z15\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0017","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push16\",\"pop16\",\"accept16\"],\"input_alphabet\":[\"a16\",\"b16\"],\"stack_alphabet\":[\"Z16\",\"A16\"],\"start_state\":\"push16\",\"bottom_symbol\":\"Z16\",\"final_states\":[\"accept16\"],\"transitions\":[[\"push16\",\"a16\",\"Z16\",\"push16\",[\"Z16\",\"A16\"]],[\"push16\",\"a16\",\"A16\",\"push16\",[\"A16\",\"A16\"]],[\"push16\",\"b16\",\"A16\",\"pop16\",[]],[\"pop16\",\"b16\",\"A16\",\"pop16\",[]],[\"push16\",null,\"Z16\",\"accept16\",[\"Z16\"]],[\"pop16\",null,\"Z16\",\"accept16\",[\"Z16\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push16, pop16, accept16], [a16, b16], [Z16, A16], push16, Z16, [accept16], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push16, pop16, accept16], [a16, b16], [Z16, A16], push16, Z16, [accept16], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107017,"parameters":{"states":["push16","pop16","accept16"],"input_alphabet":["a16","b16"],"stack_alphabet":["Z16","A16"],"start_state":"push16","bottom_symbol":"Z16","final_states":["accept16"],"transitions":[["push16","a16","Z16","push16",["Z16","A16"]],["push16","a16","A16","push16",["A16","A16"]],["push16","b16","A16","pop16",[]],["pop16","b16","A16","pop16",[]],["push16",null,"Z16","accept16",["Z16"]],["pop16",null,"Z16","accept16",["Z16"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z16\",\"final_states\":[\"accept16\"],\"input_alphabet\":[\"a16\",\"b16\"],\"stack_alphabet\":[\"A16\",\"Z16\"],\"start_state\":\"push16\",\"states\":[\"accept16\",\"pop16\",\"push16\"],\"transitions\":[[\"pop16\",\"b16\",\"A16\",\"pop16\",[]],[\"pop16\",null,\"Z16\",\"accept16\",[\"Z16\"]],[\"push16\",\"a16\",\"A16\",\"push16\",[\"A16\",\"A16\"]],[\"push16\",\"a16\",\"Z16\",\"push16\",[\"Z16\",\"A16\"]],[\"push16\",\"b16\",\"A16\",\"pop16\",[]],[\"push16\",null,\"Z16\",\"accept16\",[\"Z16\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0018","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push17\",\"pop17\",\"accept17\"],\"input_alphabet\":[\"a17\",\"b17\"],\"stack_alphabet\":[\"Z17\",\"A17\"],\"start_state\":\"push17\",\"bottom_symbol\":\"Z17\",\"final_states\":[\"accept17\"],\"transitions\":[[\"push17\",\"a17\",\"Z17\",\"push17\",[\"Z17\",\"A17\"]],[\"push17\",\"a17\",\"A17\",\"push17\",[\"A17\",\"A17\"]],[\"push17\",\"b17\",\"A17\",\"pop17\",[]],[\"pop17\",\"b17\",\"A17\",\"pop17\",[]],[\"push17\",null,\"Z17\",\"accept17\",[\"Z17\"]],[\"pop17\",null,\"Z17\",\"accept17\",[\"Z17\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push17, pop17, accept17], [a17, b17], [Z17, A17], push17, Z17, [accept17], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push17, pop17, accept17], [a17, b17], [Z17, A17], push17, Z17, [accept17], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107018,"parameters":{"states":["push17","pop17","accept17"],"input_alphabet":["a17","b17"],"stack_alphabet":["Z17","A17"],"start_state":"push17","bottom_symbol":"Z17","final_states":["accept17"],"transitions":[["push17","a17","Z17","push17",["Z17","A17"]],["push17","a17","A17","push17",["A17","A17"]],["push17","b17","A17","pop17",[]],["pop17","b17","A17","pop17",[]],["push17",null,"Z17","accept17",["Z17"]],["pop17",null,"Z17","accept17",["Z17"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z17\",\"final_states\":[\"accept17\"],\"input_alphabet\":[\"a17\",\"b17\"],\"stack_alphabet\":[\"A17\",\"Z17\"],\"start_state\":\"push17\",\"states\":[\"accept17\",\"pop17\",\"push17\"],\"transitions\":[[\"pop17\",\"b17\",\"A17\",\"pop17\",[]],[\"pop17\",null,\"Z17\",\"accept17\",[\"Z17\"]],[\"push17\",\"a17\",\"A17\",\"push17\",[\"A17\",\"A17\"]],[\"push17\",\"a17\",\"Z17\",\"push17\",[\"Z17\",\"A17\"]],[\"push17\",\"b17\",\"A17\",\"pop17\",[]],[\"push17\",null,\"Z17\",\"accept17\",[\"Z17\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0019","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push18\",\"pop18\",\"accept18\"],\"input_alphabet\":[\"a18\",\"b18\"],\"stack_alphabet\":[\"Z18\",\"A18\"],\"start_state\":\"push18\",\"bottom_symbol\":\"Z18\",\"final_states\":[\"accept18\"],\"transitions\":[[\"push18\",\"a18\",\"Z18\",\"push18\",[\"Z18\",\"A18\"]],[\"push18\",\"a18\",\"A18\",\"push18\",[\"A18\",\"A18\"]],[\"push18\",\"b18\",\"A18\",\"pop18\",[]],[\"pop18\",\"b18\",\"A18\",\"pop18\",[]],[\"push18\",null,\"Z18\",\"accept18\",[\"Z18\"]],[\"pop18\",null,\"Z18\",\"accept18\",[\"Z18\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push18, pop18, accept18], [a18, b18], [Z18, A18], push18, Z18, [accept18], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push18, pop18, accept18], [a18, b18], [Z18, A18], push18, Z18, [accept18], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107019,"parameters":{"states":["push18","pop18","accept18"],"input_alphabet":["a18","b18"],"stack_alphabet":["Z18","A18"],"start_state":"push18","bottom_symbol":"Z18","final_states":["accept18"],"transitions":[["push18","a18","Z18","push18",["Z18","A18"]],["push18","a18","A18","push18",["A18","A18"]],["push18","b18","A18","pop18",[]],["pop18","b18","A18","pop18",[]],["push18",null,"Z18","accept18",["Z18"]],["pop18",null,"Z18","accept18",["Z18"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z18\",\"final_states\":[\"accept18\"],\"input_alphabet\":[\"a18\",\"b18\"],\"stack_alphabet\":[\"A18\",\"Z18\"],\"start_state\":\"push18\",\"states\":[\"accept18\",\"pop18\",\"push18\"],\"transitions\":[[\"pop18\",\"b18\",\"A18\",\"pop18\",[]],[\"pop18\",null,\"Z18\",\"accept18\",[\"Z18\"]],[\"push18\",\"a18\",\"A18\",\"push18\",[\"A18\",\"A18\"]],[\"push18\",\"a18\",\"Z18\",\"push18\",[\"Z18\",\"A18\"]],[\"push18\",\"b18\",\"A18\",\"pop18\",[]],[\"push18\",null,\"Z18\",\"accept18\",[\"Z18\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0020","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push19\",\"pop19\",\"accept19\"],\"input_alphabet\":[\"a19\",\"b19\"],\"stack_alphabet\":[\"Z19\",\"A19\"],\"start_state\":\"push19\",\"bottom_symbol\":\"Z19\",\"final_states\":[\"accept19\"],\"transitions\":[[\"push19\",\"a19\",\"Z19\",\"push19\",[\"Z19\",\"A19\"]],[\"push19\",\"a19\",\"A19\",\"push19\",[\"A19\",\"A19\"]],[\"push19\",\"b19\",\"A19\",\"pop19\",[]],[\"pop19\",\"b19\",\"A19\",\"pop19\",[]],[\"push19\",null,\"Z19\",\"accept19\",[\"Z19\"]],[\"pop19\",null,\"Z19\",\"accept19\",[\"Z19\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push19, pop19, accept19], [a19, b19], [Z19, A19], push19, Z19, [accept19], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push19, pop19, accept19], [a19, b19], [Z19, A19], push19, Z19, [accept19], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107020,"parameters":{"states":["push19","pop19","accept19"],"input_alphabet":["a19","b19"],"stack_alphabet":["Z19","A19"],"start_state":"push19","bottom_symbol":"Z19","final_states":["accept19"],"transitions":[["push19","a19","Z19","push19",["Z19","A19"]],["push19","a19","A19","push19",["A19","A19"]],["push19","b19","A19","pop19",[]],["pop19","b19","A19","pop19",[]],["push19",null,"Z19","accept19",["Z19"]],["pop19",null,"Z19","accept19",["Z19"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z19\",\"final_states\":[\"accept19\"],\"input_alphabet\":[\"a19\",\"b19\"],\"stack_alphabet\":[\"A19\",\"Z19\"],\"start_state\":\"push19\",\"states\":[\"accept19\",\"pop19\",\"push19\"],\"transitions\":[[\"pop19\",\"b19\",\"A19\",\"pop19\",[]],[\"pop19\",null,\"Z19\",\"accept19\",[\"Z19\"]],[\"push19\",\"a19\",\"A19\",\"push19\",[\"A19\",\"A19\"]],[\"push19\",\"a19\",\"Z19\",\"push19\",[\"Z19\",\"A19\"]],[\"push19\",\"b19\",\"A19\",\"pop19\",[]],[\"push19\",null,\"Z19\",\"accept19\",[\"Z19\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0021","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push20\",\"pop20\",\"accept20\"],\"input_alphabet\":[\"a20\",\"b20\"],\"stack_alphabet\":[\"Z20\",\"A20\"],\"start_state\":\"push20\",\"bottom_symbol\":\"Z20\",\"final_states\":[\"accept20\"],\"transitions\":[[\"push20\",\"a20\",\"Z20\",\"push20\",[\"Z20\",\"A20\"]],[\"push20\",\"a20\",\"A20\",\"push20\",[\"A20\",\"A20\"]],[\"push20\",\"b20\",\"A20\",\"pop20\",[]],[\"pop20\",\"b20\",\"A20\",\"pop20\",[]],[\"push20\",null,\"Z20\",\"accept20\",[\"Z20\"]],[\"pop20\",null,\"Z20\",\"accept20\",[\"Z20\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push20, pop20, accept20], [a20, b20], [Z20, A20], push20, Z20, [accept20], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push20, pop20, accept20], [a20, b20], [Z20, A20], push20, Z20, [accept20], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107021,"parameters":{"states":["push20","pop20","accept20"],"input_alphabet":["a20","b20"],"stack_alphabet":["Z20","A20"],"start_state":"push20","bottom_symbol":"Z20","final_states":["accept20"],"transitions":[["push20","a20","Z20","push20",["Z20","A20"]],["push20","a20","A20","push20",["A20","A20"]],["push20","b20","A20","pop20",[]],["pop20","b20","A20","pop20",[]],["push20",null,"Z20","accept20",["Z20"]],["pop20",null,"Z20","accept20",["Z20"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z20\",\"final_states\":[\"accept20\"],\"input_alphabet\":[\"a20\",\"b20\"],\"stack_alphabet\":[\"A20\",\"Z20\"],\"start_state\":\"push20\",\"states\":[\"accept20\",\"pop20\",\"push20\"],\"transitions\":[[\"pop20\",\"b20\",\"A20\",\"pop20\",[]],[\"pop20\",null,\"Z20\",\"accept20\",[\"Z20\"]],[\"push20\",\"a20\",\"A20\",\"push20\",[\"A20\",\"A20\"]],[\"push20\",\"a20\",\"Z20\",\"push20\",[\"Z20\",\"A20\"]],[\"push20\",\"b20\",\"A20\",\"pop20\",[]],[\"push20\",null,\"Z20\",\"accept20\",[\"Z20\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0022","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push21\",\"pop21\",\"accept21\"],\"input_alphabet\":[\"a21\",\"b21\"],\"stack_alphabet\":[\"Z21\",\"A21\"],\"start_state\":\"push21\",\"bottom_symbol\":\"Z21\",\"final_states\":[\"accept21\"],\"transitions\":[[\"push21\",\"a21\",\"Z21\",\"push21\",[\"Z21\",\"A21\"]],[\"push21\",\"a21\",\"A21\",\"push21\",[\"A21\",\"A21\"]],[\"push21\",\"b21\",\"A21\",\"pop21\",[]],[\"pop21\",\"b21\",\"A21\",\"pop21\",[]],[\"push21\",null,\"Z21\",\"accept21\",[\"Z21\"]],[\"pop21\",null,\"Z21\",\"accept21\",[\"Z21\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push21, pop21, accept21], [a21, b21], [Z21, A21], push21, Z21, [accept21], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push21, pop21, accept21], [a21, b21], [Z21, A21], push21, Z21, [accept21], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107022,"parameters":{"states":["push21","pop21","accept21"],"input_alphabet":["a21","b21"],"stack_alphabet":["Z21","A21"],"start_state":"push21","bottom_symbol":"Z21","final_states":["accept21"],"transitions":[["push21","a21","Z21","push21",["Z21","A21"]],["push21","a21","A21","push21",["A21","A21"]],["push21","b21","A21","pop21",[]],["pop21","b21","A21","pop21",[]],["push21",null,"Z21","accept21",["Z21"]],["pop21",null,"Z21","accept21",["Z21"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z21\",\"final_states\":[\"accept21\"],\"input_alphabet\":[\"a21\",\"b21\"],\"stack_alphabet\":[\"A21\",\"Z21\"],\"start_state\":\"push21\",\"states\":[\"accept21\",\"pop21\",\"push21\"],\"transitions\":[[\"pop21\",\"b21\",\"A21\",\"pop21\",[]],[\"pop21\",null,\"Z21\",\"accept21\",[\"Z21\"]],[\"push21\",\"a21\",\"A21\",\"push21\",[\"A21\",\"A21\"]],[\"push21\",\"a21\",\"Z21\",\"push21\",[\"Z21\",\"A21\"]],[\"push21\",\"b21\",\"A21\",\"pop21\",[]],[\"push21\",null,\"Z21\",\"accept21\",[\"Z21\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0023","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push22\",\"pop22\",\"accept22\"],\"input_alphabet\":[\"a22\",\"b22\"],\"stack_alphabet\":[\"Z22\",\"A22\"],\"start_state\":\"push22\",\"bottom_symbol\":\"Z22\",\"final_states\":[\"accept22\"],\"transitions\":[[\"push22\",\"a22\",\"Z22\",\"push22\",[\"Z22\",\"A22\"]],[\"push22\",\"a22\",\"A22\",\"push22\",[\"A22\",\"A22\"]],[\"push22\",\"b22\",\"A22\",\"pop22\",[]],[\"pop22\",\"b22\",\"A22\",\"pop22\",[]],[\"push22\",null,\"Z22\",\"accept22\",[\"Z22\"]],[\"pop22\",null,\"Z22\",\"accept22\",[\"Z22\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push22, pop22, accept22], [a22, b22], [Z22, A22], push22, Z22, [accept22], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push22, pop22, accept22], [a22, b22], [Z22, A22], push22, Z22, [accept22], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107023,"parameters":{"states":["push22","pop22","accept22"],"input_alphabet":["a22","b22"],"stack_alphabet":["Z22","A22"],"start_state":"push22","bottom_symbol":"Z22","final_states":["accept22"],"transitions":[["push22","a22","Z22","push22",["Z22","A22"]],["push22","a22","A22","push22",["A22","A22"]],["push22","b22","A22","pop22",[]],["pop22","b22","A22","pop22",[]],["push22",null,"Z22","accept22",["Z22"]],["pop22",null,"Z22","accept22",["Z22"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z22\",\"final_states\":[\"accept22\"],\"input_alphabet\":[\"a22\",\"b22\"],\"stack_alphabet\":[\"A22\",\"Z22\"],\"start_state\":\"push22\",\"states\":[\"accept22\",\"pop22\",\"push22\"],\"transitions\":[[\"pop22\",\"b22\",\"A22\",\"pop22\",[]],[\"pop22\",null,\"Z22\",\"accept22\",[\"Z22\"]],[\"push22\",\"a22\",\"A22\",\"push22\",[\"A22\",\"A22\"]],[\"push22\",\"a22\",\"Z22\",\"push22\",[\"Z22\",\"A22\"]],[\"push22\",\"b22\",\"A22\",\"pop22\",[]],[\"push22\",null,\"Z22\",\"accept22\",[\"Z22\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0024","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push23\",\"pop23\",\"accept23\"],\"input_alphabet\":[\"a23\",\"b23\"],\"stack_alphabet\":[\"Z23\",\"A23\"],\"start_state\":\"push23\",\"bottom_symbol\":\"Z23\",\"final_states\":[\"accept23\"],\"transitions\":[[\"push23\",\"a23\",\"Z23\",\"push23\",[\"Z23\",\"A23\"]],[\"push23\",\"a23\",\"A23\",\"push23\",[\"A23\",\"A23\"]],[\"push23\",\"b23\",\"A23\",\"pop23\",[]],[\"pop23\",\"b23\",\"A23\",\"pop23\",[]],[\"push23\",null,\"Z23\",\"accept23\",[\"Z23\"]],[\"pop23\",null,\"Z23\",\"accept23\",[\"Z23\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push23, pop23, accept23], [a23, b23], [Z23, A23], push23, Z23, [accept23], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push23, pop23, accept23], [a23, b23], [Z23, A23], push23, Z23, [accept23], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107024,"parameters":{"states":["push23","pop23","accept23"],"input_alphabet":["a23","b23"],"stack_alphabet":["Z23","A23"],"start_state":"push23","bottom_symbol":"Z23","final_states":["accept23"],"transitions":[["push23","a23","Z23","push23",["Z23","A23"]],["push23","a23","A23","push23",["A23","A23"]],["push23","b23","A23","pop23",[]],["pop23","b23","A23","pop23",[]],["push23",null,"Z23","accept23",["Z23"]],["pop23",null,"Z23","accept23",["Z23"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z23\",\"final_states\":[\"accept23\"],\"input_alphabet\":[\"a23\",\"b23\"],\"stack_alphabet\":[\"A23\",\"Z23\"],\"start_state\":\"push23\",\"states\":[\"accept23\",\"pop23\",\"push23\"],\"transitions\":[[\"pop23\",\"b23\",\"A23\",\"pop23\",[]],[\"pop23\",null,\"Z23\",\"accept23\",[\"Z23\"]],[\"push23\",\"a23\",\"A23\",\"push23\",[\"A23\",\"A23\"]],[\"push23\",\"a23\",\"Z23\",\"push23\",[\"Z23\",\"A23\"]],[\"push23\",\"b23\",\"A23\",\"pop23\",[]],[\"push23\",null,\"Z23\",\"accept23\",[\"Z23\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0025","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push24\",\"pop24\",\"accept24\"],\"input_alphabet\":[\"a24\",\"b24\"],\"stack_alphabet\":[\"Z24\",\"A24\"],\"start_state\":\"push24\",\"bottom_symbol\":\"Z24\",\"final_states\":[\"accept24\"],\"transitions\":[[\"push24\",\"a24\",\"Z24\",\"push24\",[\"Z24\",\"A24\"]],[\"push24\",\"a24\",\"A24\",\"push24\",[\"A24\",\"A24\"]],[\"push24\",\"b24\",\"A24\",\"pop24\",[]],[\"pop24\",\"b24\",\"A24\",\"pop24\",[]],[\"push24\",null,\"Z24\",\"accept24\",[\"Z24\"]],[\"pop24\",null,\"Z24\",\"accept24\",[\"Z24\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([push24, pop24, accept24], [a24, b24], [Z24, A24], push24, Z24, [accept24], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)","explanation_zh":"Wave6第四層核對=([push24, pop24, accept24], [a24, b24], [Z24, A24], push24, Z24, [accept24], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-qualification","seed":202611107025,"parameters":{"states":["push24","pop24","accept24"],"input_alphabet":["a24","b24"],"stack_alphabet":["Z24","A24"],"start_state":"push24","bottom_symbol":"Z24","final_states":["accept24"],"transitions":[["push24","a24","Z24","push24",["Z24","A24"]],["push24","a24","A24","push24",["A24","A24"]],["push24","b24","A24","pop24",[]],["pop24","b24","A24","pop24",[]],["push24",null,"Z24","accept24",["Z24"]],["pop24",null,"Z24","accept24",["Z24"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-qualification","semantic_template":"qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z24\",\"final_states\":[\"accept24\"],\"input_alphabet\":[\"a24\",\"b24\"],\"stack_alphabet\":[\"A24\",\"Z24\"],\"start_state\":\"push24\",\"states\":[\"accept24\",\"pop24\",\"push24\"],\"transitions\":[[\"pop24\",\"b24\",\"A24\",\"pop24\",[]],[\"pop24\",null,\"Z24\",\"accept24\",[\"Z24\"]],[\"push24\",\"a24\",\"A24\",\"push24\",[\"A24\",\"A24\"]],[\"push24\",\"a24\",\"Z24\",\"push24\",[\"Z24\",\"A24\"]],[\"push24\",\"b24\",\"A24\",\"pop24\",[]],[\"push24\",null,\"Z24\",\"accept24\",[\"Z24\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0026","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push0\",\"pop0\",\"accept0\"],\"input_alphabet\":[\"a0\",\"b0\"],\"stack_alphabet\":[\"Z0\",\"A0\"],\"start_state\":\"push0\",\"bottom_symbol\":\"Z0\",\"final_states\":[\"accept0\"],\"transitions\":[[\"push0\",\"a0\",\"Z0\",\"push0\",[\"Z0\",\"A0\"]],[\"push0\",\"a0\",\"A0\",\"push0\",[\"A0\",\"A0\"]],[\"push0\",\"b0\",\"A0\",\"pop0\",[]],[\"pop0\",\"b0\",\"A0\",\"pop0\",[]],[\"push0\",null,\"Z0\",\"accept0\",[\"Z0\"]],[\"pop0\",null,\"Z0\",\"accept0\",[\"Z0\"]]],\"input\":[],\"trace\":[[\"push0\",0,[\"Z0\"]],[\"accept0\",0,[\"Z0\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push0, 0, [Z0]], [accept0, 0, [Z0]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([], [[push0, 0, [Z0]], [accept0, 0, [Z0]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107026,"parameters":{"states":["push0","pop0","accept0"],"input_alphabet":["a0","b0"],"stack_alphabet":["Z0","A0"],"start_state":"push0","bottom_symbol":"Z0","final_states":["accept0"],"transitions":[["push0","a0","Z0","push0",["Z0","A0"]],["push0","a0","A0","push0",["A0","A0"]],["push0","b0","A0","pop0",[]],["pop0","b0","A0","pop0",[]],["push0",null,"Z0","accept0",["Z0"]],["pop0",null,"Z0","accept0",["Z0"]]],"input":[],"trace":[["push0",0,["Z0"]],["accept0",0,["Z0"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z0\",\"final_states\":[\"accept0\"],\"input\":[],\"input_alphabet\":[\"a0\",\"b0\"],\"stack_alphabet\":[\"A0\",\"Z0\"],\"start_state\":\"push0\",\"states\":[\"accept0\",\"pop0\",\"push0\"],\"trace\":[[\"push0\",0,[\"Z0\"]],[\"accept0\",0,[\"Z0\"]]],\"transitions\":[[\"pop0\",\"b0\",\"A0\",\"pop0\",[]],[\"pop0\",null,\"Z0\",\"accept0\",[\"Z0\"]],[\"push0\",\"a0\",\"A0\",\"push0\",[\"A0\",\"A0\"]],[\"push0\",\"a0\",\"Z0\",\"push0\",[\"Z0\",\"A0\"]],[\"push0\",\"b0\",\"A0\",\"pop0\",[]],[\"push0\",null,\"Z0\",\"accept0\",[\"Z0\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0027","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push1\",\"pop1\",\"accept1\"],\"input_alphabet\":[\"a1\",\"b1\"],\"stack_alphabet\":[\"Z1\",\"A1\"],\"start_state\":\"push1\",\"bottom_symbol\":\"Z1\",\"final_states\":[\"accept1\"],\"transitions\":[[\"push1\",\"a1\",\"Z1\",\"push1\",[\"Z1\",\"A1\"]],[\"push1\",\"a1\",\"A1\",\"push1\",[\"A1\",\"A1\"]],[\"push1\",\"b1\",\"A1\",\"pop1\",[]],[\"pop1\",\"b1\",\"A1\",\"pop1\",[]],[\"push1\",null,\"Z1\",\"accept1\",[\"Z1\"]],[\"pop1\",null,\"Z1\",\"accept1\",[\"Z1\"]]],\"input\":[\"a1\",\"b1\"],\"trace\":[[\"push1\",0,[\"Z1\"]],[\"push1\",1,[\"Z1\",\"A1\"]],[\"pop1\",2,[\"Z1\"]],[\"accept1\",2,[\"Z1\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a1, b1], [[push1, 0, [Z1]], [push1, 1, [Z1, A1]], [pop1, 2, [Z1]], [accept1, 2, [Z1]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a1, b1], [[push1, 0, [Z1]], [push1, 1, [Z1, A1]], [pop1, 2, [Z1]], [accept1, 2, [Z1]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107027,"parameters":{"states":["push1","pop1","accept1"],"input_alphabet":["a1","b1"],"stack_alphabet":["Z1","A1"],"start_state":"push1","bottom_symbol":"Z1","final_states":["accept1"],"transitions":[["push1","a1","Z1","push1",["Z1","A1"]],["push1","a1","A1","push1",["A1","A1"]],["push1","b1","A1","pop1",[]],["pop1","b1","A1","pop1",[]],["push1",null,"Z1","accept1",["Z1"]],["pop1",null,"Z1","accept1",["Z1"]]],"input":["a1","b1"],"trace":[["push1",0,["Z1"]],["push1",1,["Z1","A1"]],["pop1",2,["Z1"]],["accept1",2,["Z1"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z1\",\"final_states\":[\"accept1\"],\"input\":[\"a1\",\"b1\"],\"input_alphabet\":[\"a1\",\"b1\"],\"stack_alphabet\":[\"A1\",\"Z1\"],\"start_state\":\"push1\",\"states\":[\"accept1\",\"pop1\",\"push1\"],\"trace\":[[\"push1\",0,[\"Z1\"]],[\"push1\",1,[\"Z1\",\"A1\"]],[\"pop1\",2,[\"Z1\"]],[\"accept1\",2,[\"Z1\"]]],\"transitions\":[[\"pop1\",\"b1\",\"A1\",\"pop1\",[]],[\"pop1\",null,\"Z1\",\"accept1\",[\"Z1\"]],[\"push1\",\"a1\",\"A1\",\"push1\",[\"A1\",\"A1\"]],[\"push1\",\"a1\",\"Z1\",\"push1\",[\"Z1\",\"A1\"]],[\"push1\",\"b1\",\"A1\",\"pop1\",[]],[\"push1\",null,\"Z1\",\"accept1\",[\"Z1\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0028","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push2\",\"pop2\",\"accept2\"],\"input_alphabet\":[\"a2\",\"b2\"],\"stack_alphabet\":[\"Z2\",\"A2\"],\"start_state\":\"push2\",\"bottom_symbol\":\"Z2\",\"final_states\":[\"accept2\"],\"transitions\":[[\"push2\",\"a2\",\"Z2\",\"push2\",[\"Z2\",\"A2\"]],[\"push2\",\"a2\",\"A2\",\"push2\",[\"A2\",\"A2\"]],[\"push2\",\"b2\",\"A2\",\"pop2\",[]],[\"pop2\",\"b2\",\"A2\",\"pop2\",[]],[\"push2\",null,\"Z2\",\"accept2\",[\"Z2\"]],[\"pop2\",null,\"Z2\",\"accept2\",[\"Z2\"]]],\"input\":[\"a2\",\"a2\",\"b2\",\"b2\"],\"trace\":[[\"push2\",0,[\"Z2\"]],[\"push2\",1,[\"Z2\",\"A2\"]],[\"push2\",2,[\"Z2\",\"A2\",\"A2\"]],[\"pop2\",3,[\"Z2\",\"A2\"]],[\"pop2\",4,[\"Z2\"]],[\"accept2\",4,[\"Z2\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a2, a2, b2, b2], [[push2, 0, [Z2]], [push2, 1, [Z2, A2]], [push2, 2, [Z2, A2, A2]], [pop2, 3, [Z2, A2]], [pop2, 4, [Z2]], [accept2, 4, [Z2]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a2, a2, b2, b2], [[push2, 0, [Z2]], [push2, 1, [Z2, A2]], [push2, 2, [Z2, A2, A2]], [pop2, 3, [Z2, A2]], [pop2, 4, [Z2]], [accept2, 4, [Z2]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107028,"parameters":{"states":["push2","pop2","accept2"],"input_alphabet":["a2","b2"],"stack_alphabet":["Z2","A2"],"start_state":"push2","bottom_symbol":"Z2","final_states":["accept2"],"transitions":[["push2","a2","Z2","push2",["Z2","A2"]],["push2","a2","A2","push2",["A2","A2"]],["push2","b2","A2","pop2",[]],["pop2","b2","A2","pop2",[]],["push2",null,"Z2","accept2",["Z2"]],["pop2",null,"Z2","accept2",["Z2"]]],"input":["a2","a2","b2","b2"],"trace":[["push2",0,["Z2"]],["push2",1,["Z2","A2"]],["push2",2,["Z2","A2","A2"]],["pop2",3,["Z2","A2"]],["pop2",4,["Z2"]],["accept2",4,["Z2"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z2\",\"final_states\":[\"accept2\"],\"input\":[\"a2\",\"a2\",\"b2\",\"b2\"],\"input_alphabet\":[\"a2\",\"b2\"],\"stack_alphabet\":[\"A2\",\"Z2\"],\"start_state\":\"push2\",\"states\":[\"accept2\",\"pop2\",\"push2\"],\"trace\":[[\"push2\",0,[\"Z2\"]],[\"push2\",1,[\"Z2\",\"A2\"]],[\"push2\",2,[\"Z2\",\"A2\",\"A2\"]],[\"pop2\",3,[\"Z2\",\"A2\"]],[\"pop2\",4,[\"Z2\"]],[\"accept2\",4,[\"Z2\"]]],\"transitions\":[[\"pop2\",\"b2\",\"A2\",\"pop2\",[]],[\"pop2\",null,\"Z2\",\"accept2\",[\"Z2\"]],[\"push2\",\"a2\",\"A2\",\"push2\",[\"A2\",\"A2\"]],[\"push2\",\"a2\",\"Z2\",\"push2\",[\"Z2\",\"A2\"]],[\"push2\",\"b2\",\"A2\",\"pop2\",[]],[\"push2\",null,\"Z2\",\"accept2\",[\"Z2\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0029","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push3\",\"pop3\",\"accept3\"],\"input_alphabet\":[\"a3\",\"b3\"],\"stack_alphabet\":[\"Z3\",\"A3\"],\"start_state\":\"push3\",\"bottom_symbol\":\"Z3\",\"final_states\":[\"accept3\"],\"transitions\":[[\"push3\",\"a3\",\"Z3\",\"push3\",[\"Z3\",\"A3\"]],[\"push3\",\"a3\",\"A3\",\"push3\",[\"A3\",\"A3\"]],[\"push3\",\"b3\",\"A3\",\"pop3\",[]],[\"pop3\",\"b3\",\"A3\",\"pop3\",[]],[\"push3\",null,\"Z3\",\"accept3\",[\"Z3\"]],[\"pop3\",null,\"Z3\",\"accept3\",[\"Z3\"]]],\"input\":[\"a3\",\"a3\",\"a3\",\"b3\",\"b3\",\"b3\"],\"trace\":[[\"push3\",0,[\"Z3\"]],[\"push3\",1,[\"Z3\",\"A3\"]],[\"push3\",2,[\"Z3\",\"A3\",\"A3\"]],[\"push3\",3,[\"Z3\",\"A3\",\"A3\",\"A3\"]],[\"pop3\",4,[\"Z3\",\"A3\",\"A3\"]],[\"pop3\",5,[\"Z3\",\"A3\"]],[\"pop3\",6,[\"Z3\"]],[\"accept3\",6,[\"Z3\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a3, a3, a3, b3, b3, b3], [[push3, 0, [Z3]], [push3, 1, [Z3, A3]], [push3, 2, [Z3, A3, A3]], [push3, 3, [Z3, A3, A3, A3]], [pop3, 4, [Z3, A3, A3]], [pop3, 5, [Z3, A3]], [pop3, 6, [Z3]], [accept3, 6, [Z3]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a3, a3, a3, b3, b3, b3], [[push3, 0, [Z3]], [push3, 1, [Z3, A3]], [push3, 2, [Z3, A3, A3]], [push3, 3, [Z3, A3, A3, A3]], [pop3, 4, [Z3, A3, A3]], [pop3, 5, [Z3, A3]], [pop3, 6, [Z3]], [accept3, 6, [Z3]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107029,"parameters":{"states":["push3","pop3","accept3"],"input_alphabet":["a3","b3"],"stack_alphabet":["Z3","A3"],"start_state":"push3","bottom_symbol":"Z3","final_states":["accept3"],"transitions":[["push3","a3","Z3","push3",["Z3","A3"]],["push3","a3","A3","push3",["A3","A3"]],["push3","b3","A3","pop3",[]],["pop3","b3","A3","pop3",[]],["push3",null,"Z3","accept3",["Z3"]],["pop3",null,"Z3","accept3",["Z3"]]],"input":["a3","a3","a3","b3","b3","b3"],"trace":[["push3",0,["Z3"]],["push3",1,["Z3","A3"]],["push3",2,["Z3","A3","A3"]],["push3",3,["Z3","A3","A3","A3"]],["pop3",4,["Z3","A3","A3"]],["pop3",5,["Z3","A3"]],["pop3",6,["Z3"]],["accept3",6,["Z3"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z3\",\"final_states\":[\"accept3\"],\"input\":[\"a3\",\"a3\",\"a3\",\"b3\",\"b3\",\"b3\"],\"input_alphabet\":[\"a3\",\"b3\"],\"stack_alphabet\":[\"A3\",\"Z3\"],\"start_state\":\"push3\",\"states\":[\"accept3\",\"pop3\",\"push3\"],\"trace\":[[\"push3\",0,[\"Z3\"]],[\"push3\",1,[\"Z3\",\"A3\"]],[\"push3\",2,[\"Z3\",\"A3\",\"A3\"]],[\"push3\",3,[\"Z3\",\"A3\",\"A3\",\"A3\"]],[\"pop3\",4,[\"Z3\",\"A3\",\"A3\"]],[\"pop3\",5,[\"Z3\",\"A3\"]],[\"pop3\",6,[\"Z3\"]],[\"accept3\",6,[\"Z3\"]]],\"transitions\":[[\"pop3\",\"b3\",\"A3\",\"pop3\",[]],[\"pop3\",null,\"Z3\",\"accept3\",[\"Z3\"]],[\"push3\",\"a3\",\"A3\",\"push3\",[\"A3\",\"A3\"]],[\"push3\",\"a3\",\"Z3\",\"push3\",[\"Z3\",\"A3\"]],[\"push3\",\"b3\",\"A3\",\"pop3\",[]],[\"push3\",null,\"Z3\",\"accept3\",[\"Z3\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0030","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push4\",\"pop4\",\"accept4\"],\"input_alphabet\":[\"a4\",\"b4\"],\"stack_alphabet\":[\"Z4\",\"A4\"],\"start_state\":\"push4\",\"bottom_symbol\":\"Z4\",\"final_states\":[\"accept4\"],\"transitions\":[[\"push4\",\"a4\",\"Z4\",\"push4\",[\"Z4\",\"A4\"]],[\"push4\",\"a4\",\"A4\",\"push4\",[\"A4\",\"A4\"]],[\"push4\",\"b4\",\"A4\",\"pop4\",[]],[\"pop4\",\"b4\",\"A4\",\"pop4\",[]],[\"push4\",null,\"Z4\",\"accept4\",[\"Z4\"]],[\"pop4\",null,\"Z4\",\"accept4\",[\"Z4\"]]],\"input\":[],\"trace\":[[\"push4\",0,[\"Z4\"]],[\"accept4\",0,[\"Z4\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push4, 0, [Z4]], [accept4, 0, [Z4]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([], [[push4, 0, [Z4]], [accept4, 0, [Z4]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107030,"parameters":{"states":["push4","pop4","accept4"],"input_alphabet":["a4","b4"],"stack_alphabet":["Z4","A4"],"start_state":"push4","bottom_symbol":"Z4","final_states":["accept4"],"transitions":[["push4","a4","Z4","push4",["Z4","A4"]],["push4","a4","A4","push4",["A4","A4"]],["push4","b4","A4","pop4",[]],["pop4","b4","A4","pop4",[]],["push4",null,"Z4","accept4",["Z4"]],["pop4",null,"Z4","accept4",["Z4"]]],"input":[],"trace":[["push4",0,["Z4"]],["accept4",0,["Z4"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z4\",\"final_states\":[\"accept4\"],\"input\":[],\"input_alphabet\":[\"a4\",\"b4\"],\"stack_alphabet\":[\"A4\",\"Z4\"],\"start_state\":\"push4\",\"states\":[\"accept4\",\"pop4\",\"push4\"],\"trace\":[[\"push4\",0,[\"Z4\"]],[\"accept4\",0,[\"Z4\"]]],\"transitions\":[[\"pop4\",\"b4\",\"A4\",\"pop4\",[]],[\"pop4\",null,\"Z4\",\"accept4\",[\"Z4\"]],[\"push4\",\"a4\",\"A4\",\"push4\",[\"A4\",\"A4\"]],[\"push4\",\"a4\",\"Z4\",\"push4\",[\"Z4\",\"A4\"]],[\"push4\",\"b4\",\"A4\",\"pop4\",[]],[\"push4\",null,\"Z4\",\"accept4\",[\"Z4\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0031","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push5\",\"pop5\",\"accept5\"],\"input_alphabet\":[\"a5\",\"b5\"],\"stack_alphabet\":[\"Z5\",\"A5\"],\"start_state\":\"push5\",\"bottom_symbol\":\"Z5\",\"final_states\":[\"accept5\"],\"transitions\":[[\"push5\",\"a5\",\"Z5\",\"push5\",[\"Z5\",\"A5\"]],[\"push5\",\"a5\",\"A5\",\"push5\",[\"A5\",\"A5\"]],[\"push5\",\"b5\",\"A5\",\"pop5\",[]],[\"pop5\",\"b5\",\"A5\",\"pop5\",[]],[\"push5\",null,\"Z5\",\"accept5\",[\"Z5\"]],[\"pop5\",null,\"Z5\",\"accept5\",[\"Z5\"]]],\"input\":[\"a5\",\"b5\"],\"trace\":[[\"push5\",0,[\"Z5\"]],[\"push5\",1,[\"Z5\",\"A5\"]],[\"pop5\",2,[\"Z5\"]],[\"accept5\",2,[\"Z5\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a5, b5], [[push5, 0, [Z5]], [push5, 1, [Z5, A5]], [pop5, 2, [Z5]], [accept5, 2, [Z5]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a5, b5], [[push5, 0, [Z5]], [push5, 1, [Z5, A5]], [pop5, 2, [Z5]], [accept5, 2, [Z5]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107031,"parameters":{"states":["push5","pop5","accept5"],"input_alphabet":["a5","b5"],"stack_alphabet":["Z5","A5"],"start_state":"push5","bottom_symbol":"Z5","final_states":["accept5"],"transitions":[["push5","a5","Z5","push5",["Z5","A5"]],["push5","a5","A5","push5",["A5","A5"]],["push5","b5","A5","pop5",[]],["pop5","b5","A5","pop5",[]],["push5",null,"Z5","accept5",["Z5"]],["pop5",null,"Z5","accept5",["Z5"]]],"input":["a5","b5"],"trace":[["push5",0,["Z5"]],["push5",1,["Z5","A5"]],["pop5",2,["Z5"]],["accept5",2,["Z5"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z5\",\"final_states\":[\"accept5\"],\"input\":[\"a5\",\"b5\"],\"input_alphabet\":[\"a5\",\"b5\"],\"stack_alphabet\":[\"A5\",\"Z5\"],\"start_state\":\"push5\",\"states\":[\"accept5\",\"pop5\",\"push5\"],\"trace\":[[\"push5\",0,[\"Z5\"]],[\"push5\",1,[\"Z5\",\"A5\"]],[\"pop5\",2,[\"Z5\"]],[\"accept5\",2,[\"Z5\"]]],\"transitions\":[[\"pop5\",\"b5\",\"A5\",\"pop5\",[]],[\"pop5\",null,\"Z5\",\"accept5\",[\"Z5\"]],[\"push5\",\"a5\",\"A5\",\"push5\",[\"A5\",\"A5\"]],[\"push5\",\"a5\",\"Z5\",\"push5\",[\"Z5\",\"A5\"]],[\"push5\",\"b5\",\"A5\",\"pop5\",[]],[\"push5\",null,\"Z5\",\"accept5\",[\"Z5\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0032","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push6\",\"pop6\",\"accept6\"],\"input_alphabet\":[\"a6\",\"b6\"],\"stack_alphabet\":[\"Z6\",\"A6\"],\"start_state\":\"push6\",\"bottom_symbol\":\"Z6\",\"final_states\":[\"accept6\"],\"transitions\":[[\"push6\",\"a6\",\"Z6\",\"push6\",[\"Z6\",\"A6\"]],[\"push6\",\"a6\",\"A6\",\"push6\",[\"A6\",\"A6\"]],[\"push6\",\"b6\",\"A6\",\"pop6\",[]],[\"pop6\",\"b6\",\"A6\",\"pop6\",[]],[\"push6\",null,\"Z6\",\"accept6\",[\"Z6\"]],[\"pop6\",null,\"Z6\",\"accept6\",[\"Z6\"]]],\"input\":[\"a6\",\"a6\",\"b6\",\"b6\"],\"trace\":[[\"push6\",0,[\"Z6\"]],[\"push6\",1,[\"Z6\",\"A6\"]],[\"push6\",2,[\"Z6\",\"A6\",\"A6\"]],[\"pop6\",3,[\"Z6\",\"A6\"]],[\"pop6\",4,[\"Z6\"]],[\"accept6\",4,[\"Z6\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a6, a6, b6, b6], [[push6, 0, [Z6]], [push6, 1, [Z6, A6]], [push6, 2, [Z6, A6, A6]], [pop6, 3, [Z6, A6]], [pop6, 4, [Z6]], [accept6, 4, [Z6]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a6, a6, b6, b6], [[push6, 0, [Z6]], [push6, 1, [Z6, A6]], [push6, 2, [Z6, A6, A6]], [pop6, 3, [Z6, A6]], [pop6, 4, [Z6]], [accept6, 4, [Z6]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107032,"parameters":{"states":["push6","pop6","accept6"],"input_alphabet":["a6","b6"],"stack_alphabet":["Z6","A6"],"start_state":"push6","bottom_symbol":"Z6","final_states":["accept6"],"transitions":[["push6","a6","Z6","push6",["Z6","A6"]],["push6","a6","A6","push6",["A6","A6"]],["push6","b6","A6","pop6",[]],["pop6","b6","A6","pop6",[]],["push6",null,"Z6","accept6",["Z6"]],["pop6",null,"Z6","accept6",["Z6"]]],"input":["a6","a6","b6","b6"],"trace":[["push6",0,["Z6"]],["push6",1,["Z6","A6"]],["push6",2,["Z6","A6","A6"]],["pop6",3,["Z6","A6"]],["pop6",4,["Z6"]],["accept6",4,["Z6"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z6\",\"final_states\":[\"accept6\"],\"input\":[\"a6\",\"a6\",\"b6\",\"b6\"],\"input_alphabet\":[\"a6\",\"b6\"],\"stack_alphabet\":[\"A6\",\"Z6\"],\"start_state\":\"push6\",\"states\":[\"accept6\",\"pop6\",\"push6\"],\"trace\":[[\"push6\",0,[\"Z6\"]],[\"push6\",1,[\"Z6\",\"A6\"]],[\"push6\",2,[\"Z6\",\"A6\",\"A6\"]],[\"pop6\",3,[\"Z6\",\"A6\"]],[\"pop6\",4,[\"Z6\"]],[\"accept6\",4,[\"Z6\"]]],\"transitions\":[[\"pop6\",\"b6\",\"A6\",\"pop6\",[]],[\"pop6\",null,\"Z6\",\"accept6\",[\"Z6\"]],[\"push6\",\"a6\",\"A6\",\"push6\",[\"A6\",\"A6\"]],[\"push6\",\"a6\",\"Z6\",\"push6\",[\"Z6\",\"A6\"]],[\"push6\",\"b6\",\"A6\",\"pop6\",[]],[\"push6\",null,\"Z6\",\"accept6\",[\"Z6\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0033","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push7\",\"pop7\",\"accept7\"],\"input_alphabet\":[\"a7\",\"b7\"],\"stack_alphabet\":[\"Z7\",\"A7\"],\"start_state\":\"push7\",\"bottom_symbol\":\"Z7\",\"final_states\":[\"accept7\"],\"transitions\":[[\"push7\",\"a7\",\"Z7\",\"push7\",[\"Z7\",\"A7\"]],[\"push7\",\"a7\",\"A7\",\"push7\",[\"A7\",\"A7\"]],[\"push7\",\"b7\",\"A7\",\"pop7\",[]],[\"pop7\",\"b7\",\"A7\",\"pop7\",[]],[\"push7\",null,\"Z7\",\"accept7\",[\"Z7\"]],[\"pop7\",null,\"Z7\",\"accept7\",[\"Z7\"]]],\"input\":[\"a7\",\"a7\",\"a7\",\"b7\",\"b7\",\"b7\"],\"trace\":[[\"push7\",0,[\"Z7\"]],[\"push7\",1,[\"Z7\",\"A7\"]],[\"push7\",2,[\"Z7\",\"A7\",\"A7\"]],[\"push7\",3,[\"Z7\",\"A7\",\"A7\",\"A7\"]],[\"pop7\",4,[\"Z7\",\"A7\",\"A7\"]],[\"pop7\",5,[\"Z7\",\"A7\"]],[\"pop7\",6,[\"Z7\"]],[\"accept7\",6,[\"Z7\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a7, a7, a7, b7, b7, b7], [[push7, 0, [Z7]], [push7, 1, [Z7, A7]], [push7, 2, [Z7, A7, A7]], [push7, 3, [Z7, A7, A7, A7]], [pop7, 4, [Z7, A7, A7]], [pop7, 5, [Z7, A7]], [pop7, 6, [Z7]], [accept7, 6, [Z7]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a7, a7, a7, b7, b7, b7], [[push7, 0, [Z7]], [push7, 1, [Z7, A7]], [push7, 2, [Z7, A7, A7]], [push7, 3, [Z7, A7, A7, A7]], [pop7, 4, [Z7, A7, A7]], [pop7, 5, [Z7, A7]], [pop7, 6, [Z7]], [accept7, 6, [Z7]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107033,"parameters":{"states":["push7","pop7","accept7"],"input_alphabet":["a7","b7"],"stack_alphabet":["Z7","A7"],"start_state":"push7","bottom_symbol":"Z7","final_states":["accept7"],"transitions":[["push7","a7","Z7","push7",["Z7","A7"]],["push7","a7","A7","push7",["A7","A7"]],["push7","b7","A7","pop7",[]],["pop7","b7","A7","pop7",[]],["push7",null,"Z7","accept7",["Z7"]],["pop7",null,"Z7","accept7",["Z7"]]],"input":["a7","a7","a7","b7","b7","b7"],"trace":[["push7",0,["Z7"]],["push7",1,["Z7","A7"]],["push7",2,["Z7","A7","A7"]],["push7",3,["Z7","A7","A7","A7"]],["pop7",4,["Z7","A7","A7"]],["pop7",5,["Z7","A7"]],["pop7",6,["Z7"]],["accept7",6,["Z7"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z7\",\"final_states\":[\"accept7\"],\"input\":[\"a7\",\"a7\",\"a7\",\"b7\",\"b7\",\"b7\"],\"input_alphabet\":[\"a7\",\"b7\"],\"stack_alphabet\":[\"A7\",\"Z7\"],\"start_state\":\"push7\",\"states\":[\"accept7\",\"pop7\",\"push7\"],\"trace\":[[\"push7\",0,[\"Z7\"]],[\"push7\",1,[\"Z7\",\"A7\"]],[\"push7\",2,[\"Z7\",\"A7\",\"A7\"]],[\"push7\",3,[\"Z7\",\"A7\",\"A7\",\"A7\"]],[\"pop7\",4,[\"Z7\",\"A7\",\"A7\"]],[\"pop7\",5,[\"Z7\",\"A7\"]],[\"pop7\",6,[\"Z7\"]],[\"accept7\",6,[\"Z7\"]]],\"transitions\":[[\"pop7\",\"b7\",\"A7\",\"pop7\",[]],[\"pop7\",null,\"Z7\",\"accept7\",[\"Z7\"]],[\"push7\",\"a7\",\"A7\",\"push7\",[\"A7\",\"A7\"]],[\"push7\",\"a7\",\"Z7\",\"push7\",[\"Z7\",\"A7\"]],[\"push7\",\"b7\",\"A7\",\"pop7\",[]],[\"push7\",null,\"Z7\",\"accept7\",[\"Z7\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0034","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push8\",\"pop8\",\"accept8\"],\"input_alphabet\":[\"a8\",\"b8\"],\"stack_alphabet\":[\"Z8\",\"A8\"],\"start_state\":\"push8\",\"bottom_symbol\":\"Z8\",\"final_states\":[\"accept8\"],\"transitions\":[[\"push8\",\"a8\",\"Z8\",\"push8\",[\"Z8\",\"A8\"]],[\"push8\",\"a8\",\"A8\",\"push8\",[\"A8\",\"A8\"]],[\"push8\",\"b8\",\"A8\",\"pop8\",[]],[\"pop8\",\"b8\",\"A8\",\"pop8\",[]],[\"push8\",null,\"Z8\",\"accept8\",[\"Z8\"]],[\"pop8\",null,\"Z8\",\"accept8\",[\"Z8\"]]],\"input\":[],\"trace\":[[\"push8\",0,[\"Z8\"]],[\"accept8\",0,[\"Z8\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push8, 0, [Z8]], [accept8, 0, [Z8]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([], [[push8, 0, [Z8]], [accept8, 0, [Z8]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107034,"parameters":{"states":["push8","pop8","accept8"],"input_alphabet":["a8","b8"],"stack_alphabet":["Z8","A8"],"start_state":"push8","bottom_symbol":"Z8","final_states":["accept8"],"transitions":[["push8","a8","Z8","push8",["Z8","A8"]],["push8","a8","A8","push8",["A8","A8"]],["push8","b8","A8","pop8",[]],["pop8","b8","A8","pop8",[]],["push8",null,"Z8","accept8",["Z8"]],["pop8",null,"Z8","accept8",["Z8"]]],"input":[],"trace":[["push8",0,["Z8"]],["accept8",0,["Z8"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z8\",\"final_states\":[\"accept8\"],\"input\":[],\"input_alphabet\":[\"a8\",\"b8\"],\"stack_alphabet\":[\"A8\",\"Z8\"],\"start_state\":\"push8\",\"states\":[\"accept8\",\"pop8\",\"push8\"],\"trace\":[[\"push8\",0,[\"Z8\"]],[\"accept8\",0,[\"Z8\"]]],\"transitions\":[[\"pop8\",\"b8\",\"A8\",\"pop8\",[]],[\"pop8\",null,\"Z8\",\"accept8\",[\"Z8\"]],[\"push8\",\"a8\",\"A8\",\"push8\",[\"A8\",\"A8\"]],[\"push8\",\"a8\",\"Z8\",\"push8\",[\"Z8\",\"A8\"]],[\"push8\",\"b8\",\"A8\",\"pop8\",[]],[\"push8\",null,\"Z8\",\"accept8\",[\"Z8\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0035","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push9\",\"pop9\",\"accept9\"],\"input_alphabet\":[\"a9\",\"b9\"],\"stack_alphabet\":[\"Z9\",\"A9\"],\"start_state\":\"push9\",\"bottom_symbol\":\"Z9\",\"final_states\":[\"accept9\"],\"transitions\":[[\"push9\",\"a9\",\"Z9\",\"push9\",[\"Z9\",\"A9\"]],[\"push9\",\"a9\",\"A9\",\"push9\",[\"A9\",\"A9\"]],[\"push9\",\"b9\",\"A9\",\"pop9\",[]],[\"pop9\",\"b9\",\"A9\",\"pop9\",[]],[\"push9\",null,\"Z9\",\"accept9\",[\"Z9\"]],[\"pop9\",null,\"Z9\",\"accept9\",[\"Z9\"]]],\"input\":[\"a9\",\"b9\"],\"trace\":[[\"push9\",0,[\"Z9\"]],[\"push9\",1,[\"Z9\",\"A9\"]],[\"pop9\",2,[\"Z9\"]],[\"accept9\",2,[\"Z9\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a9, b9], [[push9, 0, [Z9]], [push9, 1, [Z9, A9]], [pop9, 2, [Z9]], [accept9, 2, [Z9]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a9, b9], [[push9, 0, [Z9]], [push9, 1, [Z9, A9]], [pop9, 2, [Z9]], [accept9, 2, [Z9]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107035,"parameters":{"states":["push9","pop9","accept9"],"input_alphabet":["a9","b9"],"stack_alphabet":["Z9","A9"],"start_state":"push9","bottom_symbol":"Z9","final_states":["accept9"],"transitions":[["push9","a9","Z9","push9",["Z9","A9"]],["push9","a9","A9","push9",["A9","A9"]],["push9","b9","A9","pop9",[]],["pop9","b9","A9","pop9",[]],["push9",null,"Z9","accept9",["Z9"]],["pop9",null,"Z9","accept9",["Z9"]]],"input":["a9","b9"],"trace":[["push9",0,["Z9"]],["push9",1,["Z9","A9"]],["pop9",2,["Z9"]],["accept9",2,["Z9"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z9\",\"final_states\":[\"accept9\"],\"input\":[\"a9\",\"b9\"],\"input_alphabet\":[\"a9\",\"b9\"],\"stack_alphabet\":[\"A9\",\"Z9\"],\"start_state\":\"push9\",\"states\":[\"accept9\",\"pop9\",\"push9\"],\"trace\":[[\"push9\",0,[\"Z9\"]],[\"push9\",1,[\"Z9\",\"A9\"]],[\"pop9\",2,[\"Z9\"]],[\"accept9\",2,[\"Z9\"]]],\"transitions\":[[\"pop9\",\"b9\",\"A9\",\"pop9\",[]],[\"pop9\",null,\"Z9\",\"accept9\",[\"Z9\"]],[\"push9\",\"a9\",\"A9\",\"push9\",[\"A9\",\"A9\"]],[\"push9\",\"a9\",\"Z9\",\"push9\",[\"Z9\",\"A9\"]],[\"push9\",\"b9\",\"A9\",\"pop9\",[]],[\"push9\",null,\"Z9\",\"accept9\",[\"Z9\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0036","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push10\",\"pop10\",\"accept10\"],\"input_alphabet\":[\"a10\",\"b10\"],\"stack_alphabet\":[\"Z10\",\"A10\"],\"start_state\":\"push10\",\"bottom_symbol\":\"Z10\",\"final_states\":[\"accept10\"],\"transitions\":[[\"push10\",\"a10\",\"Z10\",\"push10\",[\"Z10\",\"A10\"]],[\"push10\",\"a10\",\"A10\",\"push10\",[\"A10\",\"A10\"]],[\"push10\",\"b10\",\"A10\",\"pop10\",[]],[\"pop10\",\"b10\",\"A10\",\"pop10\",[]],[\"push10\",null,\"Z10\",\"accept10\",[\"Z10\"]],[\"pop10\",null,\"Z10\",\"accept10\",[\"Z10\"]]],\"input\":[\"a10\",\"a10\",\"b10\",\"b10\"],\"trace\":[[\"push10\",0,[\"Z10\"]],[\"push10\",1,[\"Z10\",\"A10\"]],[\"push10\",2,[\"Z10\",\"A10\",\"A10\"]],[\"pop10\",3,[\"Z10\",\"A10\"]],[\"pop10\",4,[\"Z10\"]],[\"accept10\",4,[\"Z10\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a10, a10, b10, b10], [[push10, 0, [Z10]], [push10, 1, [Z10, A10]], [push10, 2, [Z10, A10, A10]], [pop10, 3, [Z10, A10]], [pop10, 4, [Z10]], [accept10, 4, [Z10]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a10, a10, b10, b10], [[push10, 0, [Z10]], [push10, 1, [Z10, A10]], [push10, 2, [Z10, A10, A10]], [pop10, 3, [Z10, A10]], [pop10, 4, [Z10]], [accept10, 4, [Z10]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107036,"parameters":{"states":["push10","pop10","accept10"],"input_alphabet":["a10","b10"],"stack_alphabet":["Z10","A10"],"start_state":"push10","bottom_symbol":"Z10","final_states":["accept10"],"transitions":[["push10","a10","Z10","push10",["Z10","A10"]],["push10","a10","A10","push10",["A10","A10"]],["push10","b10","A10","pop10",[]],["pop10","b10","A10","pop10",[]],["push10",null,"Z10","accept10",["Z10"]],["pop10",null,"Z10","accept10",["Z10"]]],"input":["a10","a10","b10","b10"],"trace":[["push10",0,["Z10"]],["push10",1,["Z10","A10"]],["push10",2,["Z10","A10","A10"]],["pop10",3,["Z10","A10"]],["pop10",4,["Z10"]],["accept10",4,["Z10"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z10\",\"final_states\":[\"accept10\"],\"input\":[\"a10\",\"a10\",\"b10\",\"b10\"],\"input_alphabet\":[\"a10\",\"b10\"],\"stack_alphabet\":[\"A10\",\"Z10\"],\"start_state\":\"push10\",\"states\":[\"accept10\",\"pop10\",\"push10\"],\"trace\":[[\"push10\",0,[\"Z10\"]],[\"push10\",1,[\"Z10\",\"A10\"]],[\"push10\",2,[\"Z10\",\"A10\",\"A10\"]],[\"pop10\",3,[\"Z10\",\"A10\"]],[\"pop10\",4,[\"Z10\"]],[\"accept10\",4,[\"Z10\"]]],\"transitions\":[[\"pop10\",\"b10\",\"A10\",\"pop10\",[]],[\"pop10\",null,\"Z10\",\"accept10\",[\"Z10\"]],[\"push10\",\"a10\",\"A10\",\"push10\",[\"A10\",\"A10\"]],[\"push10\",\"a10\",\"Z10\",\"push10\",[\"Z10\",\"A10\"]],[\"push10\",\"b10\",\"A10\",\"pop10\",[]],[\"push10\",null,\"Z10\",\"accept10\",[\"Z10\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0037","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push11\",\"pop11\",\"accept11\"],\"input_alphabet\":[\"a11\",\"b11\"],\"stack_alphabet\":[\"Z11\",\"A11\"],\"start_state\":\"push11\",\"bottom_symbol\":\"Z11\",\"final_states\":[\"accept11\"],\"transitions\":[[\"push11\",\"a11\",\"Z11\",\"push11\",[\"Z11\",\"A11\"]],[\"push11\",\"a11\",\"A11\",\"push11\",[\"A11\",\"A11\"]],[\"push11\",\"b11\",\"A11\",\"pop11\",[]],[\"pop11\",\"b11\",\"A11\",\"pop11\",[]],[\"push11\",null,\"Z11\",\"accept11\",[\"Z11\"]],[\"pop11\",null,\"Z11\",\"accept11\",[\"Z11\"]]],\"input\":[\"a11\",\"a11\",\"a11\",\"b11\",\"b11\",\"b11\"],\"trace\":[[\"push11\",0,[\"Z11\"]],[\"push11\",1,[\"Z11\",\"A11\"]],[\"push11\",2,[\"Z11\",\"A11\",\"A11\"]],[\"push11\",3,[\"Z11\",\"A11\",\"A11\",\"A11\"]],[\"pop11\",4,[\"Z11\",\"A11\",\"A11\"]],[\"pop11\",5,[\"Z11\",\"A11\"]],[\"pop11\",6,[\"Z11\"]],[\"accept11\",6,[\"Z11\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a11, a11, a11, b11, b11, b11], [[push11, 0, [Z11]], [push11, 1, [Z11, A11]], [push11, 2, [Z11, A11, A11]], [push11, 3, [Z11, A11, A11, A11]], [pop11, 4, [Z11, A11, A11]], [pop11, 5, [Z11, A11]], [pop11, 6, [Z11]], [accept11, 6, [Z11]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a11, a11, a11, b11, b11, b11], [[push11, 0, [Z11]], [push11, 1, [Z11, A11]], [push11, 2, [Z11, A11, A11]], [push11, 3, [Z11, A11, A11, A11]], [pop11, 4, [Z11, A11, A11]], [pop11, 5, [Z11, A11]], [pop11, 6, [Z11]], [accept11, 6, [Z11]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107037,"parameters":{"states":["push11","pop11","accept11"],"input_alphabet":["a11","b11"],"stack_alphabet":["Z11","A11"],"start_state":"push11","bottom_symbol":"Z11","final_states":["accept11"],"transitions":[["push11","a11","Z11","push11",["Z11","A11"]],["push11","a11","A11","push11",["A11","A11"]],["push11","b11","A11","pop11",[]],["pop11","b11","A11","pop11",[]],["push11",null,"Z11","accept11",["Z11"]],["pop11",null,"Z11","accept11",["Z11"]]],"input":["a11","a11","a11","b11","b11","b11"],"trace":[["push11",0,["Z11"]],["push11",1,["Z11","A11"]],["push11",2,["Z11","A11","A11"]],["push11",3,["Z11","A11","A11","A11"]],["pop11",4,["Z11","A11","A11"]],["pop11",5,["Z11","A11"]],["pop11",6,["Z11"]],["accept11",6,["Z11"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z11\",\"final_states\":[\"accept11\"],\"input\":[\"a11\",\"a11\",\"a11\",\"b11\",\"b11\",\"b11\"],\"input_alphabet\":[\"a11\",\"b11\"],\"stack_alphabet\":[\"A11\",\"Z11\"],\"start_state\":\"push11\",\"states\":[\"accept11\",\"pop11\",\"push11\"],\"trace\":[[\"push11\",0,[\"Z11\"]],[\"push11\",1,[\"Z11\",\"A11\"]],[\"push11\",2,[\"Z11\",\"A11\",\"A11\"]],[\"push11\",3,[\"Z11\",\"A11\",\"A11\",\"A11\"]],[\"pop11\",4,[\"Z11\",\"A11\",\"A11\"]],[\"pop11\",5,[\"Z11\",\"A11\"]],[\"pop11\",6,[\"Z11\"]],[\"accept11\",6,[\"Z11\"]]],\"transitions\":[[\"pop11\",\"b11\",\"A11\",\"pop11\",[]],[\"pop11\",null,\"Z11\",\"accept11\",[\"Z11\"]],[\"push11\",\"a11\",\"A11\",\"push11\",[\"A11\",\"A11\"]],[\"push11\",\"a11\",\"Z11\",\"push11\",[\"Z11\",\"A11\"]],[\"push11\",\"b11\",\"A11\",\"pop11\",[]],[\"push11\",null,\"Z11\",\"accept11\",[\"Z11\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0038","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push12\",\"pop12\",\"accept12\"],\"input_alphabet\":[\"a12\",\"b12\"],\"stack_alphabet\":[\"Z12\",\"A12\"],\"start_state\":\"push12\",\"bottom_symbol\":\"Z12\",\"final_states\":[\"accept12\"],\"transitions\":[[\"push12\",\"a12\",\"Z12\",\"push12\",[\"Z12\",\"A12\"]],[\"push12\",\"a12\",\"A12\",\"push12\",[\"A12\",\"A12\"]],[\"push12\",\"b12\",\"A12\",\"pop12\",[]],[\"pop12\",\"b12\",\"A12\",\"pop12\",[]],[\"push12\",null,\"Z12\",\"accept12\",[\"Z12\"]],[\"pop12\",null,\"Z12\",\"accept12\",[\"Z12\"]]],\"input\":[],\"trace\":[[\"push12\",0,[\"Z12\"]],[\"accept12\",0,[\"Z12\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push12, 0, [Z12]], [accept12, 0, [Z12]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([], [[push12, 0, [Z12]], [accept12, 0, [Z12]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107038,"parameters":{"states":["push12","pop12","accept12"],"input_alphabet":["a12","b12"],"stack_alphabet":["Z12","A12"],"start_state":"push12","bottom_symbol":"Z12","final_states":["accept12"],"transitions":[["push12","a12","Z12","push12",["Z12","A12"]],["push12","a12","A12","push12",["A12","A12"]],["push12","b12","A12","pop12",[]],["pop12","b12","A12","pop12",[]],["push12",null,"Z12","accept12",["Z12"]],["pop12",null,"Z12","accept12",["Z12"]]],"input":[],"trace":[["push12",0,["Z12"]],["accept12",0,["Z12"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z12\",\"final_states\":[\"accept12\"],\"input\":[],\"input_alphabet\":[\"a12\",\"b12\"],\"stack_alphabet\":[\"A12\",\"Z12\"],\"start_state\":\"push12\",\"states\":[\"accept12\",\"pop12\",\"push12\"],\"trace\":[[\"push12\",0,[\"Z12\"]],[\"accept12\",0,[\"Z12\"]]],\"transitions\":[[\"pop12\",\"b12\",\"A12\",\"pop12\",[]],[\"pop12\",null,\"Z12\",\"accept12\",[\"Z12\"]],[\"push12\",\"a12\",\"A12\",\"push12\",[\"A12\",\"A12\"]],[\"push12\",\"a12\",\"Z12\",\"push12\",[\"Z12\",\"A12\"]],[\"push12\",\"b12\",\"A12\",\"pop12\",[]],[\"push12\",null,\"Z12\",\"accept12\",[\"Z12\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0039","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push13\",\"pop13\",\"accept13\"],\"input_alphabet\":[\"a13\",\"b13\"],\"stack_alphabet\":[\"Z13\",\"A13\"],\"start_state\":\"push13\",\"bottom_symbol\":\"Z13\",\"final_states\":[\"accept13\"],\"transitions\":[[\"push13\",\"a13\",\"Z13\",\"push13\",[\"Z13\",\"A13\"]],[\"push13\",\"a13\",\"A13\",\"push13\",[\"A13\",\"A13\"]],[\"push13\",\"b13\",\"A13\",\"pop13\",[]],[\"pop13\",\"b13\",\"A13\",\"pop13\",[]],[\"push13\",null,\"Z13\",\"accept13\",[\"Z13\"]],[\"pop13\",null,\"Z13\",\"accept13\",[\"Z13\"]]],\"input\":[\"a13\",\"b13\"],\"trace\":[[\"push13\",0,[\"Z13\"]],[\"push13\",1,[\"Z13\",\"A13\"]],[\"pop13\",2,[\"Z13\"]],[\"accept13\",2,[\"Z13\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a13, b13], [[push13, 0, [Z13]], [push13, 1, [Z13, A13]], [pop13, 2, [Z13]], [accept13, 2, [Z13]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a13, b13], [[push13, 0, [Z13]], [push13, 1, [Z13, A13]], [pop13, 2, [Z13]], [accept13, 2, [Z13]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107039,"parameters":{"states":["push13","pop13","accept13"],"input_alphabet":["a13","b13"],"stack_alphabet":["Z13","A13"],"start_state":"push13","bottom_symbol":"Z13","final_states":["accept13"],"transitions":[["push13","a13","Z13","push13",["Z13","A13"]],["push13","a13","A13","push13",["A13","A13"]],["push13","b13","A13","pop13",[]],["pop13","b13","A13","pop13",[]],["push13",null,"Z13","accept13",["Z13"]],["pop13",null,"Z13","accept13",["Z13"]]],"input":["a13","b13"],"trace":[["push13",0,["Z13"]],["push13",1,["Z13","A13"]],["pop13",2,["Z13"]],["accept13",2,["Z13"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z13\",\"final_states\":[\"accept13\"],\"input\":[\"a13\",\"b13\"],\"input_alphabet\":[\"a13\",\"b13\"],\"stack_alphabet\":[\"A13\",\"Z13\"],\"start_state\":\"push13\",\"states\":[\"accept13\",\"pop13\",\"push13\"],\"trace\":[[\"push13\",0,[\"Z13\"]],[\"push13\",1,[\"Z13\",\"A13\"]],[\"pop13\",2,[\"Z13\"]],[\"accept13\",2,[\"Z13\"]]],\"transitions\":[[\"pop13\",\"b13\",\"A13\",\"pop13\",[]],[\"pop13\",null,\"Z13\",\"accept13\",[\"Z13\"]],[\"push13\",\"a13\",\"A13\",\"push13\",[\"A13\",\"A13\"]],[\"push13\",\"a13\",\"Z13\",\"push13\",[\"Z13\",\"A13\"]],[\"push13\",\"b13\",\"A13\",\"pop13\",[]],[\"push13\",null,\"Z13\",\"accept13\",[\"Z13\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0040","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push14\",\"pop14\",\"accept14\"],\"input_alphabet\":[\"a14\",\"b14\"],\"stack_alphabet\":[\"Z14\",\"A14\"],\"start_state\":\"push14\",\"bottom_symbol\":\"Z14\",\"final_states\":[\"accept14\"],\"transitions\":[[\"push14\",\"a14\",\"Z14\",\"push14\",[\"Z14\",\"A14\"]],[\"push14\",\"a14\",\"A14\",\"push14\",[\"A14\",\"A14\"]],[\"push14\",\"b14\",\"A14\",\"pop14\",[]],[\"pop14\",\"b14\",\"A14\",\"pop14\",[]],[\"push14\",null,\"Z14\",\"accept14\",[\"Z14\"]],[\"pop14\",null,\"Z14\",\"accept14\",[\"Z14\"]]],\"input\":[\"a14\",\"a14\",\"b14\",\"b14\"],\"trace\":[[\"push14\",0,[\"Z14\"]],[\"push14\",1,[\"Z14\",\"A14\"]],[\"push14\",2,[\"Z14\",\"A14\",\"A14\"]],[\"pop14\",3,[\"Z14\",\"A14\"]],[\"pop14\",4,[\"Z14\"]],[\"accept14\",4,[\"Z14\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a14, a14, b14, b14], [[push14, 0, [Z14]], [push14, 1, [Z14, A14]], [push14, 2, [Z14, A14, A14]], [pop14, 3, [Z14, A14]], [pop14, 4, [Z14]], [accept14, 4, [Z14]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a14, a14, b14, b14], [[push14, 0, [Z14]], [push14, 1, [Z14, A14]], [push14, 2, [Z14, A14, A14]], [pop14, 3, [Z14, A14]], [pop14, 4, [Z14]], [accept14, 4, [Z14]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107040,"parameters":{"states":["push14","pop14","accept14"],"input_alphabet":["a14","b14"],"stack_alphabet":["Z14","A14"],"start_state":"push14","bottom_symbol":"Z14","final_states":["accept14"],"transitions":[["push14","a14","Z14","push14",["Z14","A14"]],["push14","a14","A14","push14",["A14","A14"]],["push14","b14","A14","pop14",[]],["pop14","b14","A14","pop14",[]],["push14",null,"Z14","accept14",["Z14"]],["pop14",null,"Z14","accept14",["Z14"]]],"input":["a14","a14","b14","b14"],"trace":[["push14",0,["Z14"]],["push14",1,["Z14","A14"]],["push14",2,["Z14","A14","A14"]],["pop14",3,["Z14","A14"]],["pop14",4,["Z14"]],["accept14",4,["Z14"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z14\",\"final_states\":[\"accept14\"],\"input\":[\"a14\",\"a14\",\"b14\",\"b14\"],\"input_alphabet\":[\"a14\",\"b14\"],\"stack_alphabet\":[\"A14\",\"Z14\"],\"start_state\":\"push14\",\"states\":[\"accept14\",\"pop14\",\"push14\"],\"trace\":[[\"push14\",0,[\"Z14\"]],[\"push14\",1,[\"Z14\",\"A14\"]],[\"push14\",2,[\"Z14\",\"A14\",\"A14\"]],[\"pop14\",3,[\"Z14\",\"A14\"]],[\"pop14\",4,[\"Z14\"]],[\"accept14\",4,[\"Z14\"]]],\"transitions\":[[\"pop14\",\"b14\",\"A14\",\"pop14\",[]],[\"pop14\",null,\"Z14\",\"accept14\",[\"Z14\"]],[\"push14\",\"a14\",\"A14\",\"push14\",[\"A14\",\"A14\"]],[\"push14\",\"a14\",\"Z14\",\"push14\",[\"Z14\",\"A14\"]],[\"push14\",\"b14\",\"A14\",\"pop14\",[]],[\"push14\",null,\"Z14\",\"accept14\",[\"Z14\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0041","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push15\",\"pop15\",\"accept15\"],\"input_alphabet\":[\"a15\",\"b15\"],\"stack_alphabet\":[\"Z15\",\"A15\"],\"start_state\":\"push15\",\"bottom_symbol\":\"Z15\",\"final_states\":[\"accept15\"],\"transitions\":[[\"push15\",\"a15\",\"Z15\",\"push15\",[\"Z15\",\"A15\"]],[\"push15\",\"a15\",\"A15\",\"push15\",[\"A15\",\"A15\"]],[\"push15\",\"b15\",\"A15\",\"pop15\",[]],[\"pop15\",\"b15\",\"A15\",\"pop15\",[]],[\"push15\",null,\"Z15\",\"accept15\",[\"Z15\"]],[\"pop15\",null,\"Z15\",\"accept15\",[\"Z15\"]]],\"input\":[\"a15\",\"a15\",\"a15\",\"b15\",\"b15\",\"b15\"],\"trace\":[[\"push15\",0,[\"Z15\"]],[\"push15\",1,[\"Z15\",\"A15\"]],[\"push15\",2,[\"Z15\",\"A15\",\"A15\"]],[\"push15\",3,[\"Z15\",\"A15\",\"A15\",\"A15\"]],[\"pop15\",4,[\"Z15\",\"A15\",\"A15\"]],[\"pop15\",5,[\"Z15\",\"A15\"]],[\"pop15\",6,[\"Z15\"]],[\"accept15\",6,[\"Z15\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a15, a15, a15, b15, b15, b15], [[push15, 0, [Z15]], [push15, 1, [Z15, A15]], [push15, 2, [Z15, A15, A15]], [push15, 3, [Z15, A15, A15, A15]], [pop15, 4, [Z15, A15, A15]], [pop15, 5, [Z15, A15]], [pop15, 6, [Z15]], [accept15, 6, [Z15]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a15, a15, a15, b15, b15, b15], [[push15, 0, [Z15]], [push15, 1, [Z15, A15]], [push15, 2, [Z15, A15, A15]], [push15, 3, [Z15, A15, A15, A15]], [pop15, 4, [Z15, A15, A15]], [pop15, 5, [Z15, A15]], [pop15, 6, [Z15]], [accept15, 6, [Z15]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107041,"parameters":{"states":["push15","pop15","accept15"],"input_alphabet":["a15","b15"],"stack_alphabet":["Z15","A15"],"start_state":"push15","bottom_symbol":"Z15","final_states":["accept15"],"transitions":[["push15","a15","Z15","push15",["Z15","A15"]],["push15","a15","A15","push15",["A15","A15"]],["push15","b15","A15","pop15",[]],["pop15","b15","A15","pop15",[]],["push15",null,"Z15","accept15",["Z15"]],["pop15",null,"Z15","accept15",["Z15"]]],"input":["a15","a15","a15","b15","b15","b15"],"trace":[["push15",0,["Z15"]],["push15",1,["Z15","A15"]],["push15",2,["Z15","A15","A15"]],["push15",3,["Z15","A15","A15","A15"]],["pop15",4,["Z15","A15","A15"]],["pop15",5,["Z15","A15"]],["pop15",6,["Z15"]],["accept15",6,["Z15"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z15\",\"final_states\":[\"accept15\"],\"input\":[\"a15\",\"a15\",\"a15\",\"b15\",\"b15\",\"b15\"],\"input_alphabet\":[\"a15\",\"b15\"],\"stack_alphabet\":[\"A15\",\"Z15\"],\"start_state\":\"push15\",\"states\":[\"accept15\",\"pop15\",\"push15\"],\"trace\":[[\"push15\",0,[\"Z15\"]],[\"push15\",1,[\"Z15\",\"A15\"]],[\"push15\",2,[\"Z15\",\"A15\",\"A15\"]],[\"push15\",3,[\"Z15\",\"A15\",\"A15\",\"A15\"]],[\"pop15\",4,[\"Z15\",\"A15\",\"A15\"]],[\"pop15\",5,[\"Z15\",\"A15\"]],[\"pop15\",6,[\"Z15\"]],[\"accept15\",6,[\"Z15\"]]],\"transitions\":[[\"pop15\",\"b15\",\"A15\",\"pop15\",[]],[\"pop15\",null,\"Z15\",\"accept15\",[\"Z15\"]],[\"push15\",\"a15\",\"A15\",\"push15\",[\"A15\",\"A15\"]],[\"push15\",\"a15\",\"Z15\",\"push15\",[\"Z15\",\"A15\"]],[\"push15\",\"b15\",\"A15\",\"pop15\",[]],[\"push15\",null,\"Z15\",\"accept15\",[\"Z15\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0042","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push16\",\"pop16\",\"accept16\"],\"input_alphabet\":[\"a16\",\"b16\"],\"stack_alphabet\":[\"Z16\",\"A16\"],\"start_state\":\"push16\",\"bottom_symbol\":\"Z16\",\"final_states\":[\"accept16\"],\"transitions\":[[\"push16\",\"a16\",\"Z16\",\"push16\",[\"Z16\",\"A16\"]],[\"push16\",\"a16\",\"A16\",\"push16\",[\"A16\",\"A16\"]],[\"push16\",\"b16\",\"A16\",\"pop16\",[]],[\"pop16\",\"b16\",\"A16\",\"pop16\",[]],[\"push16\",null,\"Z16\",\"accept16\",[\"Z16\"]],[\"pop16\",null,\"Z16\",\"accept16\",[\"Z16\"]]],\"input\":[],\"trace\":[[\"push16\",0,[\"Z16\"]],[\"accept16\",0,[\"Z16\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push16, 0, [Z16]], [accept16, 0, [Z16]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([], [[push16, 0, [Z16]], [accept16, 0, [Z16]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107042,"parameters":{"states":["push16","pop16","accept16"],"input_alphabet":["a16","b16"],"stack_alphabet":["Z16","A16"],"start_state":"push16","bottom_symbol":"Z16","final_states":["accept16"],"transitions":[["push16","a16","Z16","push16",["Z16","A16"]],["push16","a16","A16","push16",["A16","A16"]],["push16","b16","A16","pop16",[]],["pop16","b16","A16","pop16",[]],["push16",null,"Z16","accept16",["Z16"]],["pop16",null,"Z16","accept16",["Z16"]]],"input":[],"trace":[["push16",0,["Z16"]],["accept16",0,["Z16"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z16\",\"final_states\":[\"accept16\"],\"input\":[],\"input_alphabet\":[\"a16\",\"b16\"],\"stack_alphabet\":[\"A16\",\"Z16\"],\"start_state\":\"push16\",\"states\":[\"accept16\",\"pop16\",\"push16\"],\"trace\":[[\"push16\",0,[\"Z16\"]],[\"accept16\",0,[\"Z16\"]]],\"transitions\":[[\"pop16\",\"b16\",\"A16\",\"pop16\",[]],[\"pop16\",null,\"Z16\",\"accept16\",[\"Z16\"]],[\"push16\",\"a16\",\"A16\",\"push16\",[\"A16\",\"A16\"]],[\"push16\",\"a16\",\"Z16\",\"push16\",[\"Z16\",\"A16\"]],[\"push16\",\"b16\",\"A16\",\"pop16\",[]],[\"push16\",null,\"Z16\",\"accept16\",[\"Z16\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0043","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push17\",\"pop17\",\"accept17\"],\"input_alphabet\":[\"a17\",\"b17\"],\"stack_alphabet\":[\"Z17\",\"A17\"],\"start_state\":\"push17\",\"bottom_symbol\":\"Z17\",\"final_states\":[\"accept17\"],\"transitions\":[[\"push17\",\"a17\",\"Z17\",\"push17\",[\"Z17\",\"A17\"]],[\"push17\",\"a17\",\"A17\",\"push17\",[\"A17\",\"A17\"]],[\"push17\",\"b17\",\"A17\",\"pop17\",[]],[\"pop17\",\"b17\",\"A17\",\"pop17\",[]],[\"push17\",null,\"Z17\",\"accept17\",[\"Z17\"]],[\"pop17\",null,\"Z17\",\"accept17\",[\"Z17\"]]],\"input\":[\"a17\",\"b17\"],\"trace\":[[\"push17\",0,[\"Z17\"]],[\"push17\",1,[\"Z17\",\"A17\"]],[\"pop17\",2,[\"Z17\"]],[\"accept17\",2,[\"Z17\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a17, b17], [[push17, 0, [Z17]], [push17, 1, [Z17, A17]], [pop17, 2, [Z17]], [accept17, 2, [Z17]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a17, b17], [[push17, 0, [Z17]], [push17, 1, [Z17, A17]], [pop17, 2, [Z17]], [accept17, 2, [Z17]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107043,"parameters":{"states":["push17","pop17","accept17"],"input_alphabet":["a17","b17"],"stack_alphabet":["Z17","A17"],"start_state":"push17","bottom_symbol":"Z17","final_states":["accept17"],"transitions":[["push17","a17","Z17","push17",["Z17","A17"]],["push17","a17","A17","push17",["A17","A17"]],["push17","b17","A17","pop17",[]],["pop17","b17","A17","pop17",[]],["push17",null,"Z17","accept17",["Z17"]],["pop17",null,"Z17","accept17",["Z17"]]],"input":["a17","b17"],"trace":[["push17",0,["Z17"]],["push17",1,["Z17","A17"]],["pop17",2,["Z17"]],["accept17",2,["Z17"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z17\",\"final_states\":[\"accept17\"],\"input\":[\"a17\",\"b17\"],\"input_alphabet\":[\"a17\",\"b17\"],\"stack_alphabet\":[\"A17\",\"Z17\"],\"start_state\":\"push17\",\"states\":[\"accept17\",\"pop17\",\"push17\"],\"trace\":[[\"push17\",0,[\"Z17\"]],[\"push17\",1,[\"Z17\",\"A17\"]],[\"pop17\",2,[\"Z17\"]],[\"accept17\",2,[\"Z17\"]]],\"transitions\":[[\"pop17\",\"b17\",\"A17\",\"pop17\",[]],[\"pop17\",null,\"Z17\",\"accept17\",[\"Z17\"]],[\"push17\",\"a17\",\"A17\",\"push17\",[\"A17\",\"A17\"]],[\"push17\",\"a17\",\"Z17\",\"push17\",[\"Z17\",\"A17\"]],[\"push17\",\"b17\",\"A17\",\"pop17\",[]],[\"push17\",null,\"Z17\",\"accept17\",[\"Z17\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0044","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push18\",\"pop18\",\"accept18\"],\"input_alphabet\":[\"a18\",\"b18\"],\"stack_alphabet\":[\"Z18\",\"A18\"],\"start_state\":\"push18\",\"bottom_symbol\":\"Z18\",\"final_states\":[\"accept18\"],\"transitions\":[[\"push18\",\"a18\",\"Z18\",\"push18\",[\"Z18\",\"A18\"]],[\"push18\",\"a18\",\"A18\",\"push18\",[\"A18\",\"A18\"]],[\"push18\",\"b18\",\"A18\",\"pop18\",[]],[\"pop18\",\"b18\",\"A18\",\"pop18\",[]],[\"push18\",null,\"Z18\",\"accept18\",[\"Z18\"]],[\"pop18\",null,\"Z18\",\"accept18\",[\"Z18\"]]],\"input\":[\"a18\",\"a18\",\"b18\",\"b18\"],\"trace\":[[\"push18\",0,[\"Z18\"]],[\"push18\",1,[\"Z18\",\"A18\"]],[\"push18\",2,[\"Z18\",\"A18\",\"A18\"]],[\"pop18\",3,[\"Z18\",\"A18\"]],[\"pop18\",4,[\"Z18\"]],[\"accept18\",4,[\"Z18\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a18, a18, b18, b18], [[push18, 0, [Z18]], [push18, 1, [Z18, A18]], [push18, 2, [Z18, A18, A18]], [pop18, 3, [Z18, A18]], [pop18, 4, [Z18]], [accept18, 4, [Z18]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a18, a18, b18, b18], [[push18, 0, [Z18]], [push18, 1, [Z18, A18]], [push18, 2, [Z18, A18, A18]], [pop18, 3, [Z18, A18]], [pop18, 4, [Z18]], [accept18, 4, [Z18]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107044,"parameters":{"states":["push18","pop18","accept18"],"input_alphabet":["a18","b18"],"stack_alphabet":["Z18","A18"],"start_state":"push18","bottom_symbol":"Z18","final_states":["accept18"],"transitions":[["push18","a18","Z18","push18",["Z18","A18"]],["push18","a18","A18","push18",["A18","A18"]],["push18","b18","A18","pop18",[]],["pop18","b18","A18","pop18",[]],["push18",null,"Z18","accept18",["Z18"]],["pop18",null,"Z18","accept18",["Z18"]]],"input":["a18","a18","b18","b18"],"trace":[["push18",0,["Z18"]],["push18",1,["Z18","A18"]],["push18",2,["Z18","A18","A18"]],["pop18",3,["Z18","A18"]],["pop18",4,["Z18"]],["accept18",4,["Z18"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z18\",\"final_states\":[\"accept18\"],\"input\":[\"a18\",\"a18\",\"b18\",\"b18\"],\"input_alphabet\":[\"a18\",\"b18\"],\"stack_alphabet\":[\"A18\",\"Z18\"],\"start_state\":\"push18\",\"states\":[\"accept18\",\"pop18\",\"push18\"],\"trace\":[[\"push18\",0,[\"Z18\"]],[\"push18\",1,[\"Z18\",\"A18\"]],[\"push18\",2,[\"Z18\",\"A18\",\"A18\"]],[\"pop18\",3,[\"Z18\",\"A18\"]],[\"pop18\",4,[\"Z18\"]],[\"accept18\",4,[\"Z18\"]]],\"transitions\":[[\"pop18\",\"b18\",\"A18\",\"pop18\",[]],[\"pop18\",null,\"Z18\",\"accept18\",[\"Z18\"]],[\"push18\",\"a18\",\"A18\",\"push18\",[\"A18\",\"A18\"]],[\"push18\",\"a18\",\"Z18\",\"push18\",[\"Z18\",\"A18\"]],[\"push18\",\"b18\",\"A18\",\"pop18\",[]],[\"push18\",null,\"Z18\",\"accept18\",[\"Z18\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0045","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push19\",\"pop19\",\"accept19\"],\"input_alphabet\":[\"a19\",\"b19\"],\"stack_alphabet\":[\"Z19\",\"A19\"],\"start_state\":\"push19\",\"bottom_symbol\":\"Z19\",\"final_states\":[\"accept19\"],\"transitions\":[[\"push19\",\"a19\",\"Z19\",\"push19\",[\"Z19\",\"A19\"]],[\"push19\",\"a19\",\"A19\",\"push19\",[\"A19\",\"A19\"]],[\"push19\",\"b19\",\"A19\",\"pop19\",[]],[\"pop19\",\"b19\",\"A19\",\"pop19\",[]],[\"push19\",null,\"Z19\",\"accept19\",[\"Z19\"]],[\"pop19\",null,\"Z19\",\"accept19\",[\"Z19\"]]],\"input\":[\"a19\",\"a19\",\"a19\",\"b19\",\"b19\",\"b19\"],\"trace\":[[\"push19\",0,[\"Z19\"]],[\"push19\",1,[\"Z19\",\"A19\"]],[\"push19\",2,[\"Z19\",\"A19\",\"A19\"]],[\"push19\",3,[\"Z19\",\"A19\",\"A19\",\"A19\"]],[\"pop19\",4,[\"Z19\",\"A19\",\"A19\"]],[\"pop19\",5,[\"Z19\",\"A19\"]],[\"pop19\",6,[\"Z19\"]],[\"accept19\",6,[\"Z19\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a19, a19, a19, b19, b19, b19], [[push19, 0, [Z19]], [push19, 1, [Z19, A19]], [push19, 2, [Z19, A19, A19]], [push19, 3, [Z19, A19, A19, A19]], [pop19, 4, [Z19, A19, A19]], [pop19, 5, [Z19, A19]], [pop19, 6, [Z19]], [accept19, 6, [Z19]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a19, a19, a19, b19, b19, b19], [[push19, 0, [Z19]], [push19, 1, [Z19, A19]], [push19, 2, [Z19, A19, A19]], [push19, 3, [Z19, A19, A19, A19]], [pop19, 4, [Z19, A19, A19]], [pop19, 5, [Z19, A19]], [pop19, 6, [Z19]], [accept19, 6, [Z19]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107045,"parameters":{"states":["push19","pop19","accept19"],"input_alphabet":["a19","b19"],"stack_alphabet":["Z19","A19"],"start_state":"push19","bottom_symbol":"Z19","final_states":["accept19"],"transitions":[["push19","a19","Z19","push19",["Z19","A19"]],["push19","a19","A19","push19",["A19","A19"]],["push19","b19","A19","pop19",[]],["pop19","b19","A19","pop19",[]],["push19",null,"Z19","accept19",["Z19"]],["pop19",null,"Z19","accept19",["Z19"]]],"input":["a19","a19","a19","b19","b19","b19"],"trace":[["push19",0,["Z19"]],["push19",1,["Z19","A19"]],["push19",2,["Z19","A19","A19"]],["push19",3,["Z19","A19","A19","A19"]],["pop19",4,["Z19","A19","A19"]],["pop19",5,["Z19","A19"]],["pop19",6,["Z19"]],["accept19",6,["Z19"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z19\",\"final_states\":[\"accept19\"],\"input\":[\"a19\",\"a19\",\"a19\",\"b19\",\"b19\",\"b19\"],\"input_alphabet\":[\"a19\",\"b19\"],\"stack_alphabet\":[\"A19\",\"Z19\"],\"start_state\":\"push19\",\"states\":[\"accept19\",\"pop19\",\"push19\"],\"trace\":[[\"push19\",0,[\"Z19\"]],[\"push19\",1,[\"Z19\",\"A19\"]],[\"push19\",2,[\"Z19\",\"A19\",\"A19\"]],[\"push19\",3,[\"Z19\",\"A19\",\"A19\",\"A19\"]],[\"pop19\",4,[\"Z19\",\"A19\",\"A19\"]],[\"pop19\",5,[\"Z19\",\"A19\"]],[\"pop19\",6,[\"Z19\"]],[\"accept19\",6,[\"Z19\"]]],\"transitions\":[[\"pop19\",\"b19\",\"A19\",\"pop19\",[]],[\"pop19\",null,\"Z19\",\"accept19\",[\"Z19\"]],[\"push19\",\"a19\",\"A19\",\"push19\",[\"A19\",\"A19\"]],[\"push19\",\"a19\",\"Z19\",\"push19\",[\"Z19\",\"A19\"]],[\"push19\",\"b19\",\"A19\",\"pop19\",[]],[\"push19\",null,\"Z19\",\"accept19\",[\"Z19\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0046","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push20\",\"pop20\",\"accept20\"],\"input_alphabet\":[\"a20\",\"b20\"],\"stack_alphabet\":[\"Z20\",\"A20\"],\"start_state\":\"push20\",\"bottom_symbol\":\"Z20\",\"final_states\":[\"accept20\"],\"transitions\":[[\"push20\",\"a20\",\"Z20\",\"push20\",[\"Z20\",\"A20\"]],[\"push20\",\"a20\",\"A20\",\"push20\",[\"A20\",\"A20\"]],[\"push20\",\"b20\",\"A20\",\"pop20\",[]],[\"pop20\",\"b20\",\"A20\",\"pop20\",[]],[\"push20\",null,\"Z20\",\"accept20\",[\"Z20\"]],[\"pop20\",null,\"Z20\",\"accept20\",[\"Z20\"]]],\"input\":[],\"trace\":[[\"push20\",0,[\"Z20\"]],[\"accept20\",0,[\"Z20\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push20, 0, [Z20]], [accept20, 0, [Z20]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([], [[push20, 0, [Z20]], [accept20, 0, [Z20]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107046,"parameters":{"states":["push20","pop20","accept20"],"input_alphabet":["a20","b20"],"stack_alphabet":["Z20","A20"],"start_state":"push20","bottom_symbol":"Z20","final_states":["accept20"],"transitions":[["push20","a20","Z20","push20",["Z20","A20"]],["push20","a20","A20","push20",["A20","A20"]],["push20","b20","A20","pop20",[]],["pop20","b20","A20","pop20",[]],["push20",null,"Z20","accept20",["Z20"]],["pop20",null,"Z20","accept20",["Z20"]]],"input":[],"trace":[["push20",0,["Z20"]],["accept20",0,["Z20"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z20\",\"final_states\":[\"accept20\"],\"input\":[],\"input_alphabet\":[\"a20\",\"b20\"],\"stack_alphabet\":[\"A20\",\"Z20\"],\"start_state\":\"push20\",\"states\":[\"accept20\",\"pop20\",\"push20\"],\"trace\":[[\"push20\",0,[\"Z20\"]],[\"accept20\",0,[\"Z20\"]]],\"transitions\":[[\"pop20\",\"b20\",\"A20\",\"pop20\",[]],[\"pop20\",null,\"Z20\",\"accept20\",[\"Z20\"]],[\"push20\",\"a20\",\"A20\",\"push20\",[\"A20\",\"A20\"]],[\"push20\",\"a20\",\"Z20\",\"push20\",[\"Z20\",\"A20\"]],[\"push20\",\"b20\",\"A20\",\"pop20\",[]],[\"push20\",null,\"Z20\",\"accept20\",[\"Z20\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0047","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push21\",\"pop21\",\"accept21\"],\"input_alphabet\":[\"a21\",\"b21\"],\"stack_alphabet\":[\"Z21\",\"A21\"],\"start_state\":\"push21\",\"bottom_symbol\":\"Z21\",\"final_states\":[\"accept21\"],\"transitions\":[[\"push21\",\"a21\",\"Z21\",\"push21\",[\"Z21\",\"A21\"]],[\"push21\",\"a21\",\"A21\",\"push21\",[\"A21\",\"A21\"]],[\"push21\",\"b21\",\"A21\",\"pop21\",[]],[\"pop21\",\"b21\",\"A21\",\"pop21\",[]],[\"push21\",null,\"Z21\",\"accept21\",[\"Z21\"]],[\"pop21\",null,\"Z21\",\"accept21\",[\"Z21\"]]],\"input\":[\"a21\",\"b21\"],\"trace\":[[\"push21\",0,[\"Z21\"]],[\"push21\",1,[\"Z21\",\"A21\"]],[\"pop21\",2,[\"Z21\"]],[\"accept21\",2,[\"Z21\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a21, b21], [[push21, 0, [Z21]], [push21, 1, [Z21, A21]], [pop21, 2, [Z21]], [accept21, 2, [Z21]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a21, b21], [[push21, 0, [Z21]], [push21, 1, [Z21, A21]], [pop21, 2, [Z21]], [accept21, 2, [Z21]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107047,"parameters":{"states":["push21","pop21","accept21"],"input_alphabet":["a21","b21"],"stack_alphabet":["Z21","A21"],"start_state":"push21","bottom_symbol":"Z21","final_states":["accept21"],"transitions":[["push21","a21","Z21","push21",["Z21","A21"]],["push21","a21","A21","push21",["A21","A21"]],["push21","b21","A21","pop21",[]],["pop21","b21","A21","pop21",[]],["push21",null,"Z21","accept21",["Z21"]],["pop21",null,"Z21","accept21",["Z21"]]],"input":["a21","b21"],"trace":[["push21",0,["Z21"]],["push21",1,["Z21","A21"]],["pop21",2,["Z21"]],["accept21",2,["Z21"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z21\",\"final_states\":[\"accept21\"],\"input\":[\"a21\",\"b21\"],\"input_alphabet\":[\"a21\",\"b21\"],\"stack_alphabet\":[\"A21\",\"Z21\"],\"start_state\":\"push21\",\"states\":[\"accept21\",\"pop21\",\"push21\"],\"trace\":[[\"push21\",0,[\"Z21\"]],[\"push21\",1,[\"Z21\",\"A21\"]],[\"pop21\",2,[\"Z21\"]],[\"accept21\",2,[\"Z21\"]]],\"transitions\":[[\"pop21\",\"b21\",\"A21\",\"pop21\",[]],[\"pop21\",null,\"Z21\",\"accept21\",[\"Z21\"]],[\"push21\",\"a21\",\"A21\",\"push21\",[\"A21\",\"A21\"]],[\"push21\",\"a21\",\"Z21\",\"push21\",[\"Z21\",\"A21\"]],[\"push21\",\"b21\",\"A21\",\"pop21\",[]],[\"push21\",null,\"Z21\",\"accept21\",[\"Z21\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0048","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push22\",\"pop22\",\"accept22\"],\"input_alphabet\":[\"a22\",\"b22\"],\"stack_alphabet\":[\"Z22\",\"A22\"],\"start_state\":\"push22\",\"bottom_symbol\":\"Z22\",\"final_states\":[\"accept22\"],\"transitions\":[[\"push22\",\"a22\",\"Z22\",\"push22\",[\"Z22\",\"A22\"]],[\"push22\",\"a22\",\"A22\",\"push22\",[\"A22\",\"A22\"]],[\"push22\",\"b22\",\"A22\",\"pop22\",[]],[\"pop22\",\"b22\",\"A22\",\"pop22\",[]],[\"push22\",null,\"Z22\",\"accept22\",[\"Z22\"]],[\"pop22\",null,\"Z22\",\"accept22\",[\"Z22\"]]],\"input\":[\"a22\",\"a22\",\"b22\",\"b22\"],\"trace\":[[\"push22\",0,[\"Z22\"]],[\"push22\",1,[\"Z22\",\"A22\"]],[\"push22\",2,[\"Z22\",\"A22\",\"A22\"]],[\"pop22\",3,[\"Z22\",\"A22\"]],[\"pop22\",4,[\"Z22\"]],[\"accept22\",4,[\"Z22\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a22, a22, b22, b22], [[push22, 0, [Z22]], [push22, 1, [Z22, A22]], [push22, 2, [Z22, A22, A22]], [pop22, 3, [Z22, A22]], [pop22, 4, [Z22]], [accept22, 4, [Z22]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a22, a22, b22, b22], [[push22, 0, [Z22]], [push22, 1, [Z22, A22]], [push22, 2, [Z22, A22, A22]], [pop22, 3, [Z22, A22]], [pop22, 4, [Z22]], [accept22, 4, [Z22]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107048,"parameters":{"states":["push22","pop22","accept22"],"input_alphabet":["a22","b22"],"stack_alphabet":["Z22","A22"],"start_state":"push22","bottom_symbol":"Z22","final_states":["accept22"],"transitions":[["push22","a22","Z22","push22",["Z22","A22"]],["push22","a22","A22","push22",["A22","A22"]],["push22","b22","A22","pop22",[]],["pop22","b22","A22","pop22",[]],["push22",null,"Z22","accept22",["Z22"]],["pop22",null,"Z22","accept22",["Z22"]]],"input":["a22","a22","b22","b22"],"trace":[["push22",0,["Z22"]],["push22",1,["Z22","A22"]],["push22",2,["Z22","A22","A22"]],["pop22",3,["Z22","A22"]],["pop22",4,["Z22"]],["accept22",4,["Z22"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z22\",\"final_states\":[\"accept22\"],\"input\":[\"a22\",\"a22\",\"b22\",\"b22\"],\"input_alphabet\":[\"a22\",\"b22\"],\"stack_alphabet\":[\"A22\",\"Z22\"],\"start_state\":\"push22\",\"states\":[\"accept22\",\"pop22\",\"push22\"],\"trace\":[[\"push22\",0,[\"Z22\"]],[\"push22\",1,[\"Z22\",\"A22\"]],[\"push22\",2,[\"Z22\",\"A22\",\"A22\"]],[\"pop22\",3,[\"Z22\",\"A22\"]],[\"pop22\",4,[\"Z22\"]],[\"accept22\",4,[\"Z22\"]]],\"transitions\":[[\"pop22\",\"b22\",\"A22\",\"pop22\",[]],[\"pop22\",null,\"Z22\",\"accept22\",[\"Z22\"]],[\"push22\",\"a22\",\"A22\",\"push22\",[\"A22\",\"A22\"]],[\"push22\",\"a22\",\"Z22\",\"push22\",[\"Z22\",\"A22\"]],[\"push22\",\"b22\",\"A22\",\"pop22\",[]],[\"push22\",null,\"Z22\",\"accept22\",[\"Z22\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0049","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push23\",\"pop23\",\"accept23\"],\"input_alphabet\":[\"a23\",\"b23\"],\"stack_alphabet\":[\"Z23\",\"A23\"],\"start_state\":\"push23\",\"bottom_symbol\":\"Z23\",\"final_states\":[\"accept23\"],\"transitions\":[[\"push23\",\"a23\",\"Z23\",\"push23\",[\"Z23\",\"A23\"]],[\"push23\",\"a23\",\"A23\",\"push23\",[\"A23\",\"A23\"]],[\"push23\",\"b23\",\"A23\",\"pop23\",[]],[\"pop23\",\"b23\",\"A23\",\"pop23\",[]],[\"push23\",null,\"Z23\",\"accept23\",[\"Z23\"]],[\"pop23\",null,\"Z23\",\"accept23\",[\"Z23\"]]],\"input\":[\"a23\",\"a23\",\"a23\",\"b23\",\"b23\",\"b23\"],\"trace\":[[\"push23\",0,[\"Z23\"]],[\"push23\",1,[\"Z23\",\"A23\"]],[\"push23\",2,[\"Z23\",\"A23\",\"A23\"]],[\"push23\",3,[\"Z23\",\"A23\",\"A23\",\"A23\"]],[\"pop23\",4,[\"Z23\",\"A23\",\"A23\"]],[\"pop23\",5,[\"Z23\",\"A23\"]],[\"pop23\",6,[\"Z23\"]],[\"accept23\",6,[\"Z23\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a23, a23, a23, b23, b23, b23], [[push23, 0, [Z23]], [push23, 1, [Z23, A23]], [push23, 2, [Z23, A23, A23]], [push23, 3, [Z23, A23, A23, A23]], [pop23, 4, [Z23, A23, A23]], [pop23, 5, [Z23, A23]], [pop23, 6, [Z23]], [accept23, 6, [Z23]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([a23, a23, a23, b23, b23, b23], [[push23, 0, [Z23]], [push23, 1, [Z23, A23]], [push23, 2, [Z23, A23, A23]], [push23, 3, [Z23, A23, A23, A23]], [pop23, 4, [Z23, A23, A23]], [pop23, 5, [Z23, A23]], [pop23, 6, [Z23]], [accept23, 6, [Z23]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107049,"parameters":{"states":["push23","pop23","accept23"],"input_alphabet":["a23","b23"],"stack_alphabet":["Z23","A23"],"start_state":"push23","bottom_symbol":"Z23","final_states":["accept23"],"transitions":[["push23","a23","Z23","push23",["Z23","A23"]],["push23","a23","A23","push23",["A23","A23"]],["push23","b23","A23","pop23",[]],["pop23","b23","A23","pop23",[]],["push23",null,"Z23","accept23",["Z23"]],["pop23",null,"Z23","accept23",["Z23"]]],"input":["a23","a23","a23","b23","b23","b23"],"trace":[["push23",0,["Z23"]],["push23",1,["Z23","A23"]],["push23",2,["Z23","A23","A23"]],["push23",3,["Z23","A23","A23","A23"]],["pop23",4,["Z23","A23","A23"]],["pop23",5,["Z23","A23"]],["pop23",6,["Z23"]],["accept23",6,["Z23"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z23\",\"final_states\":[\"accept23\"],\"input\":[\"a23\",\"a23\",\"a23\",\"b23\",\"b23\",\"b23\"],\"input_alphabet\":[\"a23\",\"b23\"],\"stack_alphabet\":[\"A23\",\"Z23\"],\"start_state\":\"push23\",\"states\":[\"accept23\",\"pop23\",\"push23\"],\"trace\":[[\"push23\",0,[\"Z23\"]],[\"push23\",1,[\"Z23\",\"A23\"]],[\"push23\",2,[\"Z23\",\"A23\",\"A23\"]],[\"push23\",3,[\"Z23\",\"A23\",\"A23\",\"A23\"]],[\"pop23\",4,[\"Z23\",\"A23\",\"A23\"]],[\"pop23\",5,[\"Z23\",\"A23\"]],[\"pop23\",6,[\"Z23\"]],[\"accept23\",6,[\"Z23\"]]],\"transitions\":[[\"pop23\",\"b23\",\"A23\",\"pop23\",[]],[\"pop23\",null,\"Z23\",\"accept23\",[\"Z23\"]],[\"push23\",\"a23\",\"A23\",\"push23\",[\"A23\",\"A23\"]],[\"push23\",\"a23\",\"Z23\",\"push23\",[\"Z23\",\"A23\"]],[\"push23\",\"b23\",\"A23\",\"pop23\",[]],[\"push23\",null,\"Z23\",\"accept23\",[\"Z23\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0050","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={\"states\":[\"push24\",\"pop24\",\"accept24\"],\"input_alphabet\":[\"a24\",\"b24\"],\"stack_alphabet\":[\"Z24\",\"A24\"],\"start_state\":\"push24\",\"bottom_symbol\":\"Z24\",\"final_states\":[\"accept24\"],\"transitions\":[[\"push24\",\"a24\",\"Z24\",\"push24\",[\"Z24\",\"A24\"]],[\"push24\",\"a24\",\"A24\",\"push24\",[\"A24\",\"A24\"]],[\"push24\",\"b24\",\"A24\",\"pop24\",[]],[\"pop24\",\"b24\",\"A24\",\"pop24\",[]],[\"push24\",null,\"Z24\",\"accept24\",[\"Z24\"]],[\"pop24\",null,\"Z24\",\"accept24\",[\"Z24\"]]],\"input\":[],\"trace\":[[\"push24\",0,[\"Z24\"]],[\"accept24\",0,[\"Z24\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push24, 0, [Z24]], [accept24, 0, [Z24]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)","explanation_zh":"Wave6第四層核對=([], [[push24, 0, [Z24]], [accept24, 0, [Z24]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-trace-audit","seed":202611107050,"parameters":{"states":["push24","pop24","accept24"],"input_alphabet":["a24","b24"],"stack_alphabet":["Z24","A24"],"start_state":"push24","bottom_symbol":"Z24","final_states":["accept24"],"transitions":[["push24","a24","Z24","push24",["Z24","A24"]],["push24","a24","A24","push24",["A24","A24"]],["push24","b24","A24","pop24",[]],["pop24","b24","A24","pop24",[]],["push24",null,"Z24","accept24",["Z24"]],["pop24",null,"Z24","accept24",["Z24"]]],"input":[],"trace":[["push24",0,["Z24"]],["accept24",0,["Z24"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-trace-audit","semantic_template":"qf-mod41-pda-trace-audit/{\"bottom_symbol\":\"Z24\",\"final_states\":[\"accept24\"],\"input\":[],\"input_alphabet\":[\"a24\",\"b24\"],\"stack_alphabet\":[\"A24\",\"Z24\"],\"start_state\":\"push24\",\"states\":[\"accept24\",\"pop24\",\"push24\"],\"trace\":[[\"push24\",0,[\"Z24\"]],[\"accept24\",0,[\"Z24\"]]],\"transitions\":[[\"pop24\",\"b24\",\"A24\",\"pop24\",[]],[\"pop24\",null,\"Z24\",\"accept24\",[\"Z24\"]],[\"push24\",\"a24\",\"A24\",\"push24\",[\"A24\",\"A24\"]],[\"push24\",\"a24\",\"Z24\",\"push24\",[\"Z24\",\"A24\"]],[\"push24\",\"b24\",\"A24\",\"pop24\",[]],[\"push24\",null,\"Z24\",\"accept24\",[\"Z24\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0051","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push0\",\"pop0\",\"accept0\"],\"input_alphabet\":[\"a0\",\"b0\"],\"stack_alphabet\":[\"Z0\",\"A0\"],\"start_state\":\"push0\",\"bottom_symbol\":\"Z0\",\"final_states\":[\"accept0\"],\"transitions\":[[\"push0\",\"a0\",\"Z0\",\"push0\",[\"Z0\",\"A0\"]],[\"push0\",\"a0\",\"A0\",\"push0\",[\"A0\",\"A0\"]],[\"push0\",\"b0\",\"A0\",\"pop0\",[]],[\"pop0\",\"b0\",\"A0\",\"pop0\",[]],[\"push0\",null,\"Z0\",\"accept0\",[\"Z0\"]],[\"pop0\",null,\"Z0\",\"accept0\",[\"Z0\"]]],\"input\":[],\"trace\":[[\"push0\",0,[\"Z0\"]],[\"accept0\",0,[\"Z0\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push0, 0, [Z0]], [accept0, 0, [Z0]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([], [[push0, 0, [Z0]], [accept0, 0, [Z0]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107051,"parameters":{"states":["push0","pop0","accept0"],"input_alphabet":["a0","b0"],"stack_alphabet":["Z0","A0"],"start_state":"push0","bottom_symbol":"Z0","final_states":["accept0"],"transitions":[["push0","a0","Z0","push0",["Z0","A0"]],["push0","a0","A0","push0",["A0","A0"]],["push0","b0","A0","pop0",[]],["pop0","b0","A0","pop0",[]],["push0",null,"Z0","accept0",["Z0"]],["pop0",null,"Z0","accept0",["Z0"]]],"input":[],"trace":[["push0",0,["Z0"]],["accept0",0,["Z0"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z0\",\"final_states\":[\"accept0\"],\"input\":[],\"input_alphabet\":[\"a0\",\"b0\"],\"stack_alphabet\":[\"A0\",\"Z0\"],\"start_state\":\"push0\",\"states\":[\"accept0\",\"pop0\",\"push0\"],\"trace\":[[\"push0\",0,[\"Z0\"]],[\"accept0\",0,[\"Z0\"]]],\"transitions\":[[\"pop0\",\"b0\",\"A0\",\"pop0\",[]],[\"pop0\",null,\"Z0\",\"accept0\",[\"Z0\"]],[\"push0\",\"a0\",\"A0\",\"push0\",[\"A0\",\"A0\"]],[\"push0\",\"a0\",\"Z0\",\"push0\",[\"Z0\",\"A0\"]],[\"push0\",\"b0\",\"A0\",\"pop0\",[]],[\"push0\",null,\"Z0\",\"accept0\",[\"Z0\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0052","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push1\",\"pop1\",\"accept1\"],\"input_alphabet\":[\"a1\",\"b1\"],\"stack_alphabet\":[\"Z1\",\"A1\"],\"start_state\":\"push1\",\"bottom_symbol\":\"Z1\",\"final_states\":[\"accept1\"],\"transitions\":[[\"push1\",\"a1\",\"Z1\",\"push1\",[\"Z1\",\"A1\"]],[\"push1\",\"a1\",\"A1\",\"push1\",[\"A1\",\"A1\"]],[\"push1\",\"b1\",\"A1\",\"pop1\",[]],[\"pop1\",\"b1\",\"A1\",\"pop1\",[]],[\"push1\",null,\"Z1\",\"accept1\",[\"Z1\"]],[\"pop1\",null,\"Z1\",\"accept1\",[\"Z1\"]]],\"input\":[\"a1\",\"b1\"],\"trace\":[[\"push1\",0,[\"Z1\"]],[\"push1\",1,[\"Z1\",\"A1\"]],[\"pop1\",2,[\"Z1\"]],[\"accept1\",2,[\"Z1\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a1, b1], [[push1, 0, [Z1]], [push1, 1, [Z1, A1]], [pop1, 2, [Z1]], [accept1, 2, [Z1]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a1, b1], [[push1, 0, [Z1]], [push1, 1, [Z1, A1]], [pop1, 2, [Z1]], [accept1, 2, [Z1]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107052,"parameters":{"states":["push1","pop1","accept1"],"input_alphabet":["a1","b1"],"stack_alphabet":["Z1","A1"],"start_state":"push1","bottom_symbol":"Z1","final_states":["accept1"],"transitions":[["push1","a1","Z1","push1",["Z1","A1"]],["push1","a1","A1","push1",["A1","A1"]],["push1","b1","A1","pop1",[]],["pop1","b1","A1","pop1",[]],["push1",null,"Z1","accept1",["Z1"]],["pop1",null,"Z1","accept1",["Z1"]]],"input":["a1","b1"],"trace":[["push1",0,["Z1"]],["push1",1,["Z1","A1"]],["pop1",2,["Z1"]],["accept1",2,["Z1"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z1\",\"final_states\":[\"accept1\"],\"input\":[\"a1\",\"b1\"],\"input_alphabet\":[\"a1\",\"b1\"],\"stack_alphabet\":[\"A1\",\"Z1\"],\"start_state\":\"push1\",\"states\":[\"accept1\",\"pop1\",\"push1\"],\"trace\":[[\"push1\",0,[\"Z1\"]],[\"push1\",1,[\"Z1\",\"A1\"]],[\"pop1\",2,[\"Z1\"]],[\"accept1\",2,[\"Z1\"]]],\"transitions\":[[\"pop1\",\"b1\",\"A1\",\"pop1\",[]],[\"pop1\",null,\"Z1\",\"accept1\",[\"Z1\"]],[\"push1\",\"a1\",\"A1\",\"push1\",[\"A1\",\"A1\"]],[\"push1\",\"a1\",\"Z1\",\"push1\",[\"Z1\",\"A1\"]],[\"push1\",\"b1\",\"A1\",\"pop1\",[]],[\"push1\",null,\"Z1\",\"accept1\",[\"Z1\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0053","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push2\",\"pop2\",\"accept2\"],\"input_alphabet\":[\"a2\",\"b2\"],\"stack_alphabet\":[\"Z2\",\"A2\"],\"start_state\":\"push2\",\"bottom_symbol\":\"Z2\",\"final_states\":[\"accept2\"],\"transitions\":[[\"push2\",\"a2\",\"Z2\",\"push2\",[\"Z2\",\"A2\"]],[\"push2\",\"a2\",\"A2\",\"push2\",[\"A2\",\"A2\"]],[\"push2\",\"b2\",\"A2\",\"pop2\",[]],[\"pop2\",\"b2\",\"A2\",\"pop2\",[]],[\"push2\",null,\"Z2\",\"accept2\",[\"Z2\"]],[\"pop2\",null,\"Z2\",\"accept2\",[\"Z2\"]]],\"input\":[\"a2\",\"a2\",\"b2\",\"b2\"],\"trace\":[[\"push2\",0,[\"Z2\"]],[\"push2\",1,[\"Z2\",\"A2\"]],[\"push2\",2,[\"Z2\",\"A2\",\"A2\"]],[\"pop2\",3,[\"Z2\",\"A2\"]],[\"pop2\",4,[\"Z2\"]],[\"accept2\",4,[\"Z2\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a2, a2, b2, b2], [[push2, 0, [Z2]], [push2, 1, [Z2, A2]], [push2, 2, [Z2, A2, A2]], [pop2, 3, [Z2, A2]], [pop2, 4, [Z2]], [accept2, 4, [Z2]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a2, a2, b2, b2], [[push2, 0, [Z2]], [push2, 1, [Z2, A2]], [push2, 2, [Z2, A2, A2]], [pop2, 3, [Z2, A2]], [pop2, 4, [Z2]], [accept2, 4, [Z2]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107053,"parameters":{"states":["push2","pop2","accept2"],"input_alphabet":["a2","b2"],"stack_alphabet":["Z2","A2"],"start_state":"push2","bottom_symbol":"Z2","final_states":["accept2"],"transitions":[["push2","a2","Z2","push2",["Z2","A2"]],["push2","a2","A2","push2",["A2","A2"]],["push2","b2","A2","pop2",[]],["pop2","b2","A2","pop2",[]],["push2",null,"Z2","accept2",["Z2"]],["pop2",null,"Z2","accept2",["Z2"]]],"input":["a2","a2","b2","b2"],"trace":[["push2",0,["Z2"]],["push2",1,["Z2","A2"]],["push2",2,["Z2","A2","A2"]],["pop2",3,["Z2","A2"]],["pop2",4,["Z2"]],["accept2",4,["Z2"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z2\",\"final_states\":[\"accept2\"],\"input\":[\"a2\",\"a2\",\"b2\",\"b2\"],\"input_alphabet\":[\"a2\",\"b2\"],\"stack_alphabet\":[\"A2\",\"Z2\"],\"start_state\":\"push2\",\"states\":[\"accept2\",\"pop2\",\"push2\"],\"trace\":[[\"push2\",0,[\"Z2\"]],[\"push2\",1,[\"Z2\",\"A2\"]],[\"push2\",2,[\"Z2\",\"A2\",\"A2\"]],[\"pop2\",3,[\"Z2\",\"A2\"]],[\"pop2\",4,[\"Z2\"]],[\"accept2\",4,[\"Z2\"]]],\"transitions\":[[\"pop2\",\"b2\",\"A2\",\"pop2\",[]],[\"pop2\",null,\"Z2\",\"accept2\",[\"Z2\"]],[\"push2\",\"a2\",\"A2\",\"push2\",[\"A2\",\"A2\"]],[\"push2\",\"a2\",\"Z2\",\"push2\",[\"Z2\",\"A2\"]],[\"push2\",\"b2\",\"A2\",\"pop2\",[]],[\"push2\",null,\"Z2\",\"accept2\",[\"Z2\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0054","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push3\",\"pop3\",\"accept3\"],\"input_alphabet\":[\"a3\",\"b3\"],\"stack_alphabet\":[\"Z3\",\"A3\"],\"start_state\":\"push3\",\"bottom_symbol\":\"Z3\",\"final_states\":[\"accept3\"],\"transitions\":[[\"push3\",\"a3\",\"Z3\",\"push3\",[\"Z3\",\"A3\"]],[\"push3\",\"a3\",\"A3\",\"push3\",[\"A3\",\"A3\"]],[\"push3\",\"b3\",\"A3\",\"pop3\",[]],[\"pop3\",\"b3\",\"A3\",\"pop3\",[]],[\"push3\",null,\"Z3\",\"accept3\",[\"Z3\"]],[\"pop3\",null,\"Z3\",\"accept3\",[\"Z3\"]]],\"input\":[\"a3\",\"a3\",\"a3\",\"b3\",\"b3\",\"b3\"],\"trace\":[[\"push3\",0,[\"Z3\"]],[\"push3\",1,[\"Z3\",\"A3\"]],[\"push3\",2,[\"Z3\",\"A3\",\"A3\"]],[\"push3\",3,[\"Z3\",\"A3\",\"A3\",\"A3\"]],[\"pop3\",4,[\"Z3\",\"A3\",\"A3\"]],[\"pop3\",5,[\"Z3\",\"A3\"]],[\"pop3\",6,[\"Z3\"]],[\"accept3\",6,[\"Z3\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a3, a3, a3, b3, b3, b3], [[push3, 0, [Z3]], [push3, 1, [Z3, A3]], [push3, 2, [Z3, A3, A3]], [push3, 3, [Z3, A3, A3, A3]], [pop3, 4, [Z3, A3, A3]], [pop3, 5, [Z3, A3]], [pop3, 6, [Z3]], [accept3, 6, [Z3]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a3, a3, a3, b3, b3, b3], [[push3, 0, [Z3]], [push3, 1, [Z3, A3]], [push3, 2, [Z3, A3, A3]], [push3, 3, [Z3, A3, A3, A3]], [pop3, 4, [Z3, A3, A3]], [pop3, 5, [Z3, A3]], [pop3, 6, [Z3]], [accept3, 6, [Z3]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107054,"parameters":{"states":["push3","pop3","accept3"],"input_alphabet":["a3","b3"],"stack_alphabet":["Z3","A3"],"start_state":"push3","bottom_symbol":"Z3","final_states":["accept3"],"transitions":[["push3","a3","Z3","push3",["Z3","A3"]],["push3","a3","A3","push3",["A3","A3"]],["push3","b3","A3","pop3",[]],["pop3","b3","A3","pop3",[]],["push3",null,"Z3","accept3",["Z3"]],["pop3",null,"Z3","accept3",["Z3"]]],"input":["a3","a3","a3","b3","b3","b3"],"trace":[["push3",0,["Z3"]],["push3",1,["Z3","A3"]],["push3",2,["Z3","A3","A3"]],["push3",3,["Z3","A3","A3","A3"]],["pop3",4,["Z3","A3","A3"]],["pop3",5,["Z3","A3"]],["pop3",6,["Z3"]],["accept3",6,["Z3"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z3\",\"final_states\":[\"accept3\"],\"input\":[\"a3\",\"a3\",\"a3\",\"b3\",\"b3\",\"b3\"],\"input_alphabet\":[\"a3\",\"b3\"],\"stack_alphabet\":[\"A3\",\"Z3\"],\"start_state\":\"push3\",\"states\":[\"accept3\",\"pop3\",\"push3\"],\"trace\":[[\"push3\",0,[\"Z3\"]],[\"push3\",1,[\"Z3\",\"A3\"]],[\"push3\",2,[\"Z3\",\"A3\",\"A3\"]],[\"push3\",3,[\"Z3\",\"A3\",\"A3\",\"A3\"]],[\"pop3\",4,[\"Z3\",\"A3\",\"A3\"]],[\"pop3\",5,[\"Z3\",\"A3\"]],[\"pop3\",6,[\"Z3\"]],[\"accept3\",6,[\"Z3\"]]],\"transitions\":[[\"pop3\",\"b3\",\"A3\",\"pop3\",[]],[\"pop3\",null,\"Z3\",\"accept3\",[\"Z3\"]],[\"push3\",\"a3\",\"A3\",\"push3\",[\"A3\",\"A3\"]],[\"push3\",\"a3\",\"Z3\",\"push3\",[\"Z3\",\"A3\"]],[\"push3\",\"b3\",\"A3\",\"pop3\",[]],[\"push3\",null,\"Z3\",\"accept3\",[\"Z3\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0055","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push4\",\"pop4\",\"accept4\"],\"input_alphabet\":[\"a4\",\"b4\"],\"stack_alphabet\":[\"Z4\",\"A4\"],\"start_state\":\"push4\",\"bottom_symbol\":\"Z4\",\"final_states\":[\"accept4\"],\"transitions\":[[\"push4\",\"a4\",\"Z4\",\"push4\",[\"Z4\",\"A4\"]],[\"push4\",\"a4\",\"A4\",\"push4\",[\"A4\",\"A4\"]],[\"push4\",\"b4\",\"A4\",\"pop4\",[]],[\"pop4\",\"b4\",\"A4\",\"pop4\",[]],[\"push4\",null,\"Z4\",\"accept4\",[\"Z4\"]],[\"pop4\",null,\"Z4\",\"accept4\",[\"Z4\"]]],\"input\":[],\"trace\":[[\"push4\",0,[\"Z4\"]],[\"accept4\",0,[\"Z4\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push4, 0, [Z4]], [accept4, 0, [Z4]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([], [[push4, 0, [Z4]], [accept4, 0, [Z4]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107055,"parameters":{"states":["push4","pop4","accept4"],"input_alphabet":["a4","b4"],"stack_alphabet":["Z4","A4"],"start_state":"push4","bottom_symbol":"Z4","final_states":["accept4"],"transitions":[["push4","a4","Z4","push4",["Z4","A4"]],["push4","a4","A4","push4",["A4","A4"]],["push4","b4","A4","pop4",[]],["pop4","b4","A4","pop4",[]],["push4",null,"Z4","accept4",["Z4"]],["pop4",null,"Z4","accept4",["Z4"]]],"input":[],"trace":[["push4",0,["Z4"]],["accept4",0,["Z4"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z4\",\"final_states\":[\"accept4\"],\"input\":[],\"input_alphabet\":[\"a4\",\"b4\"],\"stack_alphabet\":[\"A4\",\"Z4\"],\"start_state\":\"push4\",\"states\":[\"accept4\",\"pop4\",\"push4\"],\"trace\":[[\"push4\",0,[\"Z4\"]],[\"accept4\",0,[\"Z4\"]]],\"transitions\":[[\"pop4\",\"b4\",\"A4\",\"pop4\",[]],[\"pop4\",null,\"Z4\",\"accept4\",[\"Z4\"]],[\"push4\",\"a4\",\"A4\",\"push4\",[\"A4\",\"A4\"]],[\"push4\",\"a4\",\"Z4\",\"push4\",[\"Z4\",\"A4\"]],[\"push4\",\"b4\",\"A4\",\"pop4\",[]],[\"push4\",null,\"Z4\",\"accept4\",[\"Z4\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0056","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push5\",\"pop5\",\"accept5\"],\"input_alphabet\":[\"a5\",\"b5\"],\"stack_alphabet\":[\"Z5\",\"A5\"],\"start_state\":\"push5\",\"bottom_symbol\":\"Z5\",\"final_states\":[\"accept5\"],\"transitions\":[[\"push5\",\"a5\",\"Z5\",\"push5\",[\"Z5\",\"A5\"]],[\"push5\",\"a5\",\"A5\",\"push5\",[\"A5\",\"A5\"]],[\"push5\",\"b5\",\"A5\",\"pop5\",[]],[\"pop5\",\"b5\",\"A5\",\"pop5\",[]],[\"push5\",null,\"Z5\",\"accept5\",[\"Z5\"]],[\"pop5\",null,\"Z5\",\"accept5\",[\"Z5\"]]],\"input\":[\"a5\",\"b5\"],\"trace\":[[\"push5\",0,[\"Z5\"]],[\"push5\",1,[\"Z5\",\"A5\"]],[\"pop5\",2,[\"Z5\"]],[\"accept5\",2,[\"Z5\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a5, b5], [[push5, 0, [Z5]], [push5, 1, [Z5, A5]], [pop5, 2, [Z5]], [accept5, 2, [Z5]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a5, b5], [[push5, 0, [Z5]], [push5, 1, [Z5, A5]], [pop5, 2, [Z5]], [accept5, 2, [Z5]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107056,"parameters":{"states":["push5","pop5","accept5"],"input_alphabet":["a5","b5"],"stack_alphabet":["Z5","A5"],"start_state":"push5","bottom_symbol":"Z5","final_states":["accept5"],"transitions":[["push5","a5","Z5","push5",["Z5","A5"]],["push5","a5","A5","push5",["A5","A5"]],["push5","b5","A5","pop5",[]],["pop5","b5","A5","pop5",[]],["push5",null,"Z5","accept5",["Z5"]],["pop5",null,"Z5","accept5",["Z5"]]],"input":["a5","b5"],"trace":[["push5",0,["Z5"]],["push5",1,["Z5","A5"]],["pop5",2,["Z5"]],["accept5",2,["Z5"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z5\",\"final_states\":[\"accept5\"],\"input\":[\"a5\",\"b5\"],\"input_alphabet\":[\"a5\",\"b5\"],\"stack_alphabet\":[\"A5\",\"Z5\"],\"start_state\":\"push5\",\"states\":[\"accept5\",\"pop5\",\"push5\"],\"trace\":[[\"push5\",0,[\"Z5\"]],[\"push5\",1,[\"Z5\",\"A5\"]],[\"pop5\",2,[\"Z5\"]],[\"accept5\",2,[\"Z5\"]]],\"transitions\":[[\"pop5\",\"b5\",\"A5\",\"pop5\",[]],[\"pop5\",null,\"Z5\",\"accept5\",[\"Z5\"]],[\"push5\",\"a5\",\"A5\",\"push5\",[\"A5\",\"A5\"]],[\"push5\",\"a5\",\"Z5\",\"push5\",[\"Z5\",\"A5\"]],[\"push5\",\"b5\",\"A5\",\"pop5\",[]],[\"push5\",null,\"Z5\",\"accept5\",[\"Z5\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0057","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push6\",\"pop6\",\"accept6\"],\"input_alphabet\":[\"a6\",\"b6\"],\"stack_alphabet\":[\"Z6\",\"A6\"],\"start_state\":\"push6\",\"bottom_symbol\":\"Z6\",\"final_states\":[\"accept6\"],\"transitions\":[[\"push6\",\"a6\",\"Z6\",\"push6\",[\"Z6\",\"A6\"]],[\"push6\",\"a6\",\"A6\",\"push6\",[\"A6\",\"A6\"]],[\"push6\",\"b6\",\"A6\",\"pop6\",[]],[\"pop6\",\"b6\",\"A6\",\"pop6\",[]],[\"push6\",null,\"Z6\",\"accept6\",[\"Z6\"]],[\"pop6\",null,\"Z6\",\"accept6\",[\"Z6\"]]],\"input\":[\"a6\",\"a6\",\"b6\",\"b6\"],\"trace\":[[\"push6\",0,[\"Z6\"]],[\"push6\",1,[\"Z6\",\"A6\"]],[\"push6\",2,[\"Z6\",\"A6\",\"A6\"]],[\"pop6\",3,[\"Z6\",\"A6\"]],[\"pop6\",4,[\"Z6\"]],[\"accept6\",4,[\"Z6\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a6, a6, b6, b6], [[push6, 0, [Z6]], [push6, 1, [Z6, A6]], [push6, 2, [Z6, A6, A6]], [pop6, 3, [Z6, A6]], [pop6, 4, [Z6]], [accept6, 4, [Z6]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a6, a6, b6, b6], [[push6, 0, [Z6]], [push6, 1, [Z6, A6]], [push6, 2, [Z6, A6, A6]], [pop6, 3, [Z6, A6]], [pop6, 4, [Z6]], [accept6, 4, [Z6]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107057,"parameters":{"states":["push6","pop6","accept6"],"input_alphabet":["a6","b6"],"stack_alphabet":["Z6","A6"],"start_state":"push6","bottom_symbol":"Z6","final_states":["accept6"],"transitions":[["push6","a6","Z6","push6",["Z6","A6"]],["push6","a6","A6","push6",["A6","A6"]],["push6","b6","A6","pop6",[]],["pop6","b6","A6","pop6",[]],["push6",null,"Z6","accept6",["Z6"]],["pop6",null,"Z6","accept6",["Z6"]]],"input":["a6","a6","b6","b6"],"trace":[["push6",0,["Z6"]],["push6",1,["Z6","A6"]],["push6",2,["Z6","A6","A6"]],["pop6",3,["Z6","A6"]],["pop6",4,["Z6"]],["accept6",4,["Z6"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z6\",\"final_states\":[\"accept6\"],\"input\":[\"a6\",\"a6\",\"b6\",\"b6\"],\"input_alphabet\":[\"a6\",\"b6\"],\"stack_alphabet\":[\"A6\",\"Z6\"],\"start_state\":\"push6\",\"states\":[\"accept6\",\"pop6\",\"push6\"],\"trace\":[[\"push6\",0,[\"Z6\"]],[\"push6\",1,[\"Z6\",\"A6\"]],[\"push6\",2,[\"Z6\",\"A6\",\"A6\"]],[\"pop6\",3,[\"Z6\",\"A6\"]],[\"pop6\",4,[\"Z6\"]],[\"accept6\",4,[\"Z6\"]]],\"transitions\":[[\"pop6\",\"b6\",\"A6\",\"pop6\",[]],[\"pop6\",null,\"Z6\",\"accept6\",[\"Z6\"]],[\"push6\",\"a6\",\"A6\",\"push6\",[\"A6\",\"A6\"]],[\"push6\",\"a6\",\"Z6\",\"push6\",[\"Z6\",\"A6\"]],[\"push6\",\"b6\",\"A6\",\"pop6\",[]],[\"push6\",null,\"Z6\",\"accept6\",[\"Z6\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0058","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push7\",\"pop7\",\"accept7\"],\"input_alphabet\":[\"a7\",\"b7\"],\"stack_alphabet\":[\"Z7\",\"A7\"],\"start_state\":\"push7\",\"bottom_symbol\":\"Z7\",\"final_states\":[\"accept7\"],\"transitions\":[[\"push7\",\"a7\",\"Z7\",\"push7\",[\"Z7\",\"A7\"]],[\"push7\",\"a7\",\"A7\",\"push7\",[\"A7\",\"A7\"]],[\"push7\",\"b7\",\"A7\",\"pop7\",[]],[\"pop7\",\"b7\",\"A7\",\"pop7\",[]],[\"push7\",null,\"Z7\",\"accept7\",[\"Z7\"]],[\"pop7\",null,\"Z7\",\"accept7\",[\"Z7\"]]],\"input\":[\"a7\",\"a7\",\"a7\",\"b7\",\"b7\",\"b7\"],\"trace\":[[\"push7\",0,[\"Z7\"]],[\"push7\",1,[\"Z7\",\"A7\"]],[\"push7\",2,[\"Z7\",\"A7\",\"A7\"]],[\"push7\",3,[\"Z7\",\"A7\",\"A7\",\"A7\"]],[\"pop7\",4,[\"Z7\",\"A7\",\"A7\"]],[\"pop7\",5,[\"Z7\",\"A7\"]],[\"pop7\",6,[\"Z7\"]],[\"accept7\",6,[\"Z7\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a7, a7, a7, b7, b7, b7], [[push7, 0, [Z7]], [push7, 1, [Z7, A7]], [push7, 2, [Z7, A7, A7]], [push7, 3, [Z7, A7, A7, A7]], [pop7, 4, [Z7, A7, A7]], [pop7, 5, [Z7, A7]], [pop7, 6, [Z7]], [accept7, 6, [Z7]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a7, a7, a7, b7, b7, b7], [[push7, 0, [Z7]], [push7, 1, [Z7, A7]], [push7, 2, [Z7, A7, A7]], [push7, 3, [Z7, A7, A7, A7]], [pop7, 4, [Z7, A7, A7]], [pop7, 5, [Z7, A7]], [pop7, 6, [Z7]], [accept7, 6, [Z7]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107058,"parameters":{"states":["push7","pop7","accept7"],"input_alphabet":["a7","b7"],"stack_alphabet":["Z7","A7"],"start_state":"push7","bottom_symbol":"Z7","final_states":["accept7"],"transitions":[["push7","a7","Z7","push7",["Z7","A7"]],["push7","a7","A7","push7",["A7","A7"]],["push7","b7","A7","pop7",[]],["pop7","b7","A7","pop7",[]],["push7",null,"Z7","accept7",["Z7"]],["pop7",null,"Z7","accept7",["Z7"]]],"input":["a7","a7","a7","b7","b7","b7"],"trace":[["push7",0,["Z7"]],["push7",1,["Z7","A7"]],["push7",2,["Z7","A7","A7"]],["push7",3,["Z7","A7","A7","A7"]],["pop7",4,["Z7","A7","A7"]],["pop7",5,["Z7","A7"]],["pop7",6,["Z7"]],["accept7",6,["Z7"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z7\",\"final_states\":[\"accept7\"],\"input\":[\"a7\",\"a7\",\"a7\",\"b7\",\"b7\",\"b7\"],\"input_alphabet\":[\"a7\",\"b7\"],\"stack_alphabet\":[\"A7\",\"Z7\"],\"start_state\":\"push7\",\"states\":[\"accept7\",\"pop7\",\"push7\"],\"trace\":[[\"push7\",0,[\"Z7\"]],[\"push7\",1,[\"Z7\",\"A7\"]],[\"push7\",2,[\"Z7\",\"A7\",\"A7\"]],[\"push7\",3,[\"Z7\",\"A7\",\"A7\",\"A7\"]],[\"pop7\",4,[\"Z7\",\"A7\",\"A7\"]],[\"pop7\",5,[\"Z7\",\"A7\"]],[\"pop7\",6,[\"Z7\"]],[\"accept7\",6,[\"Z7\"]]],\"transitions\":[[\"pop7\",\"b7\",\"A7\",\"pop7\",[]],[\"pop7\",null,\"Z7\",\"accept7\",[\"Z7\"]],[\"push7\",\"a7\",\"A7\",\"push7\",[\"A7\",\"A7\"]],[\"push7\",\"a7\",\"Z7\",\"push7\",[\"Z7\",\"A7\"]],[\"push7\",\"b7\",\"A7\",\"pop7\",[]],[\"push7\",null,\"Z7\",\"accept7\",[\"Z7\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0059","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push8\",\"pop8\",\"accept8\"],\"input_alphabet\":[\"a8\",\"b8\"],\"stack_alphabet\":[\"Z8\",\"A8\"],\"start_state\":\"push8\",\"bottom_symbol\":\"Z8\",\"final_states\":[\"accept8\"],\"transitions\":[[\"push8\",\"a8\",\"Z8\",\"push8\",[\"Z8\",\"A8\"]],[\"push8\",\"a8\",\"A8\",\"push8\",[\"A8\",\"A8\"]],[\"push8\",\"b8\",\"A8\",\"pop8\",[]],[\"pop8\",\"b8\",\"A8\",\"pop8\",[]],[\"push8\",null,\"Z8\",\"accept8\",[\"Z8\"]],[\"pop8\",null,\"Z8\",\"accept8\",[\"Z8\"]]],\"input\":[],\"trace\":[[\"push8\",0,[\"Z8\"]],[\"accept8\",0,[\"Z8\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push8, 0, [Z8]], [accept8, 0, [Z8]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([], [[push8, 0, [Z8]], [accept8, 0, [Z8]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107059,"parameters":{"states":["push8","pop8","accept8"],"input_alphabet":["a8","b8"],"stack_alphabet":["Z8","A8"],"start_state":"push8","bottom_symbol":"Z8","final_states":["accept8"],"transitions":[["push8","a8","Z8","push8",["Z8","A8"]],["push8","a8","A8","push8",["A8","A8"]],["push8","b8","A8","pop8",[]],["pop8","b8","A8","pop8",[]],["push8",null,"Z8","accept8",["Z8"]],["pop8",null,"Z8","accept8",["Z8"]]],"input":[],"trace":[["push8",0,["Z8"]],["accept8",0,["Z8"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z8\",\"final_states\":[\"accept8\"],\"input\":[],\"input_alphabet\":[\"a8\",\"b8\"],\"stack_alphabet\":[\"A8\",\"Z8\"],\"start_state\":\"push8\",\"states\":[\"accept8\",\"pop8\",\"push8\"],\"trace\":[[\"push8\",0,[\"Z8\"]],[\"accept8\",0,[\"Z8\"]]],\"transitions\":[[\"pop8\",\"b8\",\"A8\",\"pop8\",[]],[\"pop8\",null,\"Z8\",\"accept8\",[\"Z8\"]],[\"push8\",\"a8\",\"A8\",\"push8\",[\"A8\",\"A8\"]],[\"push8\",\"a8\",\"Z8\",\"push8\",[\"Z8\",\"A8\"]],[\"push8\",\"b8\",\"A8\",\"pop8\",[]],[\"push8\",null,\"Z8\",\"accept8\",[\"Z8\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0060","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push9\",\"pop9\",\"accept9\"],\"input_alphabet\":[\"a9\",\"b9\"],\"stack_alphabet\":[\"Z9\",\"A9\"],\"start_state\":\"push9\",\"bottom_symbol\":\"Z9\",\"final_states\":[\"accept9\"],\"transitions\":[[\"push9\",\"a9\",\"Z9\",\"push9\",[\"Z9\",\"A9\"]],[\"push9\",\"a9\",\"A9\",\"push9\",[\"A9\",\"A9\"]],[\"push9\",\"b9\",\"A9\",\"pop9\",[]],[\"pop9\",\"b9\",\"A9\",\"pop9\",[]],[\"push9\",null,\"Z9\",\"accept9\",[\"Z9\"]],[\"pop9\",null,\"Z9\",\"accept9\",[\"Z9\"]]],\"input\":[\"a9\",\"b9\"],\"trace\":[[\"push9\",0,[\"Z9\"]],[\"push9\",1,[\"Z9\",\"A9\"]],[\"pop9\",2,[\"Z9\"]],[\"accept9\",2,[\"Z9\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a9, b9], [[push9, 0, [Z9]], [push9, 1, [Z9, A9]], [pop9, 2, [Z9]], [accept9, 2, [Z9]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a9, b9], [[push9, 0, [Z9]], [push9, 1, [Z9, A9]], [pop9, 2, [Z9]], [accept9, 2, [Z9]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107060,"parameters":{"states":["push9","pop9","accept9"],"input_alphabet":["a9","b9"],"stack_alphabet":["Z9","A9"],"start_state":"push9","bottom_symbol":"Z9","final_states":["accept9"],"transitions":[["push9","a9","Z9","push9",["Z9","A9"]],["push9","a9","A9","push9",["A9","A9"]],["push9","b9","A9","pop9",[]],["pop9","b9","A9","pop9",[]],["push9",null,"Z9","accept9",["Z9"]],["pop9",null,"Z9","accept9",["Z9"]]],"input":["a9","b9"],"trace":[["push9",0,["Z9"]],["push9",1,["Z9","A9"]],["pop9",2,["Z9"]],["accept9",2,["Z9"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z9\",\"final_states\":[\"accept9\"],\"input\":[\"a9\",\"b9\"],\"input_alphabet\":[\"a9\",\"b9\"],\"stack_alphabet\":[\"A9\",\"Z9\"],\"start_state\":\"push9\",\"states\":[\"accept9\",\"pop9\",\"push9\"],\"trace\":[[\"push9\",0,[\"Z9\"]],[\"push9\",1,[\"Z9\",\"A9\"]],[\"pop9\",2,[\"Z9\"]],[\"accept9\",2,[\"Z9\"]]],\"transitions\":[[\"pop9\",\"b9\",\"A9\",\"pop9\",[]],[\"pop9\",null,\"Z9\",\"accept9\",[\"Z9\"]],[\"push9\",\"a9\",\"A9\",\"push9\",[\"A9\",\"A9\"]],[\"push9\",\"a9\",\"Z9\",\"push9\",[\"Z9\",\"A9\"]],[\"push9\",\"b9\",\"A9\",\"pop9\",[]],[\"push9\",null,\"Z9\",\"accept9\",[\"Z9\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0061","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push10\",\"pop10\",\"accept10\"],\"input_alphabet\":[\"a10\",\"b10\"],\"stack_alphabet\":[\"Z10\",\"A10\"],\"start_state\":\"push10\",\"bottom_symbol\":\"Z10\",\"final_states\":[\"accept10\"],\"transitions\":[[\"push10\",\"a10\",\"Z10\",\"push10\",[\"Z10\",\"A10\"]],[\"push10\",\"a10\",\"A10\",\"push10\",[\"A10\",\"A10\"]],[\"push10\",\"b10\",\"A10\",\"pop10\",[]],[\"pop10\",\"b10\",\"A10\",\"pop10\",[]],[\"push10\",null,\"Z10\",\"accept10\",[\"Z10\"]],[\"pop10\",null,\"Z10\",\"accept10\",[\"Z10\"]]],\"input\":[\"a10\",\"a10\",\"b10\",\"b10\"],\"trace\":[[\"push10\",0,[\"Z10\"]],[\"push10\",1,[\"Z10\",\"A10\"]],[\"push10\",2,[\"Z10\",\"A10\",\"A10\"]],[\"pop10\",3,[\"Z10\",\"A10\"]],[\"pop10\",4,[\"Z10\"]],[\"accept10\",4,[\"Z10\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a10, a10, b10, b10], [[push10, 0, [Z10]], [push10, 1, [Z10, A10]], [push10, 2, [Z10, A10, A10]], [pop10, 3, [Z10, A10]], [pop10, 4, [Z10]], [accept10, 4, [Z10]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a10, a10, b10, b10], [[push10, 0, [Z10]], [push10, 1, [Z10, A10]], [push10, 2, [Z10, A10, A10]], [pop10, 3, [Z10, A10]], [pop10, 4, [Z10]], [accept10, 4, [Z10]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107061,"parameters":{"states":["push10","pop10","accept10"],"input_alphabet":["a10","b10"],"stack_alphabet":["Z10","A10"],"start_state":"push10","bottom_symbol":"Z10","final_states":["accept10"],"transitions":[["push10","a10","Z10","push10",["Z10","A10"]],["push10","a10","A10","push10",["A10","A10"]],["push10","b10","A10","pop10",[]],["pop10","b10","A10","pop10",[]],["push10",null,"Z10","accept10",["Z10"]],["pop10",null,"Z10","accept10",["Z10"]]],"input":["a10","a10","b10","b10"],"trace":[["push10",0,["Z10"]],["push10",1,["Z10","A10"]],["push10",2,["Z10","A10","A10"]],["pop10",3,["Z10","A10"]],["pop10",4,["Z10"]],["accept10",4,["Z10"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z10\",\"final_states\":[\"accept10\"],\"input\":[\"a10\",\"a10\",\"b10\",\"b10\"],\"input_alphabet\":[\"a10\",\"b10\"],\"stack_alphabet\":[\"A10\",\"Z10\"],\"start_state\":\"push10\",\"states\":[\"accept10\",\"pop10\",\"push10\"],\"trace\":[[\"push10\",0,[\"Z10\"]],[\"push10\",1,[\"Z10\",\"A10\"]],[\"push10\",2,[\"Z10\",\"A10\",\"A10\"]],[\"pop10\",3,[\"Z10\",\"A10\"]],[\"pop10\",4,[\"Z10\"]],[\"accept10\",4,[\"Z10\"]]],\"transitions\":[[\"pop10\",\"b10\",\"A10\",\"pop10\",[]],[\"pop10\",null,\"Z10\",\"accept10\",[\"Z10\"]],[\"push10\",\"a10\",\"A10\",\"push10\",[\"A10\",\"A10\"]],[\"push10\",\"a10\",\"Z10\",\"push10\",[\"Z10\",\"A10\"]],[\"push10\",\"b10\",\"A10\",\"pop10\",[]],[\"push10\",null,\"Z10\",\"accept10\",[\"Z10\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0062","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push11\",\"pop11\",\"accept11\"],\"input_alphabet\":[\"a11\",\"b11\"],\"stack_alphabet\":[\"Z11\",\"A11\"],\"start_state\":\"push11\",\"bottom_symbol\":\"Z11\",\"final_states\":[\"accept11\"],\"transitions\":[[\"push11\",\"a11\",\"Z11\",\"push11\",[\"Z11\",\"A11\"]],[\"push11\",\"a11\",\"A11\",\"push11\",[\"A11\",\"A11\"]],[\"push11\",\"b11\",\"A11\",\"pop11\",[]],[\"pop11\",\"b11\",\"A11\",\"pop11\",[]],[\"push11\",null,\"Z11\",\"accept11\",[\"Z11\"]],[\"pop11\",null,\"Z11\",\"accept11\",[\"Z11\"]]],\"input\":[\"a11\",\"a11\",\"a11\",\"b11\",\"b11\",\"b11\"],\"trace\":[[\"push11\",0,[\"Z11\"]],[\"push11\",1,[\"Z11\",\"A11\"]],[\"push11\",2,[\"Z11\",\"A11\",\"A11\"]],[\"push11\",3,[\"Z11\",\"A11\",\"A11\",\"A11\"]],[\"pop11\",4,[\"Z11\",\"A11\",\"A11\"]],[\"pop11\",5,[\"Z11\",\"A11\"]],[\"pop11\",6,[\"Z11\"]],[\"accept11\",6,[\"Z11\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a11, a11, a11, b11, b11, b11], [[push11, 0, [Z11]], [push11, 1, [Z11, A11]], [push11, 2, [Z11, A11, A11]], [push11, 3, [Z11, A11, A11, A11]], [pop11, 4, [Z11, A11, A11]], [pop11, 5, [Z11, A11]], [pop11, 6, [Z11]], [accept11, 6, [Z11]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a11, a11, a11, b11, b11, b11], [[push11, 0, [Z11]], [push11, 1, [Z11, A11]], [push11, 2, [Z11, A11, A11]], [push11, 3, [Z11, A11, A11, A11]], [pop11, 4, [Z11, A11, A11]], [pop11, 5, [Z11, A11]], [pop11, 6, [Z11]], [accept11, 6, [Z11]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107062,"parameters":{"states":["push11","pop11","accept11"],"input_alphabet":["a11","b11"],"stack_alphabet":["Z11","A11"],"start_state":"push11","bottom_symbol":"Z11","final_states":["accept11"],"transitions":[["push11","a11","Z11","push11",["Z11","A11"]],["push11","a11","A11","push11",["A11","A11"]],["push11","b11","A11","pop11",[]],["pop11","b11","A11","pop11",[]],["push11",null,"Z11","accept11",["Z11"]],["pop11",null,"Z11","accept11",["Z11"]]],"input":["a11","a11","a11","b11","b11","b11"],"trace":[["push11",0,["Z11"]],["push11",1,["Z11","A11"]],["push11",2,["Z11","A11","A11"]],["push11",3,["Z11","A11","A11","A11"]],["pop11",4,["Z11","A11","A11"]],["pop11",5,["Z11","A11"]],["pop11",6,["Z11"]],["accept11",6,["Z11"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z11\",\"final_states\":[\"accept11\"],\"input\":[\"a11\",\"a11\",\"a11\",\"b11\",\"b11\",\"b11\"],\"input_alphabet\":[\"a11\",\"b11\"],\"stack_alphabet\":[\"A11\",\"Z11\"],\"start_state\":\"push11\",\"states\":[\"accept11\",\"pop11\",\"push11\"],\"trace\":[[\"push11\",0,[\"Z11\"]],[\"push11\",1,[\"Z11\",\"A11\"]],[\"push11\",2,[\"Z11\",\"A11\",\"A11\"]],[\"push11\",3,[\"Z11\",\"A11\",\"A11\",\"A11\"]],[\"pop11\",4,[\"Z11\",\"A11\",\"A11\"]],[\"pop11\",5,[\"Z11\",\"A11\"]],[\"pop11\",6,[\"Z11\"]],[\"accept11\",6,[\"Z11\"]]],\"transitions\":[[\"pop11\",\"b11\",\"A11\",\"pop11\",[]],[\"pop11\",null,\"Z11\",\"accept11\",[\"Z11\"]],[\"push11\",\"a11\",\"A11\",\"push11\",[\"A11\",\"A11\"]],[\"push11\",\"a11\",\"Z11\",\"push11\",[\"Z11\",\"A11\"]],[\"push11\",\"b11\",\"A11\",\"pop11\",[]],[\"push11\",null,\"Z11\",\"accept11\",[\"Z11\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0063","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push12\",\"pop12\",\"accept12\"],\"input_alphabet\":[\"a12\",\"b12\"],\"stack_alphabet\":[\"Z12\",\"A12\"],\"start_state\":\"push12\",\"bottom_symbol\":\"Z12\",\"final_states\":[\"accept12\"],\"transitions\":[[\"push12\",\"a12\",\"Z12\",\"push12\",[\"Z12\",\"A12\"]],[\"push12\",\"a12\",\"A12\",\"push12\",[\"A12\",\"A12\"]],[\"push12\",\"b12\",\"A12\",\"pop12\",[]],[\"pop12\",\"b12\",\"A12\",\"pop12\",[]],[\"push12\",null,\"Z12\",\"accept12\",[\"Z12\"]],[\"pop12\",null,\"Z12\",\"accept12\",[\"Z12\"]]],\"input\":[],\"trace\":[[\"push12\",0,[\"Z12\"]],[\"accept12\",0,[\"Z12\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push12, 0, [Z12]], [accept12, 0, [Z12]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([], [[push12, 0, [Z12]], [accept12, 0, [Z12]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107063,"parameters":{"states":["push12","pop12","accept12"],"input_alphabet":["a12","b12"],"stack_alphabet":["Z12","A12"],"start_state":"push12","bottom_symbol":"Z12","final_states":["accept12"],"transitions":[["push12","a12","Z12","push12",["Z12","A12"]],["push12","a12","A12","push12",["A12","A12"]],["push12","b12","A12","pop12",[]],["pop12","b12","A12","pop12",[]],["push12",null,"Z12","accept12",["Z12"]],["pop12",null,"Z12","accept12",["Z12"]]],"input":[],"trace":[["push12",0,["Z12"]],["accept12",0,["Z12"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z12\",\"final_states\":[\"accept12\"],\"input\":[],\"input_alphabet\":[\"a12\",\"b12\"],\"stack_alphabet\":[\"A12\",\"Z12\"],\"start_state\":\"push12\",\"states\":[\"accept12\",\"pop12\",\"push12\"],\"trace\":[[\"push12\",0,[\"Z12\"]],[\"accept12\",0,[\"Z12\"]]],\"transitions\":[[\"pop12\",\"b12\",\"A12\",\"pop12\",[]],[\"pop12\",null,\"Z12\",\"accept12\",[\"Z12\"]],[\"push12\",\"a12\",\"A12\",\"push12\",[\"A12\",\"A12\"]],[\"push12\",\"a12\",\"Z12\",\"push12\",[\"Z12\",\"A12\"]],[\"push12\",\"b12\",\"A12\",\"pop12\",[]],[\"push12\",null,\"Z12\",\"accept12\",[\"Z12\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0064","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push13\",\"pop13\",\"accept13\"],\"input_alphabet\":[\"a13\",\"b13\"],\"stack_alphabet\":[\"Z13\",\"A13\"],\"start_state\":\"push13\",\"bottom_symbol\":\"Z13\",\"final_states\":[\"accept13\"],\"transitions\":[[\"push13\",\"a13\",\"Z13\",\"push13\",[\"Z13\",\"A13\"]],[\"push13\",\"a13\",\"A13\",\"push13\",[\"A13\",\"A13\"]],[\"push13\",\"b13\",\"A13\",\"pop13\",[]],[\"pop13\",\"b13\",\"A13\",\"pop13\",[]],[\"push13\",null,\"Z13\",\"accept13\",[\"Z13\"]],[\"pop13\",null,\"Z13\",\"accept13\",[\"Z13\"]]],\"input\":[\"a13\",\"b13\"],\"trace\":[[\"push13\",0,[\"Z13\"]],[\"push13\",1,[\"Z13\",\"A13\"]],[\"pop13\",2,[\"Z13\"]],[\"accept13\",2,[\"Z13\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a13, b13], [[push13, 0, [Z13]], [push13, 1, [Z13, A13]], [pop13, 2, [Z13]], [accept13, 2, [Z13]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a13, b13], [[push13, 0, [Z13]], [push13, 1, [Z13, A13]], [pop13, 2, [Z13]], [accept13, 2, [Z13]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107064,"parameters":{"states":["push13","pop13","accept13"],"input_alphabet":["a13","b13"],"stack_alphabet":["Z13","A13"],"start_state":"push13","bottom_symbol":"Z13","final_states":["accept13"],"transitions":[["push13","a13","Z13","push13",["Z13","A13"]],["push13","a13","A13","push13",["A13","A13"]],["push13","b13","A13","pop13",[]],["pop13","b13","A13","pop13",[]],["push13",null,"Z13","accept13",["Z13"]],["pop13",null,"Z13","accept13",["Z13"]]],"input":["a13","b13"],"trace":[["push13",0,["Z13"]],["push13",1,["Z13","A13"]],["pop13",2,["Z13"]],["accept13",2,["Z13"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z13\",\"final_states\":[\"accept13\"],\"input\":[\"a13\",\"b13\"],\"input_alphabet\":[\"a13\",\"b13\"],\"stack_alphabet\":[\"A13\",\"Z13\"],\"start_state\":\"push13\",\"states\":[\"accept13\",\"pop13\",\"push13\"],\"trace\":[[\"push13\",0,[\"Z13\"]],[\"push13\",1,[\"Z13\",\"A13\"]],[\"pop13\",2,[\"Z13\"]],[\"accept13\",2,[\"Z13\"]]],\"transitions\":[[\"pop13\",\"b13\",\"A13\",\"pop13\",[]],[\"pop13\",null,\"Z13\",\"accept13\",[\"Z13\"]],[\"push13\",\"a13\",\"A13\",\"push13\",[\"A13\",\"A13\"]],[\"push13\",\"a13\",\"Z13\",\"push13\",[\"Z13\",\"A13\"]],[\"push13\",\"b13\",\"A13\",\"pop13\",[]],[\"push13\",null,\"Z13\",\"accept13\",[\"Z13\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0065","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push14\",\"pop14\",\"accept14\"],\"input_alphabet\":[\"a14\",\"b14\"],\"stack_alphabet\":[\"Z14\",\"A14\"],\"start_state\":\"push14\",\"bottom_symbol\":\"Z14\",\"final_states\":[\"accept14\"],\"transitions\":[[\"push14\",\"a14\",\"Z14\",\"push14\",[\"Z14\",\"A14\"]],[\"push14\",\"a14\",\"A14\",\"push14\",[\"A14\",\"A14\"]],[\"push14\",\"b14\",\"A14\",\"pop14\",[]],[\"pop14\",\"b14\",\"A14\",\"pop14\",[]],[\"push14\",null,\"Z14\",\"accept14\",[\"Z14\"]],[\"pop14\",null,\"Z14\",\"accept14\",[\"Z14\"]]],\"input\":[\"a14\",\"a14\",\"b14\",\"b14\"],\"trace\":[[\"push14\",0,[\"Z14\"]],[\"push14\",1,[\"Z14\",\"A14\"]],[\"push14\",2,[\"Z14\",\"A14\",\"A14\"]],[\"pop14\",3,[\"Z14\",\"A14\"]],[\"pop14\",4,[\"Z14\"]],[\"accept14\",4,[\"Z14\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a14, a14, b14, b14], [[push14, 0, [Z14]], [push14, 1, [Z14, A14]], [push14, 2, [Z14, A14, A14]], [pop14, 3, [Z14, A14]], [pop14, 4, [Z14]], [accept14, 4, [Z14]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a14, a14, b14, b14], [[push14, 0, [Z14]], [push14, 1, [Z14, A14]], [push14, 2, [Z14, A14, A14]], [pop14, 3, [Z14, A14]], [pop14, 4, [Z14]], [accept14, 4, [Z14]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107065,"parameters":{"states":["push14","pop14","accept14"],"input_alphabet":["a14","b14"],"stack_alphabet":["Z14","A14"],"start_state":"push14","bottom_symbol":"Z14","final_states":["accept14"],"transitions":[["push14","a14","Z14","push14",["Z14","A14"]],["push14","a14","A14","push14",["A14","A14"]],["push14","b14","A14","pop14",[]],["pop14","b14","A14","pop14",[]],["push14",null,"Z14","accept14",["Z14"]],["pop14",null,"Z14","accept14",["Z14"]]],"input":["a14","a14","b14","b14"],"trace":[["push14",0,["Z14"]],["push14",1,["Z14","A14"]],["push14",2,["Z14","A14","A14"]],["pop14",3,["Z14","A14"]],["pop14",4,["Z14"]],["accept14",4,["Z14"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z14\",\"final_states\":[\"accept14\"],\"input\":[\"a14\",\"a14\",\"b14\",\"b14\"],\"input_alphabet\":[\"a14\",\"b14\"],\"stack_alphabet\":[\"A14\",\"Z14\"],\"start_state\":\"push14\",\"states\":[\"accept14\",\"pop14\",\"push14\"],\"trace\":[[\"push14\",0,[\"Z14\"]],[\"push14\",1,[\"Z14\",\"A14\"]],[\"push14\",2,[\"Z14\",\"A14\",\"A14\"]],[\"pop14\",3,[\"Z14\",\"A14\"]],[\"pop14\",4,[\"Z14\"]],[\"accept14\",4,[\"Z14\"]]],\"transitions\":[[\"pop14\",\"b14\",\"A14\",\"pop14\",[]],[\"pop14\",null,\"Z14\",\"accept14\",[\"Z14\"]],[\"push14\",\"a14\",\"A14\",\"push14\",[\"A14\",\"A14\"]],[\"push14\",\"a14\",\"Z14\",\"push14\",[\"Z14\",\"A14\"]],[\"push14\",\"b14\",\"A14\",\"pop14\",[]],[\"push14\",null,\"Z14\",\"accept14\",[\"Z14\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0066","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push15\",\"pop15\",\"accept15\"],\"input_alphabet\":[\"a15\",\"b15\"],\"stack_alphabet\":[\"Z15\",\"A15\"],\"start_state\":\"push15\",\"bottom_symbol\":\"Z15\",\"final_states\":[\"accept15\"],\"transitions\":[[\"push15\",\"a15\",\"Z15\",\"push15\",[\"Z15\",\"A15\"]],[\"push15\",\"a15\",\"A15\",\"push15\",[\"A15\",\"A15\"]],[\"push15\",\"b15\",\"A15\",\"pop15\",[]],[\"pop15\",\"b15\",\"A15\",\"pop15\",[]],[\"push15\",null,\"Z15\",\"accept15\",[\"Z15\"]],[\"pop15\",null,\"Z15\",\"accept15\",[\"Z15\"]]],\"input\":[\"a15\",\"a15\",\"a15\",\"b15\",\"b15\",\"b15\"],\"trace\":[[\"push15\",0,[\"Z15\"]],[\"push15\",1,[\"Z15\",\"A15\"]],[\"push15\",2,[\"Z15\",\"A15\",\"A15\"]],[\"push15\",3,[\"Z15\",\"A15\",\"A15\",\"A15\"]],[\"pop15\",4,[\"Z15\",\"A15\",\"A15\"]],[\"pop15\",5,[\"Z15\",\"A15\"]],[\"pop15\",6,[\"Z15\"]],[\"accept15\",6,[\"Z15\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a15, a15, a15, b15, b15, b15], [[push15, 0, [Z15]], [push15, 1, [Z15, A15]], [push15, 2, [Z15, A15, A15]], [push15, 3, [Z15, A15, A15, A15]], [pop15, 4, [Z15, A15, A15]], [pop15, 5, [Z15, A15]], [pop15, 6, [Z15]], [accept15, 6, [Z15]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a15, a15, a15, b15, b15, b15], [[push15, 0, [Z15]], [push15, 1, [Z15, A15]], [push15, 2, [Z15, A15, A15]], [push15, 3, [Z15, A15, A15, A15]], [pop15, 4, [Z15, A15, A15]], [pop15, 5, [Z15, A15]], [pop15, 6, [Z15]], [accept15, 6, [Z15]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107066,"parameters":{"states":["push15","pop15","accept15"],"input_alphabet":["a15","b15"],"stack_alphabet":["Z15","A15"],"start_state":"push15","bottom_symbol":"Z15","final_states":["accept15"],"transitions":[["push15","a15","Z15","push15",["Z15","A15"]],["push15","a15","A15","push15",["A15","A15"]],["push15","b15","A15","pop15",[]],["pop15","b15","A15","pop15",[]],["push15",null,"Z15","accept15",["Z15"]],["pop15",null,"Z15","accept15",["Z15"]]],"input":["a15","a15","a15","b15","b15","b15"],"trace":[["push15",0,["Z15"]],["push15",1,["Z15","A15"]],["push15",2,["Z15","A15","A15"]],["push15",3,["Z15","A15","A15","A15"]],["pop15",4,["Z15","A15","A15"]],["pop15",5,["Z15","A15"]],["pop15",6,["Z15"]],["accept15",6,["Z15"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z15\",\"final_states\":[\"accept15\"],\"input\":[\"a15\",\"a15\",\"a15\",\"b15\",\"b15\",\"b15\"],\"input_alphabet\":[\"a15\",\"b15\"],\"stack_alphabet\":[\"A15\",\"Z15\"],\"start_state\":\"push15\",\"states\":[\"accept15\",\"pop15\",\"push15\"],\"trace\":[[\"push15\",0,[\"Z15\"]],[\"push15\",1,[\"Z15\",\"A15\"]],[\"push15\",2,[\"Z15\",\"A15\",\"A15\"]],[\"push15\",3,[\"Z15\",\"A15\",\"A15\",\"A15\"]],[\"pop15\",4,[\"Z15\",\"A15\",\"A15\"]],[\"pop15\",5,[\"Z15\",\"A15\"]],[\"pop15\",6,[\"Z15\"]],[\"accept15\",6,[\"Z15\"]]],\"transitions\":[[\"pop15\",\"b15\",\"A15\",\"pop15\",[]],[\"pop15\",null,\"Z15\",\"accept15\",[\"Z15\"]],[\"push15\",\"a15\",\"A15\",\"push15\",[\"A15\",\"A15\"]],[\"push15\",\"a15\",\"Z15\",\"push15\",[\"Z15\",\"A15\"]],[\"push15\",\"b15\",\"A15\",\"pop15\",[]],[\"push15\",null,\"Z15\",\"accept15\",[\"Z15\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0067","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push16\",\"pop16\",\"accept16\"],\"input_alphabet\":[\"a16\",\"b16\"],\"stack_alphabet\":[\"Z16\",\"A16\"],\"start_state\":\"push16\",\"bottom_symbol\":\"Z16\",\"final_states\":[\"accept16\"],\"transitions\":[[\"push16\",\"a16\",\"Z16\",\"push16\",[\"Z16\",\"A16\"]],[\"push16\",\"a16\",\"A16\",\"push16\",[\"A16\",\"A16\"]],[\"push16\",\"b16\",\"A16\",\"pop16\",[]],[\"pop16\",\"b16\",\"A16\",\"pop16\",[]],[\"push16\",null,\"Z16\",\"accept16\",[\"Z16\"]],[\"pop16\",null,\"Z16\",\"accept16\",[\"Z16\"]]],\"input\":[],\"trace\":[[\"push16\",0,[\"Z16\"]],[\"accept16\",0,[\"Z16\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push16, 0, [Z16]], [accept16, 0, [Z16]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([], [[push16, 0, [Z16]], [accept16, 0, [Z16]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107067,"parameters":{"states":["push16","pop16","accept16"],"input_alphabet":["a16","b16"],"stack_alphabet":["Z16","A16"],"start_state":"push16","bottom_symbol":"Z16","final_states":["accept16"],"transitions":[["push16","a16","Z16","push16",["Z16","A16"]],["push16","a16","A16","push16",["A16","A16"]],["push16","b16","A16","pop16",[]],["pop16","b16","A16","pop16",[]],["push16",null,"Z16","accept16",["Z16"]],["pop16",null,"Z16","accept16",["Z16"]]],"input":[],"trace":[["push16",0,["Z16"]],["accept16",0,["Z16"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z16\",\"final_states\":[\"accept16\"],\"input\":[],\"input_alphabet\":[\"a16\",\"b16\"],\"stack_alphabet\":[\"A16\",\"Z16\"],\"start_state\":\"push16\",\"states\":[\"accept16\",\"pop16\",\"push16\"],\"trace\":[[\"push16\",0,[\"Z16\"]],[\"accept16\",0,[\"Z16\"]]],\"transitions\":[[\"pop16\",\"b16\",\"A16\",\"pop16\",[]],[\"pop16\",null,\"Z16\",\"accept16\",[\"Z16\"]],[\"push16\",\"a16\",\"A16\",\"push16\",[\"A16\",\"A16\"]],[\"push16\",\"a16\",\"Z16\",\"push16\",[\"Z16\",\"A16\"]],[\"push16\",\"b16\",\"A16\",\"pop16\",[]],[\"push16\",null,\"Z16\",\"accept16\",[\"Z16\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0068","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push17\",\"pop17\",\"accept17\"],\"input_alphabet\":[\"a17\",\"b17\"],\"stack_alphabet\":[\"Z17\",\"A17\"],\"start_state\":\"push17\",\"bottom_symbol\":\"Z17\",\"final_states\":[\"accept17\"],\"transitions\":[[\"push17\",\"a17\",\"Z17\",\"push17\",[\"Z17\",\"A17\"]],[\"push17\",\"a17\",\"A17\",\"push17\",[\"A17\",\"A17\"]],[\"push17\",\"b17\",\"A17\",\"pop17\",[]],[\"pop17\",\"b17\",\"A17\",\"pop17\",[]],[\"push17\",null,\"Z17\",\"accept17\",[\"Z17\"]],[\"pop17\",null,\"Z17\",\"accept17\",[\"Z17\"]]],\"input\":[\"a17\",\"b17\"],\"trace\":[[\"push17\",0,[\"Z17\"]],[\"push17\",1,[\"Z17\",\"A17\"]],[\"pop17\",2,[\"Z17\"]],[\"accept17\",2,[\"Z17\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a17, b17], [[push17, 0, [Z17]], [push17, 1, [Z17, A17]], [pop17, 2, [Z17]], [accept17, 2, [Z17]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a17, b17], [[push17, 0, [Z17]], [push17, 1, [Z17, A17]], [pop17, 2, [Z17]], [accept17, 2, [Z17]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107068,"parameters":{"states":["push17","pop17","accept17"],"input_alphabet":["a17","b17"],"stack_alphabet":["Z17","A17"],"start_state":"push17","bottom_symbol":"Z17","final_states":["accept17"],"transitions":[["push17","a17","Z17","push17",["Z17","A17"]],["push17","a17","A17","push17",["A17","A17"]],["push17","b17","A17","pop17",[]],["pop17","b17","A17","pop17",[]],["push17",null,"Z17","accept17",["Z17"]],["pop17",null,"Z17","accept17",["Z17"]]],"input":["a17","b17"],"trace":[["push17",0,["Z17"]],["push17",1,["Z17","A17"]],["pop17",2,["Z17"]],["accept17",2,["Z17"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z17\",\"final_states\":[\"accept17\"],\"input\":[\"a17\",\"b17\"],\"input_alphabet\":[\"a17\",\"b17\"],\"stack_alphabet\":[\"A17\",\"Z17\"],\"start_state\":\"push17\",\"states\":[\"accept17\",\"pop17\",\"push17\"],\"trace\":[[\"push17\",0,[\"Z17\"]],[\"push17\",1,[\"Z17\",\"A17\"]],[\"pop17\",2,[\"Z17\"]],[\"accept17\",2,[\"Z17\"]]],\"transitions\":[[\"pop17\",\"b17\",\"A17\",\"pop17\",[]],[\"pop17\",null,\"Z17\",\"accept17\",[\"Z17\"]],[\"push17\",\"a17\",\"A17\",\"push17\",[\"A17\",\"A17\"]],[\"push17\",\"a17\",\"Z17\",\"push17\",[\"Z17\",\"A17\"]],[\"push17\",\"b17\",\"A17\",\"pop17\",[]],[\"push17\",null,\"Z17\",\"accept17\",[\"Z17\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0069","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push18\",\"pop18\",\"accept18\"],\"input_alphabet\":[\"a18\",\"b18\"],\"stack_alphabet\":[\"Z18\",\"A18\"],\"start_state\":\"push18\",\"bottom_symbol\":\"Z18\",\"final_states\":[\"accept18\"],\"transitions\":[[\"push18\",\"a18\",\"Z18\",\"push18\",[\"Z18\",\"A18\"]],[\"push18\",\"a18\",\"A18\",\"push18\",[\"A18\",\"A18\"]],[\"push18\",\"b18\",\"A18\",\"pop18\",[]],[\"pop18\",\"b18\",\"A18\",\"pop18\",[]],[\"push18\",null,\"Z18\",\"accept18\",[\"Z18\"]],[\"pop18\",null,\"Z18\",\"accept18\",[\"Z18\"]]],\"input\":[\"a18\",\"a18\",\"b18\",\"b18\"],\"trace\":[[\"push18\",0,[\"Z18\"]],[\"push18\",1,[\"Z18\",\"A18\"]],[\"push18\",2,[\"Z18\",\"A18\",\"A18\"]],[\"pop18\",3,[\"Z18\",\"A18\"]],[\"pop18\",4,[\"Z18\"]],[\"accept18\",4,[\"Z18\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a18, a18, b18, b18], [[push18, 0, [Z18]], [push18, 1, [Z18, A18]], [push18, 2, [Z18, A18, A18]], [pop18, 3, [Z18, A18]], [pop18, 4, [Z18]], [accept18, 4, [Z18]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a18, a18, b18, b18], [[push18, 0, [Z18]], [push18, 1, [Z18, A18]], [push18, 2, [Z18, A18, A18]], [pop18, 3, [Z18, A18]], [pop18, 4, [Z18]], [accept18, 4, [Z18]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107069,"parameters":{"states":["push18","pop18","accept18"],"input_alphabet":["a18","b18"],"stack_alphabet":["Z18","A18"],"start_state":"push18","bottom_symbol":"Z18","final_states":["accept18"],"transitions":[["push18","a18","Z18","push18",["Z18","A18"]],["push18","a18","A18","push18",["A18","A18"]],["push18","b18","A18","pop18",[]],["pop18","b18","A18","pop18",[]],["push18",null,"Z18","accept18",["Z18"]],["pop18",null,"Z18","accept18",["Z18"]]],"input":["a18","a18","b18","b18"],"trace":[["push18",0,["Z18"]],["push18",1,["Z18","A18"]],["push18",2,["Z18","A18","A18"]],["pop18",3,["Z18","A18"]],["pop18",4,["Z18"]],["accept18",4,["Z18"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z18\",\"final_states\":[\"accept18\"],\"input\":[\"a18\",\"a18\",\"b18\",\"b18\"],\"input_alphabet\":[\"a18\",\"b18\"],\"stack_alphabet\":[\"A18\",\"Z18\"],\"start_state\":\"push18\",\"states\":[\"accept18\",\"pop18\",\"push18\"],\"trace\":[[\"push18\",0,[\"Z18\"]],[\"push18\",1,[\"Z18\",\"A18\"]],[\"push18\",2,[\"Z18\",\"A18\",\"A18\"]],[\"pop18\",3,[\"Z18\",\"A18\"]],[\"pop18\",4,[\"Z18\"]],[\"accept18\",4,[\"Z18\"]]],\"transitions\":[[\"pop18\",\"b18\",\"A18\",\"pop18\",[]],[\"pop18\",null,\"Z18\",\"accept18\",[\"Z18\"]],[\"push18\",\"a18\",\"A18\",\"push18\",[\"A18\",\"A18\"]],[\"push18\",\"a18\",\"Z18\",\"push18\",[\"Z18\",\"A18\"]],[\"push18\",\"b18\",\"A18\",\"pop18\",[]],[\"push18\",null,\"Z18\",\"accept18\",[\"Z18\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0070","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push19\",\"pop19\",\"accept19\"],\"input_alphabet\":[\"a19\",\"b19\"],\"stack_alphabet\":[\"Z19\",\"A19\"],\"start_state\":\"push19\",\"bottom_symbol\":\"Z19\",\"final_states\":[\"accept19\"],\"transitions\":[[\"push19\",\"a19\",\"Z19\",\"push19\",[\"Z19\",\"A19\"]],[\"push19\",\"a19\",\"A19\",\"push19\",[\"A19\",\"A19\"]],[\"push19\",\"b19\",\"A19\",\"pop19\",[]],[\"pop19\",\"b19\",\"A19\",\"pop19\",[]],[\"push19\",null,\"Z19\",\"accept19\",[\"Z19\"]],[\"pop19\",null,\"Z19\",\"accept19\",[\"Z19\"]]],\"input\":[\"a19\",\"a19\",\"a19\",\"b19\",\"b19\",\"b19\"],\"trace\":[[\"push19\",0,[\"Z19\"]],[\"push19\",1,[\"Z19\",\"A19\"]],[\"push19\",2,[\"Z19\",\"A19\",\"A19\"]],[\"push19\",3,[\"Z19\",\"A19\",\"A19\",\"A19\"]],[\"pop19\",4,[\"Z19\",\"A19\",\"A19\"]],[\"pop19\",5,[\"Z19\",\"A19\"]],[\"pop19\",6,[\"Z19\"]],[\"accept19\",6,[\"Z19\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a19, a19, a19, b19, b19, b19], [[push19, 0, [Z19]], [push19, 1, [Z19, A19]], [push19, 2, [Z19, A19, A19]], [push19, 3, [Z19, A19, A19, A19]], [pop19, 4, [Z19, A19, A19]], [pop19, 5, [Z19, A19]], [pop19, 6, [Z19]], [accept19, 6, [Z19]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a19, a19, a19, b19, b19, b19], [[push19, 0, [Z19]], [push19, 1, [Z19, A19]], [push19, 2, [Z19, A19, A19]], [push19, 3, [Z19, A19, A19, A19]], [pop19, 4, [Z19, A19, A19]], [pop19, 5, [Z19, A19]], [pop19, 6, [Z19]], [accept19, 6, [Z19]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107070,"parameters":{"states":["push19","pop19","accept19"],"input_alphabet":["a19","b19"],"stack_alphabet":["Z19","A19"],"start_state":"push19","bottom_symbol":"Z19","final_states":["accept19"],"transitions":[["push19","a19","Z19","push19",["Z19","A19"]],["push19","a19","A19","push19",["A19","A19"]],["push19","b19","A19","pop19",[]],["pop19","b19","A19","pop19",[]],["push19",null,"Z19","accept19",["Z19"]],["pop19",null,"Z19","accept19",["Z19"]]],"input":["a19","a19","a19","b19","b19","b19"],"trace":[["push19",0,["Z19"]],["push19",1,["Z19","A19"]],["push19",2,["Z19","A19","A19"]],["push19",3,["Z19","A19","A19","A19"]],["pop19",4,["Z19","A19","A19"]],["pop19",5,["Z19","A19"]],["pop19",6,["Z19"]],["accept19",6,["Z19"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z19\",\"final_states\":[\"accept19\"],\"input\":[\"a19\",\"a19\",\"a19\",\"b19\",\"b19\",\"b19\"],\"input_alphabet\":[\"a19\",\"b19\"],\"stack_alphabet\":[\"A19\",\"Z19\"],\"start_state\":\"push19\",\"states\":[\"accept19\",\"pop19\",\"push19\"],\"trace\":[[\"push19\",0,[\"Z19\"]],[\"push19\",1,[\"Z19\",\"A19\"]],[\"push19\",2,[\"Z19\",\"A19\",\"A19\"]],[\"push19\",3,[\"Z19\",\"A19\",\"A19\",\"A19\"]],[\"pop19\",4,[\"Z19\",\"A19\",\"A19\"]],[\"pop19\",5,[\"Z19\",\"A19\"]],[\"pop19\",6,[\"Z19\"]],[\"accept19\",6,[\"Z19\"]]],\"transitions\":[[\"pop19\",\"b19\",\"A19\",\"pop19\",[]],[\"pop19\",null,\"Z19\",\"accept19\",[\"Z19\"]],[\"push19\",\"a19\",\"A19\",\"push19\",[\"A19\",\"A19\"]],[\"push19\",\"a19\",\"Z19\",\"push19\",[\"Z19\",\"A19\"]],[\"push19\",\"b19\",\"A19\",\"pop19\",[]],[\"push19\",null,\"Z19\",\"accept19\",[\"Z19\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0071","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push20\",\"pop20\",\"accept20\"],\"input_alphabet\":[\"a20\",\"b20\"],\"stack_alphabet\":[\"Z20\",\"A20\"],\"start_state\":\"push20\",\"bottom_symbol\":\"Z20\",\"final_states\":[\"accept20\"],\"transitions\":[[\"push20\",\"a20\",\"Z20\",\"push20\",[\"Z20\",\"A20\"]],[\"push20\",\"a20\",\"A20\",\"push20\",[\"A20\",\"A20\"]],[\"push20\",\"b20\",\"A20\",\"pop20\",[]],[\"pop20\",\"b20\",\"A20\",\"pop20\",[]],[\"push20\",null,\"Z20\",\"accept20\",[\"Z20\"]],[\"pop20\",null,\"Z20\",\"accept20\",[\"Z20\"]]],\"input\":[],\"trace\":[[\"push20\",0,[\"Z20\"]],[\"accept20\",0,[\"Z20\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push20, 0, [Z20]], [accept20, 0, [Z20]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([], [[push20, 0, [Z20]], [accept20, 0, [Z20]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107071,"parameters":{"states":["push20","pop20","accept20"],"input_alphabet":["a20","b20"],"stack_alphabet":["Z20","A20"],"start_state":"push20","bottom_symbol":"Z20","final_states":["accept20"],"transitions":[["push20","a20","Z20","push20",["Z20","A20"]],["push20","a20","A20","push20",["A20","A20"]],["push20","b20","A20","pop20",[]],["pop20","b20","A20","pop20",[]],["push20",null,"Z20","accept20",["Z20"]],["pop20",null,"Z20","accept20",["Z20"]]],"input":[],"trace":[["push20",0,["Z20"]],["accept20",0,["Z20"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z20\",\"final_states\":[\"accept20\"],\"input\":[],\"input_alphabet\":[\"a20\",\"b20\"],\"stack_alphabet\":[\"A20\",\"Z20\"],\"start_state\":\"push20\",\"states\":[\"accept20\",\"pop20\",\"push20\"],\"trace\":[[\"push20\",0,[\"Z20\"]],[\"accept20\",0,[\"Z20\"]]],\"transitions\":[[\"pop20\",\"b20\",\"A20\",\"pop20\",[]],[\"pop20\",null,\"Z20\",\"accept20\",[\"Z20\"]],[\"push20\",\"a20\",\"A20\",\"push20\",[\"A20\",\"A20\"]],[\"push20\",\"a20\",\"Z20\",\"push20\",[\"Z20\",\"A20\"]],[\"push20\",\"b20\",\"A20\",\"pop20\",[]],[\"push20\",null,\"Z20\",\"accept20\",[\"Z20\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0072","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push21\",\"pop21\",\"accept21\"],\"input_alphabet\":[\"a21\",\"b21\"],\"stack_alphabet\":[\"Z21\",\"A21\"],\"start_state\":\"push21\",\"bottom_symbol\":\"Z21\",\"final_states\":[\"accept21\"],\"transitions\":[[\"push21\",\"a21\",\"Z21\",\"push21\",[\"Z21\",\"A21\"]],[\"push21\",\"a21\",\"A21\",\"push21\",[\"A21\",\"A21\"]],[\"push21\",\"b21\",\"A21\",\"pop21\",[]],[\"pop21\",\"b21\",\"A21\",\"pop21\",[]],[\"push21\",null,\"Z21\",\"accept21\",[\"Z21\"]],[\"pop21\",null,\"Z21\",\"accept21\",[\"Z21\"]]],\"input\":[\"a21\",\"b21\"],\"trace\":[[\"push21\",0,[\"Z21\"]],[\"push21\",1,[\"Z21\",\"A21\"]],[\"pop21\",2,[\"Z21\"]],[\"accept21\",2,[\"Z21\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a21, b21], [[push21, 0, [Z21]], [push21, 1, [Z21, A21]], [pop21, 2, [Z21]], [accept21, 2, [Z21]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a21, b21], [[push21, 0, [Z21]], [push21, 1, [Z21, A21]], [pop21, 2, [Z21]], [accept21, 2, [Z21]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107072,"parameters":{"states":["push21","pop21","accept21"],"input_alphabet":["a21","b21"],"stack_alphabet":["Z21","A21"],"start_state":"push21","bottom_symbol":"Z21","final_states":["accept21"],"transitions":[["push21","a21","Z21","push21",["Z21","A21"]],["push21","a21","A21","push21",["A21","A21"]],["push21","b21","A21","pop21",[]],["pop21","b21","A21","pop21",[]],["push21",null,"Z21","accept21",["Z21"]],["pop21",null,"Z21","accept21",["Z21"]]],"input":["a21","b21"],"trace":[["push21",0,["Z21"]],["push21",1,["Z21","A21"]],["pop21",2,["Z21"]],["accept21",2,["Z21"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z21\",\"final_states\":[\"accept21\"],\"input\":[\"a21\",\"b21\"],\"input_alphabet\":[\"a21\",\"b21\"],\"stack_alphabet\":[\"A21\",\"Z21\"],\"start_state\":\"push21\",\"states\":[\"accept21\",\"pop21\",\"push21\"],\"trace\":[[\"push21\",0,[\"Z21\"]],[\"push21\",1,[\"Z21\",\"A21\"]],[\"pop21\",2,[\"Z21\"]],[\"accept21\",2,[\"Z21\"]]],\"transitions\":[[\"pop21\",\"b21\",\"A21\",\"pop21\",[]],[\"pop21\",null,\"Z21\",\"accept21\",[\"Z21\"]],[\"push21\",\"a21\",\"A21\",\"push21\",[\"A21\",\"A21\"]],[\"push21\",\"a21\",\"Z21\",\"push21\",[\"Z21\",\"A21\"]],[\"push21\",\"b21\",\"A21\",\"pop21\",[]],[\"push21\",null,\"Z21\",\"accept21\",[\"Z21\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0073","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push22\",\"pop22\",\"accept22\"],\"input_alphabet\":[\"a22\",\"b22\"],\"stack_alphabet\":[\"Z22\",\"A22\"],\"start_state\":\"push22\",\"bottom_symbol\":\"Z22\",\"final_states\":[\"accept22\"],\"transitions\":[[\"push22\",\"a22\",\"Z22\",\"push22\",[\"Z22\",\"A22\"]],[\"push22\",\"a22\",\"A22\",\"push22\",[\"A22\",\"A22\"]],[\"push22\",\"b22\",\"A22\",\"pop22\",[]],[\"pop22\",\"b22\",\"A22\",\"pop22\",[]],[\"push22\",null,\"Z22\",\"accept22\",[\"Z22\"]],[\"pop22\",null,\"Z22\",\"accept22\",[\"Z22\"]]],\"input\":[\"a22\",\"a22\",\"b22\",\"b22\"],\"trace\":[[\"push22\",0,[\"Z22\"]],[\"push22\",1,[\"Z22\",\"A22\"]],[\"push22\",2,[\"Z22\",\"A22\",\"A22\"]],[\"pop22\",3,[\"Z22\",\"A22\"]],[\"pop22\",4,[\"Z22\"]],[\"accept22\",4,[\"Z22\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a22, a22, b22, b22], [[push22, 0, [Z22]], [push22, 1, [Z22, A22]], [push22, 2, [Z22, A22, A22]], [pop22, 3, [Z22, A22]], [pop22, 4, [Z22]], [accept22, 4, [Z22]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a22, a22, b22, b22], [[push22, 0, [Z22]], [push22, 1, [Z22, A22]], [push22, 2, [Z22, A22, A22]], [pop22, 3, [Z22, A22]], [pop22, 4, [Z22]], [accept22, 4, [Z22]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107073,"parameters":{"states":["push22","pop22","accept22"],"input_alphabet":["a22","b22"],"stack_alphabet":["Z22","A22"],"start_state":"push22","bottom_symbol":"Z22","final_states":["accept22"],"transitions":[["push22","a22","Z22","push22",["Z22","A22"]],["push22","a22","A22","push22",["A22","A22"]],["push22","b22","A22","pop22",[]],["pop22","b22","A22","pop22",[]],["push22",null,"Z22","accept22",["Z22"]],["pop22",null,"Z22","accept22",["Z22"]]],"input":["a22","a22","b22","b22"],"trace":[["push22",0,["Z22"]],["push22",1,["Z22","A22"]],["push22",2,["Z22","A22","A22"]],["pop22",3,["Z22","A22"]],["pop22",4,["Z22"]],["accept22",4,["Z22"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z22\",\"final_states\":[\"accept22\"],\"input\":[\"a22\",\"a22\",\"b22\",\"b22\"],\"input_alphabet\":[\"a22\",\"b22\"],\"stack_alphabet\":[\"A22\",\"Z22\"],\"start_state\":\"push22\",\"states\":[\"accept22\",\"pop22\",\"push22\"],\"trace\":[[\"push22\",0,[\"Z22\"]],[\"push22\",1,[\"Z22\",\"A22\"]],[\"push22\",2,[\"Z22\",\"A22\",\"A22\"]],[\"pop22\",3,[\"Z22\",\"A22\"]],[\"pop22\",4,[\"Z22\"]],[\"accept22\",4,[\"Z22\"]]],\"transitions\":[[\"pop22\",\"b22\",\"A22\",\"pop22\",[]],[\"pop22\",null,\"Z22\",\"accept22\",[\"Z22\"]],[\"push22\",\"a22\",\"A22\",\"push22\",[\"A22\",\"A22\"]],[\"push22\",\"a22\",\"Z22\",\"push22\",[\"Z22\",\"A22\"]],[\"push22\",\"b22\",\"A22\",\"pop22\",[]],[\"push22\",null,\"Z22\",\"accept22\",[\"Z22\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0074","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push23\",\"pop23\",\"accept23\"],\"input_alphabet\":[\"a23\",\"b23\"],\"stack_alphabet\":[\"Z23\",\"A23\"],\"start_state\":\"push23\",\"bottom_symbol\":\"Z23\",\"final_states\":[\"accept23\"],\"transitions\":[[\"push23\",\"a23\",\"Z23\",\"push23\",[\"Z23\",\"A23\"]],[\"push23\",\"a23\",\"A23\",\"push23\",[\"A23\",\"A23\"]],[\"push23\",\"b23\",\"A23\",\"pop23\",[]],[\"pop23\",\"b23\",\"A23\",\"pop23\",[]],[\"push23\",null,\"Z23\",\"accept23\",[\"Z23\"]],[\"pop23\",null,\"Z23\",\"accept23\",[\"Z23\"]]],\"input\":[\"a23\",\"a23\",\"a23\",\"b23\",\"b23\",\"b23\"],\"trace\":[[\"push23\",0,[\"Z23\"]],[\"push23\",1,[\"Z23\",\"A23\"]],[\"push23\",2,[\"Z23\",\"A23\",\"A23\"]],[\"push23\",3,[\"Z23\",\"A23\",\"A23\",\"A23\"]],[\"pop23\",4,[\"Z23\",\"A23\",\"A23\"]],[\"pop23\",5,[\"Z23\",\"A23\"]],[\"pop23\",6,[\"Z23\"]],[\"accept23\",6,[\"Z23\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a23, a23, a23, b23, b23, b23], [[push23, 0, [Z23]], [push23, 1, [Z23, A23]], [push23, 2, [Z23, A23, A23]], [push23, 3, [Z23, A23, A23, A23]], [pop23, 4, [Z23, A23, A23]], [pop23, 5, [Z23, A23]], [pop23, 6, [Z23]], [accept23, 6, [Z23]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([a23, a23, a23, b23, b23, b23], [[push23, 0, [Z23]], [push23, 1, [Z23, A23]], [push23, 2, [Z23, A23, A23]], [push23, 3, [Z23, A23, A23, A23]], [pop23, 4, [Z23, A23, A23]], [pop23, 5, [Z23, A23]], [pop23, 6, [Z23]], [accept23, 6, [Z23]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107074,"parameters":{"states":["push23","pop23","accept23"],"input_alphabet":["a23","b23"],"stack_alphabet":["Z23","A23"],"start_state":"push23","bottom_symbol":"Z23","final_states":["accept23"],"transitions":[["push23","a23","Z23","push23",["Z23","A23"]],["push23","a23","A23","push23",["A23","A23"]],["push23","b23","A23","pop23",[]],["pop23","b23","A23","pop23",[]],["push23",null,"Z23","accept23",["Z23"]],["pop23",null,"Z23","accept23",["Z23"]]],"input":["a23","a23","a23","b23","b23","b23"],"trace":[["push23",0,["Z23"]],["push23",1,["Z23","A23"]],["push23",2,["Z23","A23","A23"]],["push23",3,["Z23","A23","A23","A23"]],["pop23",4,["Z23","A23","A23"]],["pop23",5,["Z23","A23"]],["pop23",6,["Z23"]],["accept23",6,["Z23"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z23\",\"final_states\":[\"accept23\"],\"input\":[\"a23\",\"a23\",\"a23\",\"b23\",\"b23\",\"b23\"],\"input_alphabet\":[\"a23\",\"b23\"],\"stack_alphabet\":[\"A23\",\"Z23\"],\"start_state\":\"push23\",\"states\":[\"accept23\",\"pop23\",\"push23\"],\"trace\":[[\"push23\",0,[\"Z23\"]],[\"push23\",1,[\"Z23\",\"A23\"]],[\"push23\",2,[\"Z23\",\"A23\",\"A23\"]],[\"push23\",3,[\"Z23\",\"A23\",\"A23\",\"A23\"]],[\"pop23\",4,[\"Z23\",\"A23\",\"A23\"]],[\"pop23\",5,[\"Z23\",\"A23\"]],[\"pop23\",6,[\"Z23\"]],[\"accept23\",6,[\"Z23\"]]],\"transitions\":[[\"pop23\",\"b23\",\"A23\",\"pop23\",[]],[\"pop23\",null,\"Z23\",\"accept23\",[\"Z23\"]],[\"push23\",\"a23\",\"A23\",\"push23\",[\"A23\",\"A23\"]],[\"push23\",\"a23\",\"Z23\",\"push23\",[\"Z23\",\"A23\"]],[\"push23\",\"b23\",\"A23\",\"pop23\",[]],[\"push23\",null,\"Z23\",\"accept23\",[\"Z23\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0075","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={\"states\":[\"push24\",\"pop24\",\"accept24\"],\"input_alphabet\":[\"a24\",\"b24\"],\"stack_alphabet\":[\"Z24\",\"A24\"],\"start_state\":\"push24\",\"bottom_symbol\":\"Z24\",\"final_states\":[\"accept24\"],\"transitions\":[[\"push24\",\"a24\",\"Z24\",\"push24\",[\"Z24\",\"A24\"]],[\"push24\",\"a24\",\"A24\",\"push24\",[\"A24\",\"A24\"]],[\"push24\",\"b24\",\"A24\",\"pop24\",[]],[\"pop24\",\"b24\",\"A24\",\"pop24\",[]],[\"push24\",null,\"Z24\",\"accept24\",[\"Z24\"]],[\"pop24\",null,\"Z24\",\"accept24\",[\"Z24\"]]],\"input\":[],\"trace\":[[\"push24\",0,[\"Z24\"]],[\"accept24\",0,[\"Z24\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([], [[push24, 0, [Z24]], [accept24, 0, [Z24]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)","explanation_zh":"Wave6第四層核對=([], [[push24, 0, [Z24]], [accept24, 0, [Z24]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-accepting-run-witness","seed":202611107075,"parameters":{"states":["push24","pop24","accept24"],"input_alphabet":["a24","b24"],"stack_alphabet":["Z24","A24"],"start_state":"push24","bottom_symbol":"Z24","final_states":["accept24"],"transitions":[["push24","a24","Z24","push24",["Z24","A24"]],["push24","a24","A24","push24",["A24","A24"]],["push24","b24","A24","pop24",[]],["pop24","b24","A24","pop24",[]],["push24",null,"Z24","accept24",["Z24"]],["pop24",null,"Z24","accept24",["Z24"]]],"input":[],"trace":[["push24",0,["Z24"]],["accept24",0,["Z24"]]],"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-accepting-run-witness","semantic_template":"qf-mod41-pda-accepting-run-witness/{\"bottom_symbol\":\"Z24\",\"final_states\":[\"accept24\"],\"input\":[],\"input_alphabet\":[\"a24\",\"b24\"],\"stack_alphabet\":[\"A24\",\"Z24\"],\"start_state\":\"push24\",\"states\":[\"accept24\",\"pop24\",\"push24\"],\"trace\":[[\"push24\",0,[\"Z24\"]],[\"accept24\",0,[\"Z24\"]]],\"transitions\":[[\"pop24\",\"b24\",\"A24\",\"pop24\",[]],[\"pop24\",null,\"Z24\",\"accept24\",[\"Z24\"]],[\"push24\",\"a24\",\"A24\",\"push24\",[\"A24\",\"A24\"]],[\"push24\",\"a24\",\"Z24\",\"push24\",[\"Z24\",\"A24\"]],[\"push24\",\"b24\",\"A24\",\"pop24\",[]],[\"push24\",null,\"Z24\",\"accept24\",[\"Z24\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0076","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push0\",\"pop0\",\"accept0\"],\"input_alphabet\":[\"a0\",\"b0\"],\"stack_alphabet\":[\"Z0\",\"A0\"],\"start_state\":\"push0\",\"bottom_symbol\":\"Z0\",\"final_states\":[\"accept0\"],\"transitions\":[[\"push0\",\"a0\",\"Z0\",\"push0\",[\"Z0\",\"A0\"]],[\"push0\",\"a0\",\"A0\",\"push0\",[\"A0\",\"A0\"]],[\"push0\",\"b0\",\"A0\",\"pop0\",[]],[\"pop0\",\"b0\",\"A0\",\"pop0\",[]],[\"push0\",null,\"Z0\",\"accept0\",[\"Z0\"]],[\"pop0\",null,\"Z0\",\"accept0\",[\"Z0\"]]],\"input\":[\"a0\",\"b0\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a0, b0], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a0, b0], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107076,"parameters":{"states":["push0","pop0","accept0"],"input_alphabet":["a0","b0"],"stack_alphabet":["Z0","A0"],"start_state":"push0","bottom_symbol":"Z0","final_states":["accept0"],"transitions":[["push0","a0","Z0","push0",["Z0","A0"]],["push0","a0","A0","push0",["A0","A0"]],["push0","b0","A0","pop0",[]],["pop0","b0","A0","pop0",[]],["push0",null,"Z0","accept0",["Z0"]],["pop0",null,"Z0","accept0",["Z0"]]],"input":["a0","b0"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z0\",\"final_states\":[\"accept0\"],\"input\":[\"a0\",\"b0\"],\"input_alphabet\":[\"a0\",\"b0\"],\"max_steps\":1,\"stack_alphabet\":[\"A0\",\"Z0\"],\"start_state\":\"push0\",\"states\":[\"accept0\",\"pop0\",\"push0\"],\"transitions\":[[\"pop0\",\"b0\",\"A0\",\"pop0\",[]],[\"pop0\",null,\"Z0\",\"accept0\",[\"Z0\"]],[\"push0\",\"a0\",\"A0\",\"push0\",[\"A0\",\"A0\"]],[\"push0\",\"a0\",\"Z0\",\"push0\",[\"Z0\",\"A0\"]],[\"push0\",\"b0\",\"A0\",\"pop0\",[]],[\"push0\",null,\"Z0\",\"accept0\",[\"Z0\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0077","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push1\",\"pop1\",\"accept1\"],\"input_alphabet\":[\"a1\",\"b1\"],\"stack_alphabet\":[\"Z1\",\"A1\"],\"start_state\":\"push1\",\"bottom_symbol\":\"Z1\",\"final_states\":[\"accept1\"],\"transitions\":[[\"push1\",\"a1\",\"Z1\",\"push1\",[\"Z1\",\"A1\"]],[\"push1\",\"a1\",\"A1\",\"push1\",[\"A1\",\"A1\"]],[\"push1\",\"b1\",\"A1\",\"pop1\",[]],[\"pop1\",\"b1\",\"A1\",\"pop1\",[]],[\"push1\",null,\"Z1\",\"accept1\",[\"Z1\"]],[\"pop1\",null,\"Z1\",\"accept1\",[\"Z1\"]]],\"input\":[\"a1\",\"a1\",\"b1\",\"b1\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a1, a1, b1, b1], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a1, a1, b1, b1], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107077,"parameters":{"states":["push1","pop1","accept1"],"input_alphabet":["a1","b1"],"stack_alphabet":["Z1","A1"],"start_state":"push1","bottom_symbol":"Z1","final_states":["accept1"],"transitions":[["push1","a1","Z1","push1",["Z1","A1"]],["push1","a1","A1","push1",["A1","A1"]],["push1","b1","A1","pop1",[]],["pop1","b1","A1","pop1",[]],["push1",null,"Z1","accept1",["Z1"]],["pop1",null,"Z1","accept1",["Z1"]]],"input":["a1","a1","b1","b1"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z1\",\"final_states\":[\"accept1\"],\"input\":[\"a1\",\"a1\",\"b1\",\"b1\"],\"input_alphabet\":[\"a1\",\"b1\"],\"max_steps\":1,\"stack_alphabet\":[\"A1\",\"Z1\"],\"start_state\":\"push1\",\"states\":[\"accept1\",\"pop1\",\"push1\"],\"transitions\":[[\"pop1\",\"b1\",\"A1\",\"pop1\",[]],[\"pop1\",null,\"Z1\",\"accept1\",[\"Z1\"]],[\"push1\",\"a1\",\"A1\",\"push1\",[\"A1\",\"A1\"]],[\"push1\",\"a1\",\"Z1\",\"push1\",[\"Z1\",\"A1\"]],[\"push1\",\"b1\",\"A1\",\"pop1\",[]],[\"push1\",null,\"Z1\",\"accept1\",[\"Z1\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0078","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push2\",\"pop2\",\"accept2\"],\"input_alphabet\":[\"a2\",\"b2\"],\"stack_alphabet\":[\"Z2\",\"A2\"],\"start_state\":\"push2\",\"bottom_symbol\":\"Z2\",\"final_states\":[\"accept2\"],\"transitions\":[[\"push2\",\"a2\",\"Z2\",\"push2\",[\"Z2\",\"A2\"]],[\"push2\",\"a2\",\"A2\",\"push2\",[\"A2\",\"A2\"]],[\"push2\",\"b2\",\"A2\",\"pop2\",[]],[\"pop2\",\"b2\",\"A2\",\"pop2\",[]],[\"push2\",null,\"Z2\",\"accept2\",[\"Z2\"]],[\"pop2\",null,\"Z2\",\"accept2\",[\"Z2\"]]],\"input\":[\"a2\",\"a2\",\"a2\",\"b2\",\"b2\",\"b2\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a2, a2, a2, b2, b2, b2], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a2, a2, a2, b2, b2, b2], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107078,"parameters":{"states":["push2","pop2","accept2"],"input_alphabet":["a2","b2"],"stack_alphabet":["Z2","A2"],"start_state":"push2","bottom_symbol":"Z2","final_states":["accept2"],"transitions":[["push2","a2","Z2","push2",["Z2","A2"]],["push2","a2","A2","push2",["A2","A2"]],["push2","b2","A2","pop2",[]],["pop2","b2","A2","pop2",[]],["push2",null,"Z2","accept2",["Z2"]],["pop2",null,"Z2","accept2",["Z2"]]],"input":["a2","a2","a2","b2","b2","b2"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z2\",\"final_states\":[\"accept2\"],\"input\":[\"a2\",\"a2\",\"a2\",\"b2\",\"b2\",\"b2\"],\"input_alphabet\":[\"a2\",\"b2\"],\"max_steps\":1,\"stack_alphabet\":[\"A2\",\"Z2\"],\"start_state\":\"push2\",\"states\":[\"accept2\",\"pop2\",\"push2\"],\"transitions\":[[\"pop2\",\"b2\",\"A2\",\"pop2\",[]],[\"pop2\",null,\"Z2\",\"accept2\",[\"Z2\"]],[\"push2\",\"a2\",\"A2\",\"push2\",[\"A2\",\"A2\"]],[\"push2\",\"a2\",\"Z2\",\"push2\",[\"Z2\",\"A2\"]],[\"push2\",\"b2\",\"A2\",\"pop2\",[]],[\"push2\",null,\"Z2\",\"accept2\",[\"Z2\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0079","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push3\",\"pop3\",\"accept3\"],\"input_alphabet\":[\"a3\",\"b3\"],\"stack_alphabet\":[\"Z3\",\"A3\"],\"start_state\":\"push3\",\"bottom_symbol\":\"Z3\",\"final_states\":[\"accept3\"],\"transitions\":[[\"push3\",\"a3\",\"Z3\",\"push3\",[\"Z3\",\"A3\"]],[\"push3\",\"a3\",\"A3\",\"push3\",[\"A3\",\"A3\"]],[\"push3\",\"b3\",\"A3\",\"pop3\",[]],[\"pop3\",\"b3\",\"A3\",\"pop3\",[]],[\"push3\",null,\"Z3\",\"accept3\",[\"Z3\"]],[\"pop3\",null,\"Z3\",\"accept3\",[\"Z3\"]]],\"input\":[\"a3\",\"a3\",\"a3\",\"a3\",\"b3\",\"b3\",\"b3\",\"b3\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a3, a3, a3, a3, b3, b3, b3, b3], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a3, a3, a3, a3, b3, b3, b3, b3], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107079,"parameters":{"states":["push3","pop3","accept3"],"input_alphabet":["a3","b3"],"stack_alphabet":["Z3","A3"],"start_state":"push3","bottom_symbol":"Z3","final_states":["accept3"],"transitions":[["push3","a3","Z3","push3",["Z3","A3"]],["push3","a3","A3","push3",["A3","A3"]],["push3","b3","A3","pop3",[]],["pop3","b3","A3","pop3",[]],["push3",null,"Z3","accept3",["Z3"]],["pop3",null,"Z3","accept3",["Z3"]]],"input":["a3","a3","a3","a3","b3","b3","b3","b3"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z3\",\"final_states\":[\"accept3\"],\"input\":[\"a3\",\"a3\",\"a3\",\"a3\",\"b3\",\"b3\",\"b3\",\"b3\"],\"input_alphabet\":[\"a3\",\"b3\"],\"max_steps\":1,\"stack_alphabet\":[\"A3\",\"Z3\"],\"start_state\":\"push3\",\"states\":[\"accept3\",\"pop3\",\"push3\"],\"transitions\":[[\"pop3\",\"b3\",\"A3\",\"pop3\",[]],[\"pop3\",null,\"Z3\",\"accept3\",[\"Z3\"]],[\"push3\",\"a3\",\"A3\",\"push3\",[\"A3\",\"A3\"]],[\"push3\",\"a3\",\"Z3\",\"push3\",[\"Z3\",\"A3\"]],[\"push3\",\"b3\",\"A3\",\"pop3\",[]],[\"push3\",null,\"Z3\",\"accept3\",[\"Z3\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0080","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push4\",\"pop4\",\"accept4\"],\"input_alphabet\":[\"a4\",\"b4\"],\"stack_alphabet\":[\"Z4\",\"A4\"],\"start_state\":\"push4\",\"bottom_symbol\":\"Z4\",\"final_states\":[\"accept4\"],\"transitions\":[[\"push4\",\"a4\",\"Z4\",\"push4\",[\"Z4\",\"A4\"]],[\"push4\",\"a4\",\"A4\",\"push4\",[\"A4\",\"A4\"]],[\"push4\",\"b4\",\"A4\",\"pop4\",[]],[\"pop4\",\"b4\",\"A4\",\"pop4\",[]],[\"push4\",null,\"Z4\",\"accept4\",[\"Z4\"]],[\"pop4\",null,\"Z4\",\"accept4\",[\"Z4\"]]],\"input\":[\"a4\",\"b4\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a4, b4], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a4, b4], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107080,"parameters":{"states":["push4","pop4","accept4"],"input_alphabet":["a4","b4"],"stack_alphabet":["Z4","A4"],"start_state":"push4","bottom_symbol":"Z4","final_states":["accept4"],"transitions":[["push4","a4","Z4","push4",["Z4","A4"]],["push4","a4","A4","push4",["A4","A4"]],["push4","b4","A4","pop4",[]],["pop4","b4","A4","pop4",[]],["push4",null,"Z4","accept4",["Z4"]],["pop4",null,"Z4","accept4",["Z4"]]],"input":["a4","b4"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z4\",\"final_states\":[\"accept4\"],\"input\":[\"a4\",\"b4\"],\"input_alphabet\":[\"a4\",\"b4\"],\"max_steps\":1,\"stack_alphabet\":[\"A4\",\"Z4\"],\"start_state\":\"push4\",\"states\":[\"accept4\",\"pop4\",\"push4\"],\"transitions\":[[\"pop4\",\"b4\",\"A4\",\"pop4\",[]],[\"pop4\",null,\"Z4\",\"accept4\",[\"Z4\"]],[\"push4\",\"a4\",\"A4\",\"push4\",[\"A4\",\"A4\"]],[\"push4\",\"a4\",\"Z4\",\"push4\",[\"Z4\",\"A4\"]],[\"push4\",\"b4\",\"A4\",\"pop4\",[]],[\"push4\",null,\"Z4\",\"accept4\",[\"Z4\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0081","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push5\",\"pop5\",\"accept5\"],\"input_alphabet\":[\"a5\",\"b5\"],\"stack_alphabet\":[\"Z5\",\"A5\"],\"start_state\":\"push5\",\"bottom_symbol\":\"Z5\",\"final_states\":[\"accept5\"],\"transitions\":[[\"push5\",\"a5\",\"Z5\",\"push5\",[\"Z5\",\"A5\"]],[\"push5\",\"a5\",\"A5\",\"push5\",[\"A5\",\"A5\"]],[\"push5\",\"b5\",\"A5\",\"pop5\",[]],[\"pop5\",\"b5\",\"A5\",\"pop5\",[]],[\"push5\",null,\"Z5\",\"accept5\",[\"Z5\"]],[\"pop5\",null,\"Z5\",\"accept5\",[\"Z5\"]]],\"input\":[\"a5\",\"a5\",\"b5\",\"b5\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a5, a5, b5, b5], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a5, a5, b5, b5], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107081,"parameters":{"states":["push5","pop5","accept5"],"input_alphabet":["a5","b5"],"stack_alphabet":["Z5","A5"],"start_state":"push5","bottom_symbol":"Z5","final_states":["accept5"],"transitions":[["push5","a5","Z5","push5",["Z5","A5"]],["push5","a5","A5","push5",["A5","A5"]],["push5","b5","A5","pop5",[]],["pop5","b5","A5","pop5",[]],["push5",null,"Z5","accept5",["Z5"]],["pop5",null,"Z5","accept5",["Z5"]]],"input":["a5","a5","b5","b5"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z5\",\"final_states\":[\"accept5\"],\"input\":[\"a5\",\"a5\",\"b5\",\"b5\"],\"input_alphabet\":[\"a5\",\"b5\"],\"max_steps\":1,\"stack_alphabet\":[\"A5\",\"Z5\"],\"start_state\":\"push5\",\"states\":[\"accept5\",\"pop5\",\"push5\"],\"transitions\":[[\"pop5\",\"b5\",\"A5\",\"pop5\",[]],[\"pop5\",null,\"Z5\",\"accept5\",[\"Z5\"]],[\"push5\",\"a5\",\"A5\",\"push5\",[\"A5\",\"A5\"]],[\"push5\",\"a5\",\"Z5\",\"push5\",[\"Z5\",\"A5\"]],[\"push5\",\"b5\",\"A5\",\"pop5\",[]],[\"push5\",null,\"Z5\",\"accept5\",[\"Z5\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0082","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push6\",\"pop6\",\"accept6\"],\"input_alphabet\":[\"a6\",\"b6\"],\"stack_alphabet\":[\"Z6\",\"A6\"],\"start_state\":\"push6\",\"bottom_symbol\":\"Z6\",\"final_states\":[\"accept6\"],\"transitions\":[[\"push6\",\"a6\",\"Z6\",\"push6\",[\"Z6\",\"A6\"]],[\"push6\",\"a6\",\"A6\",\"push6\",[\"A6\",\"A6\"]],[\"push6\",\"b6\",\"A6\",\"pop6\",[]],[\"pop6\",\"b6\",\"A6\",\"pop6\",[]],[\"push6\",null,\"Z6\",\"accept6\",[\"Z6\"]],[\"pop6\",null,\"Z6\",\"accept6\",[\"Z6\"]]],\"input\":[\"a6\",\"a6\",\"a6\",\"b6\",\"b6\",\"b6\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a6, a6, a6, b6, b6, b6], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a6, a6, a6, b6, b6, b6], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107082,"parameters":{"states":["push6","pop6","accept6"],"input_alphabet":["a6","b6"],"stack_alphabet":["Z6","A6"],"start_state":"push6","bottom_symbol":"Z6","final_states":["accept6"],"transitions":[["push6","a6","Z6","push6",["Z6","A6"]],["push6","a6","A6","push6",["A6","A6"]],["push6","b6","A6","pop6",[]],["pop6","b6","A6","pop6",[]],["push6",null,"Z6","accept6",["Z6"]],["pop6",null,"Z6","accept6",["Z6"]]],"input":["a6","a6","a6","b6","b6","b6"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z6\",\"final_states\":[\"accept6\"],\"input\":[\"a6\",\"a6\",\"a6\",\"b6\",\"b6\",\"b6\"],\"input_alphabet\":[\"a6\",\"b6\"],\"max_steps\":1,\"stack_alphabet\":[\"A6\",\"Z6\"],\"start_state\":\"push6\",\"states\":[\"accept6\",\"pop6\",\"push6\"],\"transitions\":[[\"pop6\",\"b6\",\"A6\",\"pop6\",[]],[\"pop6\",null,\"Z6\",\"accept6\",[\"Z6\"]],[\"push6\",\"a6\",\"A6\",\"push6\",[\"A6\",\"A6\"]],[\"push6\",\"a6\",\"Z6\",\"push6\",[\"Z6\",\"A6\"]],[\"push6\",\"b6\",\"A6\",\"pop6\",[]],[\"push6\",null,\"Z6\",\"accept6\",[\"Z6\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0083","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push7\",\"pop7\",\"accept7\"],\"input_alphabet\":[\"a7\",\"b7\"],\"stack_alphabet\":[\"Z7\",\"A7\"],\"start_state\":\"push7\",\"bottom_symbol\":\"Z7\",\"final_states\":[\"accept7\"],\"transitions\":[[\"push7\",\"a7\",\"Z7\",\"push7\",[\"Z7\",\"A7\"]],[\"push7\",\"a7\",\"A7\",\"push7\",[\"A7\",\"A7\"]],[\"push7\",\"b7\",\"A7\",\"pop7\",[]],[\"pop7\",\"b7\",\"A7\",\"pop7\",[]],[\"push7\",null,\"Z7\",\"accept7\",[\"Z7\"]],[\"pop7\",null,\"Z7\",\"accept7\",[\"Z7\"]]],\"input\":[\"a7\",\"a7\",\"a7\",\"a7\",\"b7\",\"b7\",\"b7\",\"b7\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a7, a7, a7, a7, b7, b7, b7, b7], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a7, a7, a7, a7, b7, b7, b7, b7], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107083,"parameters":{"states":["push7","pop7","accept7"],"input_alphabet":["a7","b7"],"stack_alphabet":["Z7","A7"],"start_state":"push7","bottom_symbol":"Z7","final_states":["accept7"],"transitions":[["push7","a7","Z7","push7",["Z7","A7"]],["push7","a7","A7","push7",["A7","A7"]],["push7","b7","A7","pop7",[]],["pop7","b7","A7","pop7",[]],["push7",null,"Z7","accept7",["Z7"]],["pop7",null,"Z7","accept7",["Z7"]]],"input":["a7","a7","a7","a7","b7","b7","b7","b7"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z7\",\"final_states\":[\"accept7\"],\"input\":[\"a7\",\"a7\",\"a7\",\"a7\",\"b7\",\"b7\",\"b7\",\"b7\"],\"input_alphabet\":[\"a7\",\"b7\"],\"max_steps\":1,\"stack_alphabet\":[\"A7\",\"Z7\"],\"start_state\":\"push7\",\"states\":[\"accept7\",\"pop7\",\"push7\"],\"transitions\":[[\"pop7\",\"b7\",\"A7\",\"pop7\",[]],[\"pop7\",null,\"Z7\",\"accept7\",[\"Z7\"]],[\"push7\",\"a7\",\"A7\",\"push7\",[\"A7\",\"A7\"]],[\"push7\",\"a7\",\"Z7\",\"push7\",[\"Z7\",\"A7\"]],[\"push7\",\"b7\",\"A7\",\"pop7\",[]],[\"push7\",null,\"Z7\",\"accept7\",[\"Z7\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0084","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push8\",\"pop8\",\"accept8\"],\"input_alphabet\":[\"a8\",\"b8\"],\"stack_alphabet\":[\"Z8\",\"A8\"],\"start_state\":\"push8\",\"bottom_symbol\":\"Z8\",\"final_states\":[\"accept8\"],\"transitions\":[[\"push8\",\"a8\",\"Z8\",\"push8\",[\"Z8\",\"A8\"]],[\"push8\",\"a8\",\"A8\",\"push8\",[\"A8\",\"A8\"]],[\"push8\",\"b8\",\"A8\",\"pop8\",[]],[\"pop8\",\"b8\",\"A8\",\"pop8\",[]],[\"push8\",null,\"Z8\",\"accept8\",[\"Z8\"]],[\"pop8\",null,\"Z8\",\"accept8\",[\"Z8\"]]],\"input\":[\"a8\",\"b8\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a8, b8], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a8, b8], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107084,"parameters":{"states":["push8","pop8","accept8"],"input_alphabet":["a8","b8"],"stack_alphabet":["Z8","A8"],"start_state":"push8","bottom_symbol":"Z8","final_states":["accept8"],"transitions":[["push8","a8","Z8","push8",["Z8","A8"]],["push8","a8","A8","push8",["A8","A8"]],["push8","b8","A8","pop8",[]],["pop8","b8","A8","pop8",[]],["push8",null,"Z8","accept8",["Z8"]],["pop8",null,"Z8","accept8",["Z8"]]],"input":["a8","b8"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z8\",\"final_states\":[\"accept8\"],\"input\":[\"a8\",\"b8\"],\"input_alphabet\":[\"a8\",\"b8\"],\"max_steps\":1,\"stack_alphabet\":[\"A8\",\"Z8\"],\"start_state\":\"push8\",\"states\":[\"accept8\",\"pop8\",\"push8\"],\"transitions\":[[\"pop8\",\"b8\",\"A8\",\"pop8\",[]],[\"pop8\",null,\"Z8\",\"accept8\",[\"Z8\"]],[\"push8\",\"a8\",\"A8\",\"push8\",[\"A8\",\"A8\"]],[\"push8\",\"a8\",\"Z8\",\"push8\",[\"Z8\",\"A8\"]],[\"push8\",\"b8\",\"A8\",\"pop8\",[]],[\"push8\",null,\"Z8\",\"accept8\",[\"Z8\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0085","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push9\",\"pop9\",\"accept9\"],\"input_alphabet\":[\"a9\",\"b9\"],\"stack_alphabet\":[\"Z9\",\"A9\"],\"start_state\":\"push9\",\"bottom_symbol\":\"Z9\",\"final_states\":[\"accept9\"],\"transitions\":[[\"push9\",\"a9\",\"Z9\",\"push9\",[\"Z9\",\"A9\"]],[\"push9\",\"a9\",\"A9\",\"push9\",[\"A9\",\"A9\"]],[\"push9\",\"b9\",\"A9\",\"pop9\",[]],[\"pop9\",\"b9\",\"A9\",\"pop9\",[]],[\"push9\",null,\"Z9\",\"accept9\",[\"Z9\"]],[\"pop9\",null,\"Z9\",\"accept9\",[\"Z9\"]]],\"input\":[\"a9\",\"a9\",\"b9\",\"b9\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a9, a9, b9, b9], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a9, a9, b9, b9], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107085,"parameters":{"states":["push9","pop9","accept9"],"input_alphabet":["a9","b9"],"stack_alphabet":["Z9","A9"],"start_state":"push9","bottom_symbol":"Z9","final_states":["accept9"],"transitions":[["push9","a9","Z9","push9",["Z9","A9"]],["push9","a9","A9","push9",["A9","A9"]],["push9","b9","A9","pop9",[]],["pop9","b9","A9","pop9",[]],["push9",null,"Z9","accept9",["Z9"]],["pop9",null,"Z9","accept9",["Z9"]]],"input":["a9","a9","b9","b9"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z9\",\"final_states\":[\"accept9\"],\"input\":[\"a9\",\"a9\",\"b9\",\"b9\"],\"input_alphabet\":[\"a9\",\"b9\"],\"max_steps\":1,\"stack_alphabet\":[\"A9\",\"Z9\"],\"start_state\":\"push9\",\"states\":[\"accept9\",\"pop9\",\"push9\"],\"transitions\":[[\"pop9\",\"b9\",\"A9\",\"pop9\",[]],[\"pop9\",null,\"Z9\",\"accept9\",[\"Z9\"]],[\"push9\",\"a9\",\"A9\",\"push9\",[\"A9\",\"A9\"]],[\"push9\",\"a9\",\"Z9\",\"push9\",[\"Z9\",\"A9\"]],[\"push9\",\"b9\",\"A9\",\"pop9\",[]],[\"push9\",null,\"Z9\",\"accept9\",[\"Z9\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0086","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push10\",\"pop10\",\"accept10\"],\"input_alphabet\":[\"a10\",\"b10\"],\"stack_alphabet\":[\"Z10\",\"A10\"],\"start_state\":\"push10\",\"bottom_symbol\":\"Z10\",\"final_states\":[\"accept10\"],\"transitions\":[[\"push10\",\"a10\",\"Z10\",\"push10\",[\"Z10\",\"A10\"]],[\"push10\",\"a10\",\"A10\",\"push10\",[\"A10\",\"A10\"]],[\"push10\",\"b10\",\"A10\",\"pop10\",[]],[\"pop10\",\"b10\",\"A10\",\"pop10\",[]],[\"push10\",null,\"Z10\",\"accept10\",[\"Z10\"]],[\"pop10\",null,\"Z10\",\"accept10\",[\"Z10\"]]],\"input\":[\"a10\",\"a10\",\"a10\",\"b10\",\"b10\",\"b10\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a10, a10, a10, b10, b10, b10], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a10, a10, a10, b10, b10, b10], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107086,"parameters":{"states":["push10","pop10","accept10"],"input_alphabet":["a10","b10"],"stack_alphabet":["Z10","A10"],"start_state":"push10","bottom_symbol":"Z10","final_states":["accept10"],"transitions":[["push10","a10","Z10","push10",["Z10","A10"]],["push10","a10","A10","push10",["A10","A10"]],["push10","b10","A10","pop10",[]],["pop10","b10","A10","pop10",[]],["push10",null,"Z10","accept10",["Z10"]],["pop10",null,"Z10","accept10",["Z10"]]],"input":["a10","a10","a10","b10","b10","b10"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z10\",\"final_states\":[\"accept10\"],\"input\":[\"a10\",\"a10\",\"a10\",\"b10\",\"b10\",\"b10\"],\"input_alphabet\":[\"a10\",\"b10\"],\"max_steps\":1,\"stack_alphabet\":[\"A10\",\"Z10\"],\"start_state\":\"push10\",\"states\":[\"accept10\",\"pop10\",\"push10\"],\"transitions\":[[\"pop10\",\"b10\",\"A10\",\"pop10\",[]],[\"pop10\",null,\"Z10\",\"accept10\",[\"Z10\"]],[\"push10\",\"a10\",\"A10\",\"push10\",[\"A10\",\"A10\"]],[\"push10\",\"a10\",\"Z10\",\"push10\",[\"Z10\",\"A10\"]],[\"push10\",\"b10\",\"A10\",\"pop10\",[]],[\"push10\",null,\"Z10\",\"accept10\",[\"Z10\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0087","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push11\",\"pop11\",\"accept11\"],\"input_alphabet\":[\"a11\",\"b11\"],\"stack_alphabet\":[\"Z11\",\"A11\"],\"start_state\":\"push11\",\"bottom_symbol\":\"Z11\",\"final_states\":[\"accept11\"],\"transitions\":[[\"push11\",\"a11\",\"Z11\",\"push11\",[\"Z11\",\"A11\"]],[\"push11\",\"a11\",\"A11\",\"push11\",[\"A11\",\"A11\"]],[\"push11\",\"b11\",\"A11\",\"pop11\",[]],[\"pop11\",\"b11\",\"A11\",\"pop11\",[]],[\"push11\",null,\"Z11\",\"accept11\",[\"Z11\"]],[\"pop11\",null,\"Z11\",\"accept11\",[\"Z11\"]]],\"input\":[\"a11\",\"a11\",\"a11\",\"a11\",\"b11\",\"b11\",\"b11\",\"b11\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a11, a11, a11, a11, b11, b11, b11, b11], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a11, a11, a11, a11, b11, b11, b11, b11], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107087,"parameters":{"states":["push11","pop11","accept11"],"input_alphabet":["a11","b11"],"stack_alphabet":["Z11","A11"],"start_state":"push11","bottom_symbol":"Z11","final_states":["accept11"],"transitions":[["push11","a11","Z11","push11",["Z11","A11"]],["push11","a11","A11","push11",["A11","A11"]],["push11","b11","A11","pop11",[]],["pop11","b11","A11","pop11",[]],["push11",null,"Z11","accept11",["Z11"]],["pop11",null,"Z11","accept11",["Z11"]]],"input":["a11","a11","a11","a11","b11","b11","b11","b11"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z11\",\"final_states\":[\"accept11\"],\"input\":[\"a11\",\"a11\",\"a11\",\"a11\",\"b11\",\"b11\",\"b11\",\"b11\"],\"input_alphabet\":[\"a11\",\"b11\"],\"max_steps\":1,\"stack_alphabet\":[\"A11\",\"Z11\"],\"start_state\":\"push11\",\"states\":[\"accept11\",\"pop11\",\"push11\"],\"transitions\":[[\"pop11\",\"b11\",\"A11\",\"pop11\",[]],[\"pop11\",null,\"Z11\",\"accept11\",[\"Z11\"]],[\"push11\",\"a11\",\"A11\",\"push11\",[\"A11\",\"A11\"]],[\"push11\",\"a11\",\"Z11\",\"push11\",[\"Z11\",\"A11\"]],[\"push11\",\"b11\",\"A11\",\"pop11\",[]],[\"push11\",null,\"Z11\",\"accept11\",[\"Z11\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0088","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push12\",\"pop12\",\"accept12\"],\"input_alphabet\":[\"a12\",\"b12\"],\"stack_alphabet\":[\"Z12\",\"A12\"],\"start_state\":\"push12\",\"bottom_symbol\":\"Z12\",\"final_states\":[\"accept12\"],\"transitions\":[[\"push12\",\"a12\",\"Z12\",\"push12\",[\"Z12\",\"A12\"]],[\"push12\",\"a12\",\"A12\",\"push12\",[\"A12\",\"A12\"]],[\"push12\",\"b12\",\"A12\",\"pop12\",[]],[\"pop12\",\"b12\",\"A12\",\"pop12\",[]],[\"push12\",null,\"Z12\",\"accept12\",[\"Z12\"]],[\"pop12\",null,\"Z12\",\"accept12\",[\"Z12\"]]],\"input\":[\"a12\",\"b12\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a12, b12], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a12, b12], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107088,"parameters":{"states":["push12","pop12","accept12"],"input_alphabet":["a12","b12"],"stack_alphabet":["Z12","A12"],"start_state":"push12","bottom_symbol":"Z12","final_states":["accept12"],"transitions":[["push12","a12","Z12","push12",["Z12","A12"]],["push12","a12","A12","push12",["A12","A12"]],["push12","b12","A12","pop12",[]],["pop12","b12","A12","pop12",[]],["push12",null,"Z12","accept12",["Z12"]],["pop12",null,"Z12","accept12",["Z12"]]],"input":["a12","b12"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z12\",\"final_states\":[\"accept12\"],\"input\":[\"a12\",\"b12\"],\"input_alphabet\":[\"a12\",\"b12\"],\"max_steps\":1,\"stack_alphabet\":[\"A12\",\"Z12\"],\"start_state\":\"push12\",\"states\":[\"accept12\",\"pop12\",\"push12\"],\"transitions\":[[\"pop12\",\"b12\",\"A12\",\"pop12\",[]],[\"pop12\",null,\"Z12\",\"accept12\",[\"Z12\"]],[\"push12\",\"a12\",\"A12\",\"push12\",[\"A12\",\"A12\"]],[\"push12\",\"a12\",\"Z12\",\"push12\",[\"Z12\",\"A12\"]],[\"push12\",\"b12\",\"A12\",\"pop12\",[]],[\"push12\",null,\"Z12\",\"accept12\",[\"Z12\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0089","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push13\",\"pop13\",\"accept13\"],\"input_alphabet\":[\"a13\",\"b13\"],\"stack_alphabet\":[\"Z13\",\"A13\"],\"start_state\":\"push13\",\"bottom_symbol\":\"Z13\",\"final_states\":[\"accept13\"],\"transitions\":[[\"push13\",\"a13\",\"Z13\",\"push13\",[\"Z13\",\"A13\"]],[\"push13\",\"a13\",\"A13\",\"push13\",[\"A13\",\"A13\"]],[\"push13\",\"b13\",\"A13\",\"pop13\",[]],[\"pop13\",\"b13\",\"A13\",\"pop13\",[]],[\"push13\",null,\"Z13\",\"accept13\",[\"Z13\"]],[\"pop13\",null,\"Z13\",\"accept13\",[\"Z13\"]]],\"input\":[\"a13\",\"a13\",\"b13\",\"b13\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a13, a13, b13, b13], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a13, a13, b13, b13], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107089,"parameters":{"states":["push13","pop13","accept13"],"input_alphabet":["a13","b13"],"stack_alphabet":["Z13","A13"],"start_state":"push13","bottom_symbol":"Z13","final_states":["accept13"],"transitions":[["push13","a13","Z13","push13",["Z13","A13"]],["push13","a13","A13","push13",["A13","A13"]],["push13","b13","A13","pop13",[]],["pop13","b13","A13","pop13",[]],["push13",null,"Z13","accept13",["Z13"]],["pop13",null,"Z13","accept13",["Z13"]]],"input":["a13","a13","b13","b13"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z13\",\"final_states\":[\"accept13\"],\"input\":[\"a13\",\"a13\",\"b13\",\"b13\"],\"input_alphabet\":[\"a13\",\"b13\"],\"max_steps\":1,\"stack_alphabet\":[\"A13\",\"Z13\"],\"start_state\":\"push13\",\"states\":[\"accept13\",\"pop13\",\"push13\"],\"transitions\":[[\"pop13\",\"b13\",\"A13\",\"pop13\",[]],[\"pop13\",null,\"Z13\",\"accept13\",[\"Z13\"]],[\"push13\",\"a13\",\"A13\",\"push13\",[\"A13\",\"A13\"]],[\"push13\",\"a13\",\"Z13\",\"push13\",[\"Z13\",\"A13\"]],[\"push13\",\"b13\",\"A13\",\"pop13\",[]],[\"push13\",null,\"Z13\",\"accept13\",[\"Z13\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0090","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push14\",\"pop14\",\"accept14\"],\"input_alphabet\":[\"a14\",\"b14\"],\"stack_alphabet\":[\"Z14\",\"A14\"],\"start_state\":\"push14\",\"bottom_symbol\":\"Z14\",\"final_states\":[\"accept14\"],\"transitions\":[[\"push14\",\"a14\",\"Z14\",\"push14\",[\"Z14\",\"A14\"]],[\"push14\",\"a14\",\"A14\",\"push14\",[\"A14\",\"A14\"]],[\"push14\",\"b14\",\"A14\",\"pop14\",[]],[\"pop14\",\"b14\",\"A14\",\"pop14\",[]],[\"push14\",null,\"Z14\",\"accept14\",[\"Z14\"]],[\"pop14\",null,\"Z14\",\"accept14\",[\"Z14\"]]],\"input\":[\"a14\",\"a14\",\"a14\",\"b14\",\"b14\",\"b14\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a14, a14, a14, b14, b14, b14], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a14, a14, a14, b14, b14, b14], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107090,"parameters":{"states":["push14","pop14","accept14"],"input_alphabet":["a14","b14"],"stack_alphabet":["Z14","A14"],"start_state":"push14","bottom_symbol":"Z14","final_states":["accept14"],"transitions":[["push14","a14","Z14","push14",["Z14","A14"]],["push14","a14","A14","push14",["A14","A14"]],["push14","b14","A14","pop14",[]],["pop14","b14","A14","pop14",[]],["push14",null,"Z14","accept14",["Z14"]],["pop14",null,"Z14","accept14",["Z14"]]],"input":["a14","a14","a14","b14","b14","b14"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z14\",\"final_states\":[\"accept14\"],\"input\":[\"a14\",\"a14\",\"a14\",\"b14\",\"b14\",\"b14\"],\"input_alphabet\":[\"a14\",\"b14\"],\"max_steps\":1,\"stack_alphabet\":[\"A14\",\"Z14\"],\"start_state\":\"push14\",\"states\":[\"accept14\",\"pop14\",\"push14\"],\"transitions\":[[\"pop14\",\"b14\",\"A14\",\"pop14\",[]],[\"pop14\",null,\"Z14\",\"accept14\",[\"Z14\"]],[\"push14\",\"a14\",\"A14\",\"push14\",[\"A14\",\"A14\"]],[\"push14\",\"a14\",\"Z14\",\"push14\",[\"Z14\",\"A14\"]],[\"push14\",\"b14\",\"A14\",\"pop14\",[]],[\"push14\",null,\"Z14\",\"accept14\",[\"Z14\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0091","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push15\",\"pop15\",\"accept15\"],\"input_alphabet\":[\"a15\",\"b15\"],\"stack_alphabet\":[\"Z15\",\"A15\"],\"start_state\":\"push15\",\"bottom_symbol\":\"Z15\",\"final_states\":[\"accept15\"],\"transitions\":[[\"push15\",\"a15\",\"Z15\",\"push15\",[\"Z15\",\"A15\"]],[\"push15\",\"a15\",\"A15\",\"push15\",[\"A15\",\"A15\"]],[\"push15\",\"b15\",\"A15\",\"pop15\",[]],[\"pop15\",\"b15\",\"A15\",\"pop15\",[]],[\"push15\",null,\"Z15\",\"accept15\",[\"Z15\"]],[\"pop15\",null,\"Z15\",\"accept15\",[\"Z15\"]]],\"input\":[\"a15\",\"a15\",\"a15\",\"a15\",\"b15\",\"b15\",\"b15\",\"b15\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a15, a15, a15, a15, b15, b15, b15, b15], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a15, a15, a15, a15, b15, b15, b15, b15], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107091,"parameters":{"states":["push15","pop15","accept15"],"input_alphabet":["a15","b15"],"stack_alphabet":["Z15","A15"],"start_state":"push15","bottom_symbol":"Z15","final_states":["accept15"],"transitions":[["push15","a15","Z15","push15",["Z15","A15"]],["push15","a15","A15","push15",["A15","A15"]],["push15","b15","A15","pop15",[]],["pop15","b15","A15","pop15",[]],["push15",null,"Z15","accept15",["Z15"]],["pop15",null,"Z15","accept15",["Z15"]]],"input":["a15","a15","a15","a15","b15","b15","b15","b15"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z15\",\"final_states\":[\"accept15\"],\"input\":[\"a15\",\"a15\",\"a15\",\"a15\",\"b15\",\"b15\",\"b15\",\"b15\"],\"input_alphabet\":[\"a15\",\"b15\"],\"max_steps\":1,\"stack_alphabet\":[\"A15\",\"Z15\"],\"start_state\":\"push15\",\"states\":[\"accept15\",\"pop15\",\"push15\"],\"transitions\":[[\"pop15\",\"b15\",\"A15\",\"pop15\",[]],[\"pop15\",null,\"Z15\",\"accept15\",[\"Z15\"]],[\"push15\",\"a15\",\"A15\",\"push15\",[\"A15\",\"A15\"]],[\"push15\",\"a15\",\"Z15\",\"push15\",[\"Z15\",\"A15\"]],[\"push15\",\"b15\",\"A15\",\"pop15\",[]],[\"push15\",null,\"Z15\",\"accept15\",[\"Z15\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0092","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push16\",\"pop16\",\"accept16\"],\"input_alphabet\":[\"a16\",\"b16\"],\"stack_alphabet\":[\"Z16\",\"A16\"],\"start_state\":\"push16\",\"bottom_symbol\":\"Z16\",\"final_states\":[\"accept16\"],\"transitions\":[[\"push16\",\"a16\",\"Z16\",\"push16\",[\"Z16\",\"A16\"]],[\"push16\",\"a16\",\"A16\",\"push16\",[\"A16\",\"A16\"]],[\"push16\",\"b16\",\"A16\",\"pop16\",[]],[\"pop16\",\"b16\",\"A16\",\"pop16\",[]],[\"push16\",null,\"Z16\",\"accept16\",[\"Z16\"]],[\"pop16\",null,\"Z16\",\"accept16\",[\"Z16\"]]],\"input\":[\"a16\",\"b16\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a16, b16], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a16, b16], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107092,"parameters":{"states":["push16","pop16","accept16"],"input_alphabet":["a16","b16"],"stack_alphabet":["Z16","A16"],"start_state":"push16","bottom_symbol":"Z16","final_states":["accept16"],"transitions":[["push16","a16","Z16","push16",["Z16","A16"]],["push16","a16","A16","push16",["A16","A16"]],["push16","b16","A16","pop16",[]],["pop16","b16","A16","pop16",[]],["push16",null,"Z16","accept16",["Z16"]],["pop16",null,"Z16","accept16",["Z16"]]],"input":["a16","b16"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z16\",\"final_states\":[\"accept16\"],\"input\":[\"a16\",\"b16\"],\"input_alphabet\":[\"a16\",\"b16\"],\"max_steps\":1,\"stack_alphabet\":[\"A16\",\"Z16\"],\"start_state\":\"push16\",\"states\":[\"accept16\",\"pop16\",\"push16\"],\"transitions\":[[\"pop16\",\"b16\",\"A16\",\"pop16\",[]],[\"pop16\",null,\"Z16\",\"accept16\",[\"Z16\"]],[\"push16\",\"a16\",\"A16\",\"push16\",[\"A16\",\"A16\"]],[\"push16\",\"a16\",\"Z16\",\"push16\",[\"Z16\",\"A16\"]],[\"push16\",\"b16\",\"A16\",\"pop16\",[]],[\"push16\",null,\"Z16\",\"accept16\",[\"Z16\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0093","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push17\",\"pop17\",\"accept17\"],\"input_alphabet\":[\"a17\",\"b17\"],\"stack_alphabet\":[\"Z17\",\"A17\"],\"start_state\":\"push17\",\"bottom_symbol\":\"Z17\",\"final_states\":[\"accept17\"],\"transitions\":[[\"push17\",\"a17\",\"Z17\",\"push17\",[\"Z17\",\"A17\"]],[\"push17\",\"a17\",\"A17\",\"push17\",[\"A17\",\"A17\"]],[\"push17\",\"b17\",\"A17\",\"pop17\",[]],[\"pop17\",\"b17\",\"A17\",\"pop17\",[]],[\"push17\",null,\"Z17\",\"accept17\",[\"Z17\"]],[\"pop17\",null,\"Z17\",\"accept17\",[\"Z17\"]]],\"input\":[\"a17\",\"a17\",\"b17\",\"b17\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a17, a17, b17, b17], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a17, a17, b17, b17], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107093,"parameters":{"states":["push17","pop17","accept17"],"input_alphabet":["a17","b17"],"stack_alphabet":["Z17","A17"],"start_state":"push17","bottom_symbol":"Z17","final_states":["accept17"],"transitions":[["push17","a17","Z17","push17",["Z17","A17"]],["push17","a17","A17","push17",["A17","A17"]],["push17","b17","A17","pop17",[]],["pop17","b17","A17","pop17",[]],["push17",null,"Z17","accept17",["Z17"]],["pop17",null,"Z17","accept17",["Z17"]]],"input":["a17","a17","b17","b17"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z17\",\"final_states\":[\"accept17\"],\"input\":[\"a17\",\"a17\",\"b17\",\"b17\"],\"input_alphabet\":[\"a17\",\"b17\"],\"max_steps\":1,\"stack_alphabet\":[\"A17\",\"Z17\"],\"start_state\":\"push17\",\"states\":[\"accept17\",\"pop17\",\"push17\"],\"transitions\":[[\"pop17\",\"b17\",\"A17\",\"pop17\",[]],[\"pop17\",null,\"Z17\",\"accept17\",[\"Z17\"]],[\"push17\",\"a17\",\"A17\",\"push17\",[\"A17\",\"A17\"]],[\"push17\",\"a17\",\"Z17\",\"push17\",[\"Z17\",\"A17\"]],[\"push17\",\"b17\",\"A17\",\"pop17\",[]],[\"push17\",null,\"Z17\",\"accept17\",[\"Z17\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0094","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push18\",\"pop18\",\"accept18\"],\"input_alphabet\":[\"a18\",\"b18\"],\"stack_alphabet\":[\"Z18\",\"A18\"],\"start_state\":\"push18\",\"bottom_symbol\":\"Z18\",\"final_states\":[\"accept18\"],\"transitions\":[[\"push18\",\"a18\",\"Z18\",\"push18\",[\"Z18\",\"A18\"]],[\"push18\",\"a18\",\"A18\",\"push18\",[\"A18\",\"A18\"]],[\"push18\",\"b18\",\"A18\",\"pop18\",[]],[\"pop18\",\"b18\",\"A18\",\"pop18\",[]],[\"push18\",null,\"Z18\",\"accept18\",[\"Z18\"]],[\"pop18\",null,\"Z18\",\"accept18\",[\"Z18\"]]],\"input\":[\"a18\",\"a18\",\"a18\",\"b18\",\"b18\",\"b18\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a18, a18, a18, b18, b18, b18], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a18, a18, a18, b18, b18, b18], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107094,"parameters":{"states":["push18","pop18","accept18"],"input_alphabet":["a18","b18"],"stack_alphabet":["Z18","A18"],"start_state":"push18","bottom_symbol":"Z18","final_states":["accept18"],"transitions":[["push18","a18","Z18","push18",["Z18","A18"]],["push18","a18","A18","push18",["A18","A18"]],["push18","b18","A18","pop18",[]],["pop18","b18","A18","pop18",[]],["push18",null,"Z18","accept18",["Z18"]],["pop18",null,"Z18","accept18",["Z18"]]],"input":["a18","a18","a18","b18","b18","b18"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z18\",\"final_states\":[\"accept18\"],\"input\":[\"a18\",\"a18\",\"a18\",\"b18\",\"b18\",\"b18\"],\"input_alphabet\":[\"a18\",\"b18\"],\"max_steps\":1,\"stack_alphabet\":[\"A18\",\"Z18\"],\"start_state\":\"push18\",\"states\":[\"accept18\",\"pop18\",\"push18\"],\"transitions\":[[\"pop18\",\"b18\",\"A18\",\"pop18\",[]],[\"pop18\",null,\"Z18\",\"accept18\",[\"Z18\"]],[\"push18\",\"a18\",\"A18\",\"push18\",[\"A18\",\"A18\"]],[\"push18\",\"a18\",\"Z18\",\"push18\",[\"Z18\",\"A18\"]],[\"push18\",\"b18\",\"A18\",\"pop18\",[]],[\"push18\",null,\"Z18\",\"accept18\",[\"Z18\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0095","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push19\",\"pop19\",\"accept19\"],\"input_alphabet\":[\"a19\",\"b19\"],\"stack_alphabet\":[\"Z19\",\"A19\"],\"start_state\":\"push19\",\"bottom_symbol\":\"Z19\",\"final_states\":[\"accept19\"],\"transitions\":[[\"push19\",\"a19\",\"Z19\",\"push19\",[\"Z19\",\"A19\"]],[\"push19\",\"a19\",\"A19\",\"push19\",[\"A19\",\"A19\"]],[\"push19\",\"b19\",\"A19\",\"pop19\",[]],[\"pop19\",\"b19\",\"A19\",\"pop19\",[]],[\"push19\",null,\"Z19\",\"accept19\",[\"Z19\"]],[\"pop19\",null,\"Z19\",\"accept19\",[\"Z19\"]]],\"input\":[\"a19\",\"a19\",\"a19\",\"a19\",\"b19\",\"b19\",\"b19\",\"b19\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a19, a19, a19, a19, b19, b19, b19, b19], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a19, a19, a19, a19, b19, b19, b19, b19], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107095,"parameters":{"states":["push19","pop19","accept19"],"input_alphabet":["a19","b19"],"stack_alphabet":["Z19","A19"],"start_state":"push19","bottom_symbol":"Z19","final_states":["accept19"],"transitions":[["push19","a19","Z19","push19",["Z19","A19"]],["push19","a19","A19","push19",["A19","A19"]],["push19","b19","A19","pop19",[]],["pop19","b19","A19","pop19",[]],["push19",null,"Z19","accept19",["Z19"]],["pop19",null,"Z19","accept19",["Z19"]]],"input":["a19","a19","a19","a19","b19","b19","b19","b19"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z19\",\"final_states\":[\"accept19\"],\"input\":[\"a19\",\"a19\",\"a19\",\"a19\",\"b19\",\"b19\",\"b19\",\"b19\"],\"input_alphabet\":[\"a19\",\"b19\"],\"max_steps\":1,\"stack_alphabet\":[\"A19\",\"Z19\"],\"start_state\":\"push19\",\"states\":[\"accept19\",\"pop19\",\"push19\"],\"transitions\":[[\"pop19\",\"b19\",\"A19\",\"pop19\",[]],[\"pop19\",null,\"Z19\",\"accept19\",[\"Z19\"]],[\"push19\",\"a19\",\"A19\",\"push19\",[\"A19\",\"A19\"]],[\"push19\",\"a19\",\"Z19\",\"push19\",[\"Z19\",\"A19\"]],[\"push19\",\"b19\",\"A19\",\"pop19\",[]],[\"push19\",null,\"Z19\",\"accept19\",[\"Z19\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0096","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push20\",\"pop20\",\"accept20\"],\"input_alphabet\":[\"a20\",\"b20\"],\"stack_alphabet\":[\"Z20\",\"A20\"],\"start_state\":\"push20\",\"bottom_symbol\":\"Z20\",\"final_states\":[\"accept20\"],\"transitions\":[[\"push20\",\"a20\",\"Z20\",\"push20\",[\"Z20\",\"A20\"]],[\"push20\",\"a20\",\"A20\",\"push20\",[\"A20\",\"A20\"]],[\"push20\",\"b20\",\"A20\",\"pop20\",[]],[\"pop20\",\"b20\",\"A20\",\"pop20\",[]],[\"push20\",null,\"Z20\",\"accept20\",[\"Z20\"]],[\"pop20\",null,\"Z20\",\"accept20\",[\"Z20\"]]],\"input\":[\"a20\",\"b20\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a20, b20], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a20, b20], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107096,"parameters":{"states":["push20","pop20","accept20"],"input_alphabet":["a20","b20"],"stack_alphabet":["Z20","A20"],"start_state":"push20","bottom_symbol":"Z20","final_states":["accept20"],"transitions":[["push20","a20","Z20","push20",["Z20","A20"]],["push20","a20","A20","push20",["A20","A20"]],["push20","b20","A20","pop20",[]],["pop20","b20","A20","pop20",[]],["push20",null,"Z20","accept20",["Z20"]],["pop20",null,"Z20","accept20",["Z20"]]],"input":["a20","b20"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z20\",\"final_states\":[\"accept20\"],\"input\":[\"a20\",\"b20\"],\"input_alphabet\":[\"a20\",\"b20\"],\"max_steps\":1,\"stack_alphabet\":[\"A20\",\"Z20\"],\"start_state\":\"push20\",\"states\":[\"accept20\",\"pop20\",\"push20\"],\"transitions\":[[\"pop20\",\"b20\",\"A20\",\"pop20\",[]],[\"pop20\",null,\"Z20\",\"accept20\",[\"Z20\"]],[\"push20\",\"a20\",\"A20\",\"push20\",[\"A20\",\"A20\"]],[\"push20\",\"a20\",\"Z20\",\"push20\",[\"Z20\",\"A20\"]],[\"push20\",\"b20\",\"A20\",\"pop20\",[]],[\"push20\",null,\"Z20\",\"accept20\",[\"Z20\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0097","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push21\",\"pop21\",\"accept21\"],\"input_alphabet\":[\"a21\",\"b21\"],\"stack_alphabet\":[\"Z21\",\"A21\"],\"start_state\":\"push21\",\"bottom_symbol\":\"Z21\",\"final_states\":[\"accept21\"],\"transitions\":[[\"push21\",\"a21\",\"Z21\",\"push21\",[\"Z21\",\"A21\"]],[\"push21\",\"a21\",\"A21\",\"push21\",[\"A21\",\"A21\"]],[\"push21\",\"b21\",\"A21\",\"pop21\",[]],[\"pop21\",\"b21\",\"A21\",\"pop21\",[]],[\"push21\",null,\"Z21\",\"accept21\",[\"Z21\"]],[\"pop21\",null,\"Z21\",\"accept21\",[\"Z21\"]]],\"input\":[\"a21\",\"a21\",\"b21\",\"b21\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a21, a21, b21, b21], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a21, a21, b21, b21], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107097,"parameters":{"states":["push21","pop21","accept21"],"input_alphabet":["a21","b21"],"stack_alphabet":["Z21","A21"],"start_state":"push21","bottom_symbol":"Z21","final_states":["accept21"],"transitions":[["push21","a21","Z21","push21",["Z21","A21"]],["push21","a21","A21","push21",["A21","A21"]],["push21","b21","A21","pop21",[]],["pop21","b21","A21","pop21",[]],["push21",null,"Z21","accept21",["Z21"]],["pop21",null,"Z21","accept21",["Z21"]]],"input":["a21","a21","b21","b21"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z21\",\"final_states\":[\"accept21\"],\"input\":[\"a21\",\"a21\",\"b21\",\"b21\"],\"input_alphabet\":[\"a21\",\"b21\"],\"max_steps\":1,\"stack_alphabet\":[\"A21\",\"Z21\"],\"start_state\":\"push21\",\"states\":[\"accept21\",\"pop21\",\"push21\"],\"transitions\":[[\"pop21\",\"b21\",\"A21\",\"pop21\",[]],[\"pop21\",null,\"Z21\",\"accept21\",[\"Z21\"]],[\"push21\",\"a21\",\"A21\",\"push21\",[\"A21\",\"A21\"]],[\"push21\",\"a21\",\"Z21\",\"push21\",[\"Z21\",\"A21\"]],[\"push21\",\"b21\",\"A21\",\"pop21\",[]],[\"push21\",null,\"Z21\",\"accept21\",[\"Z21\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0098","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push22\",\"pop22\",\"accept22\"],\"input_alphabet\":[\"a22\",\"b22\"],\"stack_alphabet\":[\"Z22\",\"A22\"],\"start_state\":\"push22\",\"bottom_symbol\":\"Z22\",\"final_states\":[\"accept22\"],\"transitions\":[[\"push22\",\"a22\",\"Z22\",\"push22\",[\"Z22\",\"A22\"]],[\"push22\",\"a22\",\"A22\",\"push22\",[\"A22\",\"A22\"]],[\"push22\",\"b22\",\"A22\",\"pop22\",[]],[\"pop22\",\"b22\",\"A22\",\"pop22\",[]],[\"push22\",null,\"Z22\",\"accept22\",[\"Z22\"]],[\"pop22\",null,\"Z22\",\"accept22\",[\"Z22\"]]],\"input\":[\"a22\",\"a22\",\"a22\",\"b22\",\"b22\",\"b22\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a22, a22, a22, b22, b22, b22], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a22, a22, a22, b22, b22, b22], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107098,"parameters":{"states":["push22","pop22","accept22"],"input_alphabet":["a22","b22"],"stack_alphabet":["Z22","A22"],"start_state":"push22","bottom_symbol":"Z22","final_states":["accept22"],"transitions":[["push22","a22","Z22","push22",["Z22","A22"]],["push22","a22","A22","push22",["A22","A22"]],["push22","b22","A22","pop22",[]],["pop22","b22","A22","pop22",[]],["push22",null,"Z22","accept22",["Z22"]],["pop22",null,"Z22","accept22",["Z22"]]],"input":["a22","a22","a22","b22","b22","b22"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z22\",\"final_states\":[\"accept22\"],\"input\":[\"a22\",\"a22\",\"a22\",\"b22\",\"b22\",\"b22\"],\"input_alphabet\":[\"a22\",\"b22\"],\"max_steps\":1,\"stack_alphabet\":[\"A22\",\"Z22\"],\"start_state\":\"push22\",\"states\":[\"accept22\",\"pop22\",\"push22\"],\"transitions\":[[\"pop22\",\"b22\",\"A22\",\"pop22\",[]],[\"pop22\",null,\"Z22\",\"accept22\",[\"Z22\"]],[\"push22\",\"a22\",\"A22\",\"push22\",[\"A22\",\"A22\"]],[\"push22\",\"a22\",\"Z22\",\"push22\",[\"Z22\",\"A22\"]],[\"push22\",\"b22\",\"A22\",\"pop22\",[]],[\"push22\",null,\"Z22\",\"accept22\",[\"Z22\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0099","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push23\",\"pop23\",\"accept23\"],\"input_alphabet\":[\"a23\",\"b23\"],\"stack_alphabet\":[\"Z23\",\"A23\"],\"start_state\":\"push23\",\"bottom_symbol\":\"Z23\",\"final_states\":[\"accept23\"],\"transitions\":[[\"push23\",\"a23\",\"Z23\",\"push23\",[\"Z23\",\"A23\"]],[\"push23\",\"a23\",\"A23\",\"push23\",[\"A23\",\"A23\"]],[\"push23\",\"b23\",\"A23\",\"pop23\",[]],[\"pop23\",\"b23\",\"A23\",\"pop23\",[]],[\"push23\",null,\"Z23\",\"accept23\",[\"Z23\"]],[\"pop23\",null,\"Z23\",\"accept23\",[\"Z23\"]]],\"input\":[\"a23\",\"a23\",\"a23\",\"a23\",\"b23\",\"b23\",\"b23\",\"b23\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a23, a23, a23, a23, b23, b23, b23, b23], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a23, a23, a23, a23, b23, b23, b23, b23], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107099,"parameters":{"states":["push23","pop23","accept23"],"input_alphabet":["a23","b23"],"stack_alphabet":["Z23","A23"],"start_state":"push23","bottom_symbol":"Z23","final_states":["accept23"],"transitions":[["push23","a23","Z23","push23",["Z23","A23"]],["push23","a23","A23","push23",["A23","A23"]],["push23","b23","A23","pop23",[]],["pop23","b23","A23","pop23",[]],["push23",null,"Z23","accept23",["Z23"]],["pop23",null,"Z23","accept23",["Z23"]]],"input":["a23","a23","a23","a23","b23","b23","b23","b23"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z23\",\"final_states\":[\"accept23\"],\"input\":[\"a23\",\"a23\",\"a23\",\"a23\",\"b23\",\"b23\",\"b23\",\"b23\"],\"input_alphabet\":[\"a23\",\"b23\"],\"max_steps\":1,\"stack_alphabet\":[\"A23\",\"Z23\"],\"start_state\":\"push23\",\"states\":[\"accept23\",\"pop23\",\"push23\"],\"transitions\":[[\"pop23\",\"b23\",\"A23\",\"pop23\",[]],[\"pop23\",null,\"Z23\",\"accept23\",[\"Z23\"]],[\"push23\",\"a23\",\"A23\",\"push23\",[\"A23\",\"A23\"]],[\"push23\",\"a23\",\"Z23\",\"push23\",[\"Z23\",\"A23\"]],[\"push23\",\"b23\",\"A23\",\"pop23\",[]],[\"push23\",null,\"Z23\",\"accept23\",[\"Z23\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r07-pushdown-automaton-0100","batch_id":"batch-20261014-advance-20261110-r07-pushdown-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-pushdown-automaton"],"title_zh":"下推自動機","stem_zh":"transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={\"states\":[\"push24\",\"pop24\",\"accept24\"],\"input_alphabet\":[\"a24\",\"b24\"],\"stack_alphabet\":[\"Z24\",\"A24\"],\"start_state\":\"push24\",\"bottom_symbol\":\"Z24\",\"final_states\":[\"accept24\"],\"transitions\":[[\"push24\",\"a24\",\"Z24\",\"push24\",[\"Z24\",\"A24\"]],[\"push24\",\"a24\",\"A24\",\"push24\",[\"A24\",\"A24\"]],[\"push24\",\"b24\",\"A24\",\"pop24\",[]],[\"pop24\",\"b24\",\"A24\",\"pop24\",[]],[\"push24\",null,\"Z24\",\"accept24\",[\"Z24\"]],[\"pop24\",null,\"Z24\",\"accept24\",[\"Z24\"]]],\"input\":[\"a24\",\"b24\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a24, b24], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)","explanation_zh":"Wave6第四層核對=([a24, b24], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["下推自動機"]},"variant":{"family_id":"qf-mod41-pda-bounded-search-boundary","seed":202611107100,"parameters":{"states":["push24","pop24","accept24"],"input_alphabet":["a24","b24"],"stack_alphabet":["Z24","A24"],"start_state":"push24","bottom_symbol":"Z24","final_states":["accept24"],"transitions":[["push24","a24","Z24","push24",["Z24","A24"]],["push24","a24","A24","push24",["A24","A24"]],["push24","b24","A24","pop24",[]],["pop24","b24","A24","pop24",[]],["push24",null,"Z24","accept24",["Z24"]],["pop24",null,"Z24","accept24",["Z24"]]],"input":["a24","b24"],"max_steps":1,"domain":"Finite_nondeterministic_PDA_final_state_acceptance","operation":"pda-bounded-search-boundary","semantic_template":"qf-mod41-pda-bounded-search-boundary/{\"bottom_symbol\":\"Z24\",\"final_states\":[\"accept24\"],\"input\":[\"a24\",\"b24\"],\"input_alphabet\":[\"a24\",\"b24\"],\"max_steps\":1,\"stack_alphabet\":[\"A24\",\"Z24\"],\"start_state\":\"push24\",\"states\":[\"accept24\",\"pop24\",\"push24\"],\"transitions\":[[\"pop24\",\"b24\",\"A24\",\"pop24\",[]],[\"pop24\",null,\"Z24\",\"accept24\",[\"Z24\"]],[\"push24\",\"a24\",\"A24\",\"push24\",[\"A24\",\"A24\"]],[\"push24\",\"a24\",\"Z24\",\"push24\",[\"Z24\",\"A24\"]],[\"push24\",\"b24\",\"A24\",\"pop24\",[]],[\"push24\",null,\"Z24\",\"accept24\",[\"Z24\"]]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}