{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r07-nondeterministic-finite-automaton-0001","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s0\",\"m0\",\"f0\",\"d0\"],\"alphabet\":[\"a0\",\"b0\"],\"start_state\":\"s0\",\"final_states\":[\"f0\"],\"transitions\":[[\"s0\",null,\"m0\"],[\"s0\",null,\"d0\"],[\"m0\",\"a0\",\"m0\"],[\"m0\",\"b0\",\"f0\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s0, m0, f0, d0], [a0, b0], s0, [f0], [[s0, null, m0], [s0, null, d0], [m0, a0, m0], [m0, b0, f0]], [[s0, a0, []], [s0, b0, []], [f0, a0, []], [f0, b0, []], [d0, a0, []], [d0, b0, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s0, m0, f0, d0], [a0, b0], s0, [f0], [[s0, null, m0], [s0, null, d0], [m0, a0, m0], [m0, b0, f0]], [[s0, a0, []], [s0, b0, []], [f0, a0, []], [f0, b0, []], [d0, a0, []], [d0, b0, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117001,"parameters":{"states":["s0","m0","f0","d0"],"alphabet":["a0","b0"],"start_state":"s0","final_states":["f0"],"transitions":[["s0",null,"m0"],["s0",null,"d0"],["m0","a0","m0"],["m0","b0","f0"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a0\",\"b0\"],\"final_states\":[\"f0\"],\"start_state\":\"s0\",\"states\":[\"d0\",\"f0\",\"m0\",\"s0\"],\"transitions\":[[\"m0\",\"a0\",\"m0\"],[\"m0\",\"b0\",\"f0\"],[\"s0\",null,\"d0\"],[\"s0\",null,\"m0\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0002","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s1\",\"m1\",\"f1\",\"d1\"],\"alphabet\":[\"a1\",\"b1\"],\"start_state\":\"s1\",\"final_states\":[\"f1\"],\"transitions\":[[\"s1\",null,\"m1\"],[\"s1\",null,\"d1\"],[\"m1\",\"a1\",\"m1\"],[\"m1\",\"b1\",\"f1\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s1, m1, f1, d1], [a1, b1], s1, [f1], [[s1, null, m1], [s1, null, d1], [m1, a1, m1], [m1, b1, f1]], [[s1, a1, []], [s1, b1, []], [f1, a1, []], [f1, b1, []], [d1, a1, []], [d1, b1, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s1, m1, f1, d1], [a1, b1], s1, [f1], [[s1, null, m1], [s1, null, d1], [m1, a1, m1], [m1, b1, f1]], [[s1, a1, []], [s1, b1, []], [f1, a1, []], [f1, b1, []], [d1, a1, []], [d1, b1, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117002,"parameters":{"states":["s1","m1","f1","d1"],"alphabet":["a1","b1"],"start_state":"s1","final_states":["f1"],"transitions":[["s1",null,"m1"],["s1",null,"d1"],["m1","a1","m1"],["m1","b1","f1"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a1\",\"b1\"],\"final_states\":[\"f1\"],\"start_state\":\"s1\",\"states\":[\"d1\",\"f1\",\"m1\",\"s1\"],\"transitions\":[[\"m1\",\"a1\",\"m1\"],[\"m1\",\"b1\",\"f1\"],[\"s1\",null,\"d1\"],[\"s1\",null,\"m1\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0003","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s2\",\"m2\",\"f2\",\"d2\"],\"alphabet\":[\"a2\",\"b2\"],\"start_state\":\"s2\",\"final_states\":[\"f2\"],\"transitions\":[[\"s2\",null,\"m2\"],[\"s2\",null,\"d2\"],[\"m2\",\"a2\",\"m2\"],[\"m2\",\"b2\",\"f2\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s2, m2, f2, d2], [a2, b2], s2, [f2], [[s2, null, m2], [s2, null, d2], [m2, a2, m2], [m2, b2, f2]], [[s2, a2, []], [s2, b2, []], [f2, a2, []], [f2, b2, []], [d2, a2, []], [d2, b2, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s2, m2, f2, d2], [a2, b2], s2, [f2], [[s2, null, m2], [s2, null, d2], [m2, a2, m2], [m2, b2, f2]], [[s2, a2, []], [s2, b2, []], [f2, a2, []], [f2, b2, []], [d2, a2, []], [d2, b2, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117003,"parameters":{"states":["s2","m2","f2","d2"],"alphabet":["a2","b2"],"start_state":"s2","final_states":["f2"],"transitions":[["s2",null,"m2"],["s2",null,"d2"],["m2","a2","m2"],["m2","b2","f2"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a2\",\"b2\"],\"final_states\":[\"f2\"],\"start_state\":\"s2\",\"states\":[\"d2\",\"f2\",\"m2\",\"s2\"],\"transitions\":[[\"m2\",\"a2\",\"m2\"],[\"m2\",\"b2\",\"f2\"],[\"s2\",null,\"d2\"],[\"s2\",null,\"m2\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0004","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s3\",\"m3\",\"f3\",\"d3\"],\"alphabet\":[\"a3\",\"b3\"],\"start_state\":\"s3\",\"final_states\":[\"f3\"],\"transitions\":[[\"s3\",null,\"m3\"],[\"s3\",null,\"d3\"],[\"m3\",\"a3\",\"m3\"],[\"m3\",\"b3\",\"f3\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s3, m3, f3, d3], [a3, b3], s3, [f3], [[s3, null, m3], [s3, null, d3], [m3, a3, m3], [m3, b3, f3]], [[s3, a3, []], [s3, b3, []], [f3, a3, []], [f3, b3, []], [d3, a3, []], [d3, b3, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s3, m3, f3, d3], [a3, b3], s3, [f3], [[s3, null, m3], [s3, null, d3], [m3, a3, m3], [m3, b3, f3]], [[s3, a3, []], [s3, b3, []], [f3, a3, []], [f3, b3, []], [d3, a3, []], [d3, b3, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117004,"parameters":{"states":["s3","m3","f3","d3"],"alphabet":["a3","b3"],"start_state":"s3","final_states":["f3"],"transitions":[["s3",null,"m3"],["s3",null,"d3"],["m3","a3","m3"],["m3","b3","f3"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a3\",\"b3\"],\"final_states\":[\"f3\"],\"start_state\":\"s3\",\"states\":[\"d3\",\"f3\",\"m3\",\"s3\"],\"transitions\":[[\"m3\",\"a3\",\"m3\"],[\"m3\",\"b3\",\"f3\"],[\"s3\",null,\"d3\"],[\"s3\",null,\"m3\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0005","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s4\",\"m4\",\"f4\",\"d4\"],\"alphabet\":[\"a4\",\"b4\"],\"start_state\":\"s4\",\"final_states\":[\"f4\"],\"transitions\":[[\"s4\",null,\"m4\"],[\"s4\",null,\"d4\"],[\"m4\",\"a4\",\"m4\"],[\"m4\",\"b4\",\"f4\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s4, m4, f4, d4], [a4, b4], s4, [f4], [[s4, null, m4], [s4, null, d4], [m4, a4, m4], [m4, b4, f4]], [[s4, a4, []], [s4, b4, []], [f4, a4, []], [f4, b4, []], [d4, a4, []], [d4, b4, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s4, m4, f4, d4], [a4, b4], s4, [f4], [[s4, null, m4], [s4, null, d4], [m4, a4, m4], [m4, b4, f4]], [[s4, a4, []], [s4, b4, []], [f4, a4, []], [f4, b4, []], [d4, a4, []], [d4, b4, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117005,"parameters":{"states":["s4","m4","f4","d4"],"alphabet":["a4","b4"],"start_state":"s4","final_states":["f4"],"transitions":[["s4",null,"m4"],["s4",null,"d4"],["m4","a4","m4"],["m4","b4","f4"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a4\",\"b4\"],\"final_states\":[\"f4\"],\"start_state\":\"s4\",\"states\":[\"d4\",\"f4\",\"m4\",\"s4\"],\"transitions\":[[\"m4\",\"a4\",\"m4\"],[\"m4\",\"b4\",\"f4\"],[\"s4\",null,\"d4\"],[\"s4\",null,\"m4\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0006","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s5\",\"m5\",\"f5\",\"d5\"],\"alphabet\":[\"a5\",\"b5\"],\"start_state\":\"s5\",\"final_states\":[\"f5\"],\"transitions\":[[\"s5\",null,\"m5\"],[\"s5\",null,\"d5\"],[\"m5\",\"a5\",\"m5\"],[\"m5\",\"b5\",\"f5\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s5, m5, f5, d5], [a5, b5], s5, [f5], [[s5, null, m5], [s5, null, d5], [m5, a5, m5], [m5, b5, f5]], [[s5, a5, []], [s5, b5, []], [f5, a5, []], [f5, b5, []], [d5, a5, []], [d5, b5, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s5, m5, f5, d5], [a5, b5], s5, [f5], [[s5, null, m5], [s5, null, d5], [m5, a5, m5], [m5, b5, f5]], [[s5, a5, []], [s5, b5, []], [f5, a5, []], [f5, b5, []], [d5, a5, []], [d5, b5, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117006,"parameters":{"states":["s5","m5","f5","d5"],"alphabet":["a5","b5"],"start_state":"s5","final_states":["f5"],"transitions":[["s5",null,"m5"],["s5",null,"d5"],["m5","a5","m5"],["m5","b5","f5"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a5\",\"b5\"],\"final_states\":[\"f5\"],\"start_state\":\"s5\",\"states\":[\"d5\",\"f5\",\"m5\",\"s5\"],\"transitions\":[[\"m5\",\"a5\",\"m5\"],[\"m5\",\"b5\",\"f5\"],[\"s5\",null,\"d5\"],[\"s5\",null,\"m5\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0007","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s6\",\"m6\",\"f6\",\"d6\"],\"alphabet\":[\"a6\",\"b6\"],\"start_state\":\"s6\",\"final_states\":[\"f6\"],\"transitions\":[[\"s6\",null,\"m6\"],[\"s6\",null,\"d6\"],[\"m6\",\"a6\",\"m6\"],[\"m6\",\"b6\",\"f6\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s6, m6, f6, d6], [a6, b6], s6, [f6], [[s6, null, m6], [s6, null, d6], [m6, a6, m6], [m6, b6, f6]], [[s6, a6, []], [s6, b6, []], [f6, a6, []], [f6, b6, []], [d6, a6, []], [d6, b6, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s6, m6, f6, d6], [a6, b6], s6, [f6], [[s6, null, m6], [s6, null, d6], [m6, a6, m6], [m6, b6, f6]], [[s6, a6, []], [s6, b6, []], [f6, a6, []], [f6, b6, []], [d6, a6, []], [d6, b6, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117007,"parameters":{"states":["s6","m6","f6","d6"],"alphabet":["a6","b6"],"start_state":"s6","final_states":["f6"],"transitions":[["s6",null,"m6"],["s6",null,"d6"],["m6","a6","m6"],["m6","b6","f6"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a6\",\"b6\"],\"final_states\":[\"f6\"],\"start_state\":\"s6\",\"states\":[\"d6\",\"f6\",\"m6\",\"s6\"],\"transitions\":[[\"m6\",\"a6\",\"m6\"],[\"m6\",\"b6\",\"f6\"],[\"s6\",null,\"d6\"],[\"s6\",null,\"m6\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0008","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s7\",\"m7\",\"f7\",\"d7\"],\"alphabet\":[\"a7\",\"b7\"],\"start_state\":\"s7\",\"final_states\":[\"f7\"],\"transitions\":[[\"s7\",null,\"m7\"],[\"s7\",null,\"d7\"],[\"m7\",\"a7\",\"m7\"],[\"m7\",\"b7\",\"f7\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s7, m7, f7, d7], [a7, b7], s7, [f7], [[s7, null, m7], [s7, null, d7], [m7, a7, m7], [m7, b7, f7]], [[s7, a7, []], [s7, b7, []], [f7, a7, []], [f7, b7, []], [d7, a7, []], [d7, b7, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s7, m7, f7, d7], [a7, b7], s7, [f7], [[s7, null, m7], [s7, null, d7], [m7, a7, m7], [m7, b7, f7]], [[s7, a7, []], [s7, b7, []], [f7, a7, []], [f7, b7, []], [d7, a7, []], [d7, b7, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117008,"parameters":{"states":["s7","m7","f7","d7"],"alphabet":["a7","b7"],"start_state":"s7","final_states":["f7"],"transitions":[["s7",null,"m7"],["s7",null,"d7"],["m7","a7","m7"],["m7","b7","f7"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a7\",\"b7\"],\"final_states\":[\"f7\"],\"start_state\":\"s7\",\"states\":[\"d7\",\"f7\",\"m7\",\"s7\"],\"transitions\":[[\"m7\",\"a7\",\"m7\"],[\"m7\",\"b7\",\"f7\"],[\"s7\",null,\"d7\"],[\"s7\",null,\"m7\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0009","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s8\",\"m8\",\"f8\",\"d8\"],\"alphabet\":[\"a8\",\"b8\"],\"start_state\":\"s8\",\"final_states\":[\"f8\"],\"transitions\":[[\"s8\",null,\"m8\"],[\"s8\",null,\"d8\"],[\"m8\",\"a8\",\"m8\"],[\"m8\",\"b8\",\"f8\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s8, m8, f8, d8], [a8, b8], s8, [f8], [[s8, null, m8], [s8, null, d8], [m8, a8, m8], [m8, b8, f8]], [[s8, a8, []], [s8, b8, []], [f8, a8, []], [f8, b8, []], [d8, a8, []], [d8, b8, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s8, m8, f8, d8], [a8, b8], s8, [f8], [[s8, null, m8], [s8, null, d8], [m8, a8, m8], [m8, b8, f8]], [[s8, a8, []], [s8, b8, []], [f8, a8, []], [f8, b8, []], [d8, a8, []], [d8, b8, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117009,"parameters":{"states":["s8","m8","f8","d8"],"alphabet":["a8","b8"],"start_state":"s8","final_states":["f8"],"transitions":[["s8",null,"m8"],["s8",null,"d8"],["m8","a8","m8"],["m8","b8","f8"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a8\",\"b8\"],\"final_states\":[\"f8\"],\"start_state\":\"s8\",\"states\":[\"d8\",\"f8\",\"m8\",\"s8\"],\"transitions\":[[\"m8\",\"a8\",\"m8\"],[\"m8\",\"b8\",\"f8\"],[\"s8\",null,\"d8\"],[\"s8\",null,\"m8\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0010","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s9\",\"m9\",\"f9\",\"d9\"],\"alphabet\":[\"a9\",\"b9\"],\"start_state\":\"s9\",\"final_states\":[\"f9\"],\"transitions\":[[\"s9\",null,\"m9\"],[\"s9\",null,\"d9\"],[\"m9\",\"a9\",\"m9\"],[\"m9\",\"b9\",\"f9\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s9, m9, f9, d9], [a9, b9], s9, [f9], [[s9, null, m9], [s9, null, d9], [m9, a9, m9], [m9, b9, f9]], [[s9, a9, []], [s9, b9, []], [f9, a9, []], [f9, b9, []], [d9, a9, []], [d9, b9, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s9, m9, f9, d9], [a9, b9], s9, [f9], [[s9, null, m9], [s9, null, d9], [m9, a9, m9], [m9, b9, f9]], [[s9, a9, []], [s9, b9, []], [f9, a9, []], [f9, b9, []], [d9, a9, []], [d9, b9, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117010,"parameters":{"states":["s9","m9","f9","d9"],"alphabet":["a9","b9"],"start_state":"s9","final_states":["f9"],"transitions":[["s9",null,"m9"],["s9",null,"d9"],["m9","a9","m9"],["m9","b9","f9"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a9\",\"b9\"],\"final_states\":[\"f9\"],\"start_state\":\"s9\",\"states\":[\"d9\",\"f9\",\"m9\",\"s9\"],\"transitions\":[[\"m9\",\"a9\",\"m9\"],[\"m9\",\"b9\",\"f9\"],[\"s9\",null,\"d9\"],[\"s9\",null,\"m9\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0011","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s10\",\"m10\",\"f10\",\"d10\"],\"alphabet\":[\"a10\",\"b10\"],\"start_state\":\"s10\",\"final_states\":[\"f10\"],\"transitions\":[[\"s10\",null,\"m10\"],[\"s10\",null,\"d10\"],[\"m10\",\"a10\",\"m10\"],[\"m10\",\"b10\",\"f10\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s10, m10, f10, d10], [a10, b10], s10, [f10], [[s10, null, m10], [s10, null, d10], [m10, a10, m10], [m10, b10, f10]], [[s10, a10, []], [s10, b10, []], [f10, a10, []], [f10, b10, []], [d10, a10, []], [d10, b10, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s10, m10, f10, d10], [a10, b10], s10, [f10], [[s10, null, m10], [s10, null, d10], [m10, a10, m10], [m10, b10, f10]], [[s10, a10, []], [s10, b10, []], [f10, a10, []], [f10, b10, []], [d10, a10, []], [d10, b10, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117011,"parameters":{"states":["s10","m10","f10","d10"],"alphabet":["a10","b10"],"start_state":"s10","final_states":["f10"],"transitions":[["s10",null,"m10"],["s10",null,"d10"],["m10","a10","m10"],["m10","b10","f10"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a10\",\"b10\"],\"final_states\":[\"f10\"],\"start_state\":\"s10\",\"states\":[\"d10\",\"f10\",\"m10\",\"s10\"],\"transitions\":[[\"m10\",\"a10\",\"m10\"],[\"m10\",\"b10\",\"f10\"],[\"s10\",null,\"d10\"],[\"s10\",null,\"m10\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0012","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s11\",\"m11\",\"f11\",\"d11\"],\"alphabet\":[\"a11\",\"b11\"],\"start_state\":\"s11\",\"final_states\":[\"f11\"],\"transitions\":[[\"s11\",null,\"m11\"],[\"s11\",null,\"d11\"],[\"m11\",\"a11\",\"m11\"],[\"m11\",\"b11\",\"f11\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s11, m11, f11, d11], [a11, b11], s11, [f11], [[s11, null, m11], [s11, null, d11], [m11, a11, m11], [m11, b11, f11]], [[s11, a11, []], [s11, b11, []], [f11, a11, []], [f11, b11, []], [d11, a11, []], [d11, b11, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s11, m11, f11, d11], [a11, b11], s11, [f11], [[s11, null, m11], [s11, null, d11], [m11, a11, m11], [m11, b11, f11]], [[s11, a11, []], [s11, b11, []], [f11, a11, []], [f11, b11, []], [d11, a11, []], [d11, b11, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117012,"parameters":{"states":["s11","m11","f11","d11"],"alphabet":["a11","b11"],"start_state":"s11","final_states":["f11"],"transitions":[["s11",null,"m11"],["s11",null,"d11"],["m11","a11","m11"],["m11","b11","f11"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a11\",\"b11\"],\"final_states\":[\"f11\"],\"start_state\":\"s11\",\"states\":[\"d11\",\"f11\",\"m11\",\"s11\"],\"transitions\":[[\"m11\",\"a11\",\"m11\"],[\"m11\",\"b11\",\"f11\"],[\"s11\",null,\"d11\"],[\"s11\",null,\"m11\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0013","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s12\",\"m12\",\"f12\",\"d12\"],\"alphabet\":[\"a12\",\"b12\"],\"start_state\":\"s12\",\"final_states\":[\"f12\"],\"transitions\":[[\"s12\",null,\"m12\"],[\"s12\",null,\"d12\"],[\"m12\",\"a12\",\"m12\"],[\"m12\",\"b12\",\"f12\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s12, m12, f12, d12], [a12, b12], s12, [f12], [[s12, null, m12], [s12, null, d12], [m12, a12, m12], [m12, b12, f12]], [[s12, a12, []], [s12, b12, []], [f12, a12, []], [f12, b12, []], [d12, a12, []], [d12, b12, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s12, m12, f12, d12], [a12, b12], s12, [f12], [[s12, null, m12], [s12, null, d12], [m12, a12, m12], [m12, b12, f12]], [[s12, a12, []], [s12, b12, []], [f12, a12, []], [f12, b12, []], [d12, a12, []], [d12, b12, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117013,"parameters":{"states":["s12","m12","f12","d12"],"alphabet":["a12","b12"],"start_state":"s12","final_states":["f12"],"transitions":[["s12",null,"m12"],["s12",null,"d12"],["m12","a12","m12"],["m12","b12","f12"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a12\",\"b12\"],\"final_states\":[\"f12\"],\"start_state\":\"s12\",\"states\":[\"d12\",\"f12\",\"m12\",\"s12\"],\"transitions\":[[\"m12\",\"a12\",\"m12\"],[\"m12\",\"b12\",\"f12\"],[\"s12\",null,\"d12\"],[\"s12\",null,\"m12\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0014","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s13\",\"m13\",\"f13\",\"d13\"],\"alphabet\":[\"a13\",\"b13\"],\"start_state\":\"s13\",\"final_states\":[\"f13\"],\"transitions\":[[\"s13\",null,\"m13\"],[\"s13\",null,\"d13\"],[\"m13\",\"a13\",\"m13\"],[\"m13\",\"b13\",\"f13\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s13, m13, f13, d13], [a13, b13], s13, [f13], [[s13, null, m13], [s13, null, d13], [m13, a13, m13], [m13, b13, f13]], [[s13, a13, []], [s13, b13, []], [f13, a13, []], [f13, b13, []], [d13, a13, []], [d13, b13, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s13, m13, f13, d13], [a13, b13], s13, [f13], [[s13, null, m13], [s13, null, d13], [m13, a13, m13], [m13, b13, f13]], [[s13, a13, []], [s13, b13, []], [f13, a13, []], [f13, b13, []], [d13, a13, []], [d13, b13, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117014,"parameters":{"states":["s13","m13","f13","d13"],"alphabet":["a13","b13"],"start_state":"s13","final_states":["f13"],"transitions":[["s13",null,"m13"],["s13",null,"d13"],["m13","a13","m13"],["m13","b13","f13"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a13\",\"b13\"],\"final_states\":[\"f13\"],\"start_state\":\"s13\",\"states\":[\"d13\",\"f13\",\"m13\",\"s13\"],\"transitions\":[[\"m13\",\"a13\",\"m13\"],[\"m13\",\"b13\",\"f13\"],[\"s13\",null,\"d13\"],[\"s13\",null,\"m13\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0015","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s14\",\"m14\",\"f14\",\"d14\"],\"alphabet\":[\"a14\",\"b14\"],\"start_state\":\"s14\",\"final_states\":[\"f14\"],\"transitions\":[[\"s14\",null,\"m14\"],[\"s14\",null,\"d14\"],[\"m14\",\"a14\",\"m14\"],[\"m14\",\"b14\",\"f14\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s14, m14, f14, d14], [a14, b14], s14, [f14], [[s14, null, m14], [s14, null, d14], [m14, a14, m14], [m14, b14, f14]], [[s14, a14, []], [s14, b14, []], [f14, a14, []], [f14, b14, []], [d14, a14, []], [d14, b14, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s14, m14, f14, d14], [a14, b14], s14, [f14], [[s14, null, m14], [s14, null, d14], [m14, a14, m14], [m14, b14, f14]], [[s14, a14, []], [s14, b14, []], [f14, a14, []], [f14, b14, []], [d14, a14, []], [d14, b14, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117015,"parameters":{"states":["s14","m14","f14","d14"],"alphabet":["a14","b14"],"start_state":"s14","final_states":["f14"],"transitions":[["s14",null,"m14"],["s14",null,"d14"],["m14","a14","m14"],["m14","b14","f14"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a14\",\"b14\"],\"final_states\":[\"f14\"],\"start_state\":\"s14\",\"states\":[\"d14\",\"f14\",\"m14\",\"s14\"],\"transitions\":[[\"m14\",\"a14\",\"m14\"],[\"m14\",\"b14\",\"f14\"],[\"s14\",null,\"d14\"],[\"s14\",null,\"m14\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0016","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s15\",\"m15\",\"f15\",\"d15\"],\"alphabet\":[\"a15\",\"b15\"],\"start_state\":\"s15\",\"final_states\":[\"f15\"],\"transitions\":[[\"s15\",null,\"m15\"],[\"s15\",null,\"d15\"],[\"m15\",\"a15\",\"m15\"],[\"m15\",\"b15\",\"f15\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s15, m15, f15, d15], [a15, b15], s15, [f15], [[s15, null, m15], [s15, null, d15], [m15, a15, m15], [m15, b15, f15]], [[s15, a15, []], [s15, b15, []], [f15, a15, []], [f15, b15, []], [d15, a15, []], [d15, b15, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s15, m15, f15, d15], [a15, b15], s15, [f15], [[s15, null, m15], [s15, null, d15], [m15, a15, m15], [m15, b15, f15]], [[s15, a15, []], [s15, b15, []], [f15, a15, []], [f15, b15, []], [d15, a15, []], [d15, b15, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117016,"parameters":{"states":["s15","m15","f15","d15"],"alphabet":["a15","b15"],"start_state":"s15","final_states":["f15"],"transitions":[["s15",null,"m15"],["s15",null,"d15"],["m15","a15","m15"],["m15","b15","f15"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a15\",\"b15\"],\"final_states\":[\"f15\"],\"start_state\":\"s15\",\"states\":[\"d15\",\"f15\",\"m15\",\"s15\"],\"transitions\":[[\"m15\",\"a15\",\"m15\"],[\"m15\",\"b15\",\"f15\"],[\"s15\",null,\"d15\"],[\"s15\",null,\"m15\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0017","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s16\",\"m16\",\"f16\",\"d16\"],\"alphabet\":[\"a16\",\"b16\"],\"start_state\":\"s16\",\"final_states\":[\"f16\"],\"transitions\":[[\"s16\",null,\"m16\"],[\"s16\",null,\"d16\"],[\"m16\",\"a16\",\"m16\"],[\"m16\",\"b16\",\"f16\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s16, m16, f16, d16], [a16, b16], s16, [f16], [[s16, null, m16], [s16, null, d16], [m16, a16, m16], [m16, b16, f16]], [[s16, a16, []], [s16, b16, []], [f16, a16, []], [f16, b16, []], [d16, a16, []], [d16, b16, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s16, m16, f16, d16], [a16, b16], s16, [f16], [[s16, null, m16], [s16, null, d16], [m16, a16, m16], [m16, b16, f16]], [[s16, a16, []], [s16, b16, []], [f16, a16, []], [f16, b16, []], [d16, a16, []], [d16, b16, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117017,"parameters":{"states":["s16","m16","f16","d16"],"alphabet":["a16","b16"],"start_state":"s16","final_states":["f16"],"transitions":[["s16",null,"m16"],["s16",null,"d16"],["m16","a16","m16"],["m16","b16","f16"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a16\",\"b16\"],\"final_states\":[\"f16\"],\"start_state\":\"s16\",\"states\":[\"d16\",\"f16\",\"m16\",\"s16\"],\"transitions\":[[\"m16\",\"a16\",\"m16\"],[\"m16\",\"b16\",\"f16\"],[\"s16\",null,\"d16\"],[\"s16\",null,\"m16\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0018","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s17\",\"m17\",\"f17\",\"d17\"],\"alphabet\":[\"a17\",\"b17\"],\"start_state\":\"s17\",\"final_states\":[\"f17\"],\"transitions\":[[\"s17\",null,\"m17\"],[\"s17\",null,\"d17\"],[\"m17\",\"a17\",\"m17\"],[\"m17\",\"b17\",\"f17\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s17, m17, f17, d17], [a17, b17], s17, [f17], [[s17, null, m17], [s17, null, d17], [m17, a17, m17], [m17, b17, f17]], [[s17, a17, []], [s17, b17, []], [f17, a17, []], [f17, b17, []], [d17, a17, []], [d17, b17, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s17, m17, f17, d17], [a17, b17], s17, [f17], [[s17, null, m17], [s17, null, d17], [m17, a17, m17], [m17, b17, f17]], [[s17, a17, []], [s17, b17, []], [f17, a17, []], [f17, b17, []], [d17, a17, []], [d17, b17, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117018,"parameters":{"states":["s17","m17","f17","d17"],"alphabet":["a17","b17"],"start_state":"s17","final_states":["f17"],"transitions":[["s17",null,"m17"],["s17",null,"d17"],["m17","a17","m17"],["m17","b17","f17"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a17\",\"b17\"],\"final_states\":[\"f17\"],\"start_state\":\"s17\",\"states\":[\"d17\",\"f17\",\"m17\",\"s17\"],\"transitions\":[[\"m17\",\"a17\",\"m17\"],[\"m17\",\"b17\",\"f17\"],[\"s17\",null,\"d17\"],[\"s17\",null,\"m17\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0019","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s18\",\"m18\",\"f18\",\"d18\"],\"alphabet\":[\"a18\",\"b18\"],\"start_state\":\"s18\",\"final_states\":[\"f18\"],\"transitions\":[[\"s18\",null,\"m18\"],[\"s18\",null,\"d18\"],[\"m18\",\"a18\",\"m18\"],[\"m18\",\"b18\",\"f18\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s18, m18, f18, d18], [a18, b18], s18, [f18], [[s18, null, m18], [s18, null, d18], [m18, a18, m18], [m18, b18, f18]], [[s18, a18, []], [s18, b18, []], [f18, a18, []], [f18, b18, []], [d18, a18, []], [d18, b18, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s18, m18, f18, d18], [a18, b18], s18, [f18], [[s18, null, m18], [s18, null, d18], [m18, a18, m18], [m18, b18, f18]], [[s18, a18, []], [s18, b18, []], [f18, a18, []], [f18, b18, []], [d18, a18, []], [d18, b18, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117019,"parameters":{"states":["s18","m18","f18","d18"],"alphabet":["a18","b18"],"start_state":"s18","final_states":["f18"],"transitions":[["s18",null,"m18"],["s18",null,"d18"],["m18","a18","m18"],["m18","b18","f18"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a18\",\"b18\"],\"final_states\":[\"f18\"],\"start_state\":\"s18\",\"states\":[\"d18\",\"f18\",\"m18\",\"s18\"],\"transitions\":[[\"m18\",\"a18\",\"m18\"],[\"m18\",\"b18\",\"f18\"],[\"s18\",null,\"d18\"],[\"s18\",null,\"m18\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0020","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s19\",\"m19\",\"f19\",\"d19\"],\"alphabet\":[\"a19\",\"b19\"],\"start_state\":\"s19\",\"final_states\":[\"f19\"],\"transitions\":[[\"s19\",null,\"m19\"],[\"s19\",null,\"d19\"],[\"m19\",\"a19\",\"m19\"],[\"m19\",\"b19\",\"f19\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s19, m19, f19, d19], [a19, b19], s19, [f19], [[s19, null, m19], [s19, null, d19], [m19, a19, m19], [m19, b19, f19]], [[s19, a19, []], [s19, b19, []], [f19, a19, []], [f19, b19, []], [d19, a19, []], [d19, b19, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s19, m19, f19, d19], [a19, b19], s19, [f19], [[s19, null, m19], [s19, null, d19], [m19, a19, m19], [m19, b19, f19]], [[s19, a19, []], [s19, b19, []], [f19, a19, []], [f19, b19, []], [d19, a19, []], [d19, b19, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117020,"parameters":{"states":["s19","m19","f19","d19"],"alphabet":["a19","b19"],"start_state":"s19","final_states":["f19"],"transitions":[["s19",null,"m19"],["s19",null,"d19"],["m19","a19","m19"],["m19","b19","f19"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a19\",\"b19\"],\"final_states\":[\"f19\"],\"start_state\":\"s19\",\"states\":[\"d19\",\"f19\",\"m19\",\"s19\"],\"transitions\":[[\"m19\",\"a19\",\"m19\"],[\"m19\",\"b19\",\"f19\"],[\"s19\",null,\"d19\"],[\"s19\",null,\"m19\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0021","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s20\",\"m20\",\"f20\",\"d20\"],\"alphabet\":[\"a20\",\"b20\"],\"start_state\":\"s20\",\"final_states\":[\"f20\"],\"transitions\":[[\"s20\",null,\"m20\"],[\"s20\",null,\"d20\"],[\"m20\",\"a20\",\"m20\"],[\"m20\",\"b20\",\"f20\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s20, m20, f20, d20], [a20, b20], s20, [f20], [[s20, null, m20], [s20, null, d20], [m20, a20, m20], [m20, b20, f20]], [[s20, a20, []], [s20, b20, []], [f20, a20, []], [f20, b20, []], [d20, a20, []], [d20, b20, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s20, m20, f20, d20], [a20, b20], s20, [f20], [[s20, null, m20], [s20, null, d20], [m20, a20, m20], [m20, b20, f20]], [[s20, a20, []], [s20, b20, []], [f20, a20, []], [f20, b20, []], [d20, a20, []], [d20, b20, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117021,"parameters":{"states":["s20","m20","f20","d20"],"alphabet":["a20","b20"],"start_state":"s20","final_states":["f20"],"transitions":[["s20",null,"m20"],["s20",null,"d20"],["m20","a20","m20"],["m20","b20","f20"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a20\",\"b20\"],\"final_states\":[\"f20\"],\"start_state\":\"s20\",\"states\":[\"d20\",\"f20\",\"m20\",\"s20\"],\"transitions\":[[\"m20\",\"a20\",\"m20\"],[\"m20\",\"b20\",\"f20\"],[\"s20\",null,\"d20\"],[\"s20\",null,\"m20\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0022","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s21\",\"m21\",\"f21\",\"d21\"],\"alphabet\":[\"a21\",\"b21\"],\"start_state\":\"s21\",\"final_states\":[\"f21\"],\"transitions\":[[\"s21\",null,\"m21\"],[\"s21\",null,\"d21\"],[\"m21\",\"a21\",\"m21\"],[\"m21\",\"b21\",\"f21\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s21, m21, f21, d21], [a21, b21], s21, [f21], [[s21, null, m21], [s21, null, d21], [m21, a21, m21], [m21, b21, f21]], [[s21, a21, []], [s21, b21, []], [f21, a21, []], [f21, b21, []], [d21, a21, []], [d21, b21, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s21, m21, f21, d21], [a21, b21], s21, [f21], [[s21, null, m21], [s21, null, d21], [m21, a21, m21], [m21, b21, f21]], [[s21, a21, []], [s21, b21, []], [f21, a21, []], [f21, b21, []], [d21, a21, []], [d21, b21, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117022,"parameters":{"states":["s21","m21","f21","d21"],"alphabet":["a21","b21"],"start_state":"s21","final_states":["f21"],"transitions":[["s21",null,"m21"],["s21",null,"d21"],["m21","a21","m21"],["m21","b21","f21"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a21\",\"b21\"],\"final_states\":[\"f21\"],\"start_state\":\"s21\",\"states\":[\"d21\",\"f21\",\"m21\",\"s21\"],\"transitions\":[[\"m21\",\"a21\",\"m21\"],[\"m21\",\"b21\",\"f21\"],[\"s21\",null,\"d21\"],[\"s21\",null,\"m21\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0023","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s22\",\"m22\",\"f22\",\"d22\"],\"alphabet\":[\"a22\",\"b22\"],\"start_state\":\"s22\",\"final_states\":[\"f22\"],\"transitions\":[[\"s22\",null,\"m22\"],[\"s22\",null,\"d22\"],[\"m22\",\"a22\",\"m22\"],[\"m22\",\"b22\",\"f22\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s22, m22, f22, d22], [a22, b22], s22, [f22], [[s22, null, m22], [s22, null, d22], [m22, a22, m22], [m22, b22, f22]], [[s22, a22, []], [s22, b22, []], [f22, a22, []], [f22, b22, []], [d22, a22, []], [d22, b22, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s22, m22, f22, d22], [a22, b22], s22, [f22], [[s22, null, m22], [s22, null, d22], [m22, a22, m22], [m22, b22, f22]], [[s22, a22, []], [s22, b22, []], [f22, a22, []], [f22, b22, []], [d22, a22, []], [d22, b22, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117023,"parameters":{"states":["s22","m22","f22","d22"],"alphabet":["a22","b22"],"start_state":"s22","final_states":["f22"],"transitions":[["s22",null,"m22"],["s22",null,"d22"],["m22","a22","m22"],["m22","b22","f22"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a22\",\"b22\"],\"final_states\":[\"f22\"],\"start_state\":\"s22\",\"states\":[\"d22\",\"f22\",\"m22\",\"s22\"],\"transitions\":[[\"m22\",\"a22\",\"m22\"],[\"m22\",\"b22\",\"f22\"],[\"s22\",null,\"d22\"],[\"s22\",null,\"m22\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0024","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s23\",\"m23\",\"f23\",\"d23\"],\"alphabet\":[\"a23\",\"b23\"],\"start_state\":\"s23\",\"final_states\":[\"f23\"],\"transitions\":[[\"s23\",null,\"m23\"],[\"s23\",null,\"d23\"],[\"m23\",\"a23\",\"m23\"],[\"m23\",\"b23\",\"f23\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s23, m23, f23, d23], [a23, b23], s23, [f23], [[s23, null, m23], [s23, null, d23], [m23, a23, m23], [m23, b23, f23]], [[s23, a23, []], [s23, b23, []], [f23, a23, []], [f23, b23, []], [d23, a23, []], [d23, b23, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s23, m23, f23, d23], [a23, b23], s23, [f23], [[s23, null, m23], [s23, null, d23], [m23, a23, m23], [m23, b23, f23]], [[s23, a23, []], [s23, b23, []], [f23, a23, []], [f23, b23, []], [d23, a23, []], [d23, b23, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117024,"parameters":{"states":["s23","m23","f23","d23"],"alphabet":["a23","b23"],"start_state":"s23","final_states":["f23"],"transitions":[["s23",null,"m23"],["s23",null,"d23"],["m23","a23","m23"],["m23","b23","f23"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a23\",\"b23\"],\"final_states\":[\"f23\"],\"start_state\":\"s23\",\"states\":[\"d23\",\"f23\",\"m23\",\"s23\"],\"transitions\":[[\"m23\",\"a23\",\"m23\"],[\"m23\",\"b23\",\"f23\"],[\"s23\",null,\"d23\"],[\"s23\",null,\"m23\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0025","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={\"states\":[\"s24\",\"m24\",\"f24\",\"d24\"],\"alphabet\":[\"a24\",\"b24\"],\"start_state\":\"s24\",\"final_states\":[\"f24\"],\"transitions\":[[\"s24\",null,\"m24\"],[\"s24\",null,\"d24\"],[\"m24\",\"a24\",\"m24\"],[\"m24\",\"b24\",\"f24\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s24, m24, f24, d24], [a24, b24], s24, [f24], [[s24, null, m24], [s24, null, d24], [m24, a24, m24], [m24, b24, f24]], [[s24, a24, []], [s24, b24, []], [f24, a24, []], [f24, b24, []], [d24, a24, []], [d24, b24, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)","explanation_zh":"Wave6第五層核對=([s24, m24, f24, d24], [a24, b24], s24, [f24], [[s24, null, m24], [s24, null, d24], [m24, a24, m24], [m24, b24, f24]], [[s24, a24, []], [s24, b24, []], [f24, a24, []], [f24, b24, []], [d24, a24, []], [d24, b24, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-qualification","seed":202611117025,"parameters":{"states":["s24","m24","f24","d24"],"alphabet":["a24","b24"],"start_state":"s24","final_states":["f24"],"transitions":[["s24",null,"m24"],["s24",null,"d24"],["m24","a24","m24"],["m24","b24","f24"]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-qualification","semantic_template":"qf-mod42-nfa-qualification/{\"alphabet\":[\"a24\",\"b24\"],\"final_states\":[\"f24\"],\"start_state\":\"s24\",\"states\":[\"d24\",\"f24\",\"m24\",\"s24\"],\"transitions\":[[\"m24\",\"a24\",\"m24\"],[\"m24\",\"b24\",\"f24\"],[\"s24\",null,\"d24\"],[\"s24\",null,\"m24\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0026","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s0\",\"m0\",\"f0\",\"d0\"],\"alphabet\":[\"a0\",\"b0\"],\"start_state\":\"s0\",\"final_states\":[\"f0\"],\"transitions\":[[\"s0\",null,\"m0\"],[\"s0\",null,\"d0\"],[\"m0\",\"a0\",\"m0\"],[\"m0\",\"b0\",\"f0\"]],\"seed_states\":[\"s0\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s0], [d0, m0, s0], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s0], [d0, m0, s0], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117026,"parameters":{"states":["s0","m0","f0","d0"],"alphabet":["a0","b0"],"start_state":"s0","final_states":["f0"],"transitions":[["s0",null,"m0"],["s0",null,"d0"],["m0","a0","m0"],["m0","b0","f0"]],"seed_states":["s0"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a0\",\"b0\"],\"final_states\":[\"f0\"],\"seed_states\":[\"s0\"],\"start_state\":\"s0\",\"states\":[\"d0\",\"f0\",\"m0\",\"s0\"],\"transitions\":[[\"m0\",\"a0\",\"m0\"],[\"m0\",\"b0\",\"f0\"],[\"s0\",null,\"d0\"],[\"s0\",null,\"m0\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0027","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s1\",\"m1\",\"f1\",\"d1\"],\"alphabet\":[\"a1\",\"b1\"],\"start_state\":\"s1\",\"final_states\":[\"f1\"],\"transitions\":[[\"s1\",null,\"m1\"],[\"s1\",null,\"d1\"],[\"m1\",\"a1\",\"m1\"],[\"m1\",\"b1\",\"f1\"]],\"seed_states\":[\"s1\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s1], [d1, m1, s1], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s1], [d1, m1, s1], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117027,"parameters":{"states":["s1","m1","f1","d1"],"alphabet":["a1","b1"],"start_state":"s1","final_states":["f1"],"transitions":[["s1",null,"m1"],["s1",null,"d1"],["m1","a1","m1"],["m1","b1","f1"]],"seed_states":["s1"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a1\",\"b1\"],\"final_states\":[\"f1\"],\"seed_states\":[\"s1\"],\"start_state\":\"s1\",\"states\":[\"d1\",\"f1\",\"m1\",\"s1\"],\"transitions\":[[\"m1\",\"a1\",\"m1\"],[\"m1\",\"b1\",\"f1\"],[\"s1\",null,\"d1\"],[\"s1\",null,\"m1\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0028","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s2\",\"m2\",\"f2\",\"d2\"],\"alphabet\":[\"a2\",\"b2\"],\"start_state\":\"s2\",\"final_states\":[\"f2\"],\"transitions\":[[\"s2\",null,\"m2\"],[\"s2\",null,\"d2\"],[\"m2\",\"a2\",\"m2\"],[\"m2\",\"b2\",\"f2\"]],\"seed_states\":[\"s2\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s2], [d2, m2, s2], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s2], [d2, m2, s2], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117028,"parameters":{"states":["s2","m2","f2","d2"],"alphabet":["a2","b2"],"start_state":"s2","final_states":["f2"],"transitions":[["s2",null,"m2"],["s2",null,"d2"],["m2","a2","m2"],["m2","b2","f2"]],"seed_states":["s2"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a2\",\"b2\"],\"final_states\":[\"f2\"],\"seed_states\":[\"s2\"],\"start_state\":\"s2\",\"states\":[\"d2\",\"f2\",\"m2\",\"s2\"],\"transitions\":[[\"m2\",\"a2\",\"m2\"],[\"m2\",\"b2\",\"f2\"],[\"s2\",null,\"d2\"],[\"s2\",null,\"m2\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0029","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s3\",\"m3\",\"f3\",\"d3\"],\"alphabet\":[\"a3\",\"b3\"],\"start_state\":\"s3\",\"final_states\":[\"f3\"],\"transitions\":[[\"s3\",null,\"m3\"],[\"s3\",null,\"d3\"],[\"m3\",\"a3\",\"m3\"],[\"m3\",\"b3\",\"f3\"]],\"seed_states\":[\"s3\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s3], [d3, m3, s3], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s3], [d3, m3, s3], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117029,"parameters":{"states":["s3","m3","f3","d3"],"alphabet":["a3","b3"],"start_state":"s3","final_states":["f3"],"transitions":[["s3",null,"m3"],["s3",null,"d3"],["m3","a3","m3"],["m3","b3","f3"]],"seed_states":["s3"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a3\",\"b3\"],\"final_states\":[\"f3\"],\"seed_states\":[\"s3\"],\"start_state\":\"s3\",\"states\":[\"d3\",\"f3\",\"m3\",\"s3\"],\"transitions\":[[\"m3\",\"a3\",\"m3\"],[\"m3\",\"b3\",\"f3\"],[\"s3\",null,\"d3\"],[\"s3\",null,\"m3\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0030","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s4\",\"m4\",\"f4\",\"d4\"],\"alphabet\":[\"a4\",\"b4\"],\"start_state\":\"s4\",\"final_states\":[\"f4\"],\"transitions\":[[\"s4\",null,\"m4\"],[\"s4\",null,\"d4\"],[\"m4\",\"a4\",\"m4\"],[\"m4\",\"b4\",\"f4\"]],\"seed_states\":[\"s4\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s4], [d4, m4, s4], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s4], [d4, m4, s4], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117030,"parameters":{"states":["s4","m4","f4","d4"],"alphabet":["a4","b4"],"start_state":"s4","final_states":["f4"],"transitions":[["s4",null,"m4"],["s4",null,"d4"],["m4","a4","m4"],["m4","b4","f4"]],"seed_states":["s4"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a4\",\"b4\"],\"final_states\":[\"f4\"],\"seed_states\":[\"s4\"],\"start_state\":\"s4\",\"states\":[\"d4\",\"f4\",\"m4\",\"s4\"],\"transitions\":[[\"m4\",\"a4\",\"m4\"],[\"m4\",\"b4\",\"f4\"],[\"s4\",null,\"d4\"],[\"s4\",null,\"m4\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0031","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s5\",\"m5\",\"f5\",\"d5\"],\"alphabet\":[\"a5\",\"b5\"],\"start_state\":\"s5\",\"final_states\":[\"f5\"],\"transitions\":[[\"s5\",null,\"m5\"],[\"s5\",null,\"d5\"],[\"m5\",\"a5\",\"m5\"],[\"m5\",\"b5\",\"f5\"]],\"seed_states\":[\"s5\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s5], [d5, m5, s5], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s5], [d5, m5, s5], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117031,"parameters":{"states":["s5","m5","f5","d5"],"alphabet":["a5","b5"],"start_state":"s5","final_states":["f5"],"transitions":[["s5",null,"m5"],["s5",null,"d5"],["m5","a5","m5"],["m5","b5","f5"]],"seed_states":["s5"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a5\",\"b5\"],\"final_states\":[\"f5\"],\"seed_states\":[\"s5\"],\"start_state\":\"s5\",\"states\":[\"d5\",\"f5\",\"m5\",\"s5\"],\"transitions\":[[\"m5\",\"a5\",\"m5\"],[\"m5\",\"b5\",\"f5\"],[\"s5\",null,\"d5\"],[\"s5\",null,\"m5\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0032","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s6\",\"m6\",\"f6\",\"d6\"],\"alphabet\":[\"a6\",\"b6\"],\"start_state\":\"s6\",\"final_states\":[\"f6\"],\"transitions\":[[\"s6\",null,\"m6\"],[\"s6\",null,\"d6\"],[\"m6\",\"a6\",\"m6\"],[\"m6\",\"b6\",\"f6\"]],\"seed_states\":[\"s6\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s6], [d6, m6, s6], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s6], [d6, m6, s6], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117032,"parameters":{"states":["s6","m6","f6","d6"],"alphabet":["a6","b6"],"start_state":"s6","final_states":["f6"],"transitions":[["s6",null,"m6"],["s6",null,"d6"],["m6","a6","m6"],["m6","b6","f6"]],"seed_states":["s6"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a6\",\"b6\"],\"final_states\":[\"f6\"],\"seed_states\":[\"s6\"],\"start_state\":\"s6\",\"states\":[\"d6\",\"f6\",\"m6\",\"s6\"],\"transitions\":[[\"m6\",\"a6\",\"m6\"],[\"m6\",\"b6\",\"f6\"],[\"s6\",null,\"d6\"],[\"s6\",null,\"m6\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0033","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s7\",\"m7\",\"f7\",\"d7\"],\"alphabet\":[\"a7\",\"b7\"],\"start_state\":\"s7\",\"final_states\":[\"f7\"],\"transitions\":[[\"s7\",null,\"m7\"],[\"s7\",null,\"d7\"],[\"m7\",\"a7\",\"m7\"],[\"m7\",\"b7\",\"f7\"]],\"seed_states\":[\"s7\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s7], [d7, m7, s7], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s7], [d7, m7, s7], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117033,"parameters":{"states":["s7","m7","f7","d7"],"alphabet":["a7","b7"],"start_state":"s7","final_states":["f7"],"transitions":[["s7",null,"m7"],["s7",null,"d7"],["m7","a7","m7"],["m7","b7","f7"]],"seed_states":["s7"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a7\",\"b7\"],\"final_states\":[\"f7\"],\"seed_states\":[\"s7\"],\"start_state\":\"s7\",\"states\":[\"d7\",\"f7\",\"m7\",\"s7\"],\"transitions\":[[\"m7\",\"a7\",\"m7\"],[\"m7\",\"b7\",\"f7\"],[\"s7\",null,\"d7\"],[\"s7\",null,\"m7\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0034","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s8\",\"m8\",\"f8\",\"d8\"],\"alphabet\":[\"a8\",\"b8\"],\"start_state\":\"s8\",\"final_states\":[\"f8\"],\"transitions\":[[\"s8\",null,\"m8\"],[\"s8\",null,\"d8\"],[\"m8\",\"a8\",\"m8\"],[\"m8\",\"b8\",\"f8\"]],\"seed_states\":[\"s8\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s8], [d8, m8, s8], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s8], [d8, m8, s8], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117034,"parameters":{"states":["s8","m8","f8","d8"],"alphabet":["a8","b8"],"start_state":"s8","final_states":["f8"],"transitions":[["s8",null,"m8"],["s8",null,"d8"],["m8","a8","m8"],["m8","b8","f8"]],"seed_states":["s8"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a8\",\"b8\"],\"final_states\":[\"f8\"],\"seed_states\":[\"s8\"],\"start_state\":\"s8\",\"states\":[\"d8\",\"f8\",\"m8\",\"s8\"],\"transitions\":[[\"m8\",\"a8\",\"m8\"],[\"m8\",\"b8\",\"f8\"],[\"s8\",null,\"d8\"],[\"s8\",null,\"m8\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0035","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s9\",\"m9\",\"f9\",\"d9\"],\"alphabet\":[\"a9\",\"b9\"],\"start_state\":\"s9\",\"final_states\":[\"f9\"],\"transitions\":[[\"s9\",null,\"m9\"],[\"s9\",null,\"d9\"],[\"m9\",\"a9\",\"m9\"],[\"m9\",\"b9\",\"f9\"]],\"seed_states\":[\"s9\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s9], [d9, m9, s9], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s9], [d9, m9, s9], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117035,"parameters":{"states":["s9","m9","f9","d9"],"alphabet":["a9","b9"],"start_state":"s9","final_states":["f9"],"transitions":[["s9",null,"m9"],["s9",null,"d9"],["m9","a9","m9"],["m9","b9","f9"]],"seed_states":["s9"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a9\",\"b9\"],\"final_states\":[\"f9\"],\"seed_states\":[\"s9\"],\"start_state\":\"s9\",\"states\":[\"d9\",\"f9\",\"m9\",\"s9\"],\"transitions\":[[\"m9\",\"a9\",\"m9\"],[\"m9\",\"b9\",\"f9\"],[\"s9\",null,\"d9\"],[\"s9\",null,\"m9\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0036","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s10\",\"m10\",\"f10\",\"d10\"],\"alphabet\":[\"a10\",\"b10\"],\"start_state\":\"s10\",\"final_states\":[\"f10\"],\"transitions\":[[\"s10\",null,\"m10\"],[\"s10\",null,\"d10\"],[\"m10\",\"a10\",\"m10\"],[\"m10\",\"b10\",\"f10\"]],\"seed_states\":[\"s10\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s10], [d10, m10, s10], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s10], [d10, m10, s10], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117036,"parameters":{"states":["s10","m10","f10","d10"],"alphabet":["a10","b10"],"start_state":"s10","final_states":["f10"],"transitions":[["s10",null,"m10"],["s10",null,"d10"],["m10","a10","m10"],["m10","b10","f10"]],"seed_states":["s10"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a10\",\"b10\"],\"final_states\":[\"f10\"],\"seed_states\":[\"s10\"],\"start_state\":\"s10\",\"states\":[\"d10\",\"f10\",\"m10\",\"s10\"],\"transitions\":[[\"m10\",\"a10\",\"m10\"],[\"m10\",\"b10\",\"f10\"],[\"s10\",null,\"d10\"],[\"s10\",null,\"m10\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0037","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s11\",\"m11\",\"f11\",\"d11\"],\"alphabet\":[\"a11\",\"b11\"],\"start_state\":\"s11\",\"final_states\":[\"f11\"],\"transitions\":[[\"s11\",null,\"m11\"],[\"s11\",null,\"d11\"],[\"m11\",\"a11\",\"m11\"],[\"m11\",\"b11\",\"f11\"]],\"seed_states\":[\"s11\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s11], [d11, m11, s11], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s11], [d11, m11, s11], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117037,"parameters":{"states":["s11","m11","f11","d11"],"alphabet":["a11","b11"],"start_state":"s11","final_states":["f11"],"transitions":[["s11",null,"m11"],["s11",null,"d11"],["m11","a11","m11"],["m11","b11","f11"]],"seed_states":["s11"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a11\",\"b11\"],\"final_states\":[\"f11\"],\"seed_states\":[\"s11\"],\"start_state\":\"s11\",\"states\":[\"d11\",\"f11\",\"m11\",\"s11\"],\"transitions\":[[\"m11\",\"a11\",\"m11\"],[\"m11\",\"b11\",\"f11\"],[\"s11\",null,\"d11\"],[\"s11\",null,\"m11\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0038","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s12\",\"m12\",\"f12\",\"d12\"],\"alphabet\":[\"a12\",\"b12\"],\"start_state\":\"s12\",\"final_states\":[\"f12\"],\"transitions\":[[\"s12\",null,\"m12\"],[\"s12\",null,\"d12\"],[\"m12\",\"a12\",\"m12\"],[\"m12\",\"b12\",\"f12\"]],\"seed_states\":[\"s12\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s12], [d12, m12, s12], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s12], [d12, m12, s12], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117038,"parameters":{"states":["s12","m12","f12","d12"],"alphabet":["a12","b12"],"start_state":"s12","final_states":["f12"],"transitions":[["s12",null,"m12"],["s12",null,"d12"],["m12","a12","m12"],["m12","b12","f12"]],"seed_states":["s12"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a12\",\"b12\"],\"final_states\":[\"f12\"],\"seed_states\":[\"s12\"],\"start_state\":\"s12\",\"states\":[\"d12\",\"f12\",\"m12\",\"s12\"],\"transitions\":[[\"m12\",\"a12\",\"m12\"],[\"m12\",\"b12\",\"f12\"],[\"s12\",null,\"d12\"],[\"s12\",null,\"m12\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0039","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s13\",\"m13\",\"f13\",\"d13\"],\"alphabet\":[\"a13\",\"b13\"],\"start_state\":\"s13\",\"final_states\":[\"f13\"],\"transitions\":[[\"s13\",null,\"m13\"],[\"s13\",null,\"d13\"],[\"m13\",\"a13\",\"m13\"],[\"m13\",\"b13\",\"f13\"]],\"seed_states\":[\"s13\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s13], [d13, m13, s13], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s13], [d13, m13, s13], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117039,"parameters":{"states":["s13","m13","f13","d13"],"alphabet":["a13","b13"],"start_state":"s13","final_states":["f13"],"transitions":[["s13",null,"m13"],["s13",null,"d13"],["m13","a13","m13"],["m13","b13","f13"]],"seed_states":["s13"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a13\",\"b13\"],\"final_states\":[\"f13\"],\"seed_states\":[\"s13\"],\"start_state\":\"s13\",\"states\":[\"d13\",\"f13\",\"m13\",\"s13\"],\"transitions\":[[\"m13\",\"a13\",\"m13\"],[\"m13\",\"b13\",\"f13\"],[\"s13\",null,\"d13\"],[\"s13\",null,\"m13\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0040","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s14\",\"m14\",\"f14\",\"d14\"],\"alphabet\":[\"a14\",\"b14\"],\"start_state\":\"s14\",\"final_states\":[\"f14\"],\"transitions\":[[\"s14\",null,\"m14\"],[\"s14\",null,\"d14\"],[\"m14\",\"a14\",\"m14\"],[\"m14\",\"b14\",\"f14\"]],\"seed_states\":[\"s14\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s14], [d14, m14, s14], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s14], [d14, m14, s14], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117040,"parameters":{"states":["s14","m14","f14","d14"],"alphabet":["a14","b14"],"start_state":"s14","final_states":["f14"],"transitions":[["s14",null,"m14"],["s14",null,"d14"],["m14","a14","m14"],["m14","b14","f14"]],"seed_states":["s14"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a14\",\"b14\"],\"final_states\":[\"f14\"],\"seed_states\":[\"s14\"],\"start_state\":\"s14\",\"states\":[\"d14\",\"f14\",\"m14\",\"s14\"],\"transitions\":[[\"m14\",\"a14\",\"m14\"],[\"m14\",\"b14\",\"f14\"],[\"s14\",null,\"d14\"],[\"s14\",null,\"m14\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0041","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s15\",\"m15\",\"f15\",\"d15\"],\"alphabet\":[\"a15\",\"b15\"],\"start_state\":\"s15\",\"final_states\":[\"f15\"],\"transitions\":[[\"s15\",null,\"m15\"],[\"s15\",null,\"d15\"],[\"m15\",\"a15\",\"m15\"],[\"m15\",\"b15\",\"f15\"]],\"seed_states\":[\"s15\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s15], [d15, m15, s15], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s15], [d15, m15, s15], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117041,"parameters":{"states":["s15","m15","f15","d15"],"alphabet":["a15","b15"],"start_state":"s15","final_states":["f15"],"transitions":[["s15",null,"m15"],["s15",null,"d15"],["m15","a15","m15"],["m15","b15","f15"]],"seed_states":["s15"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a15\",\"b15\"],\"final_states\":[\"f15\"],\"seed_states\":[\"s15\"],\"start_state\":\"s15\",\"states\":[\"d15\",\"f15\",\"m15\",\"s15\"],\"transitions\":[[\"m15\",\"a15\",\"m15\"],[\"m15\",\"b15\",\"f15\"],[\"s15\",null,\"d15\"],[\"s15\",null,\"m15\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0042","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s16\",\"m16\",\"f16\",\"d16\"],\"alphabet\":[\"a16\",\"b16\"],\"start_state\":\"s16\",\"final_states\":[\"f16\"],\"transitions\":[[\"s16\",null,\"m16\"],[\"s16\",null,\"d16\"],[\"m16\",\"a16\",\"m16\"],[\"m16\",\"b16\",\"f16\"]],\"seed_states\":[\"s16\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s16], [d16, m16, s16], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s16], [d16, m16, s16], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117042,"parameters":{"states":["s16","m16","f16","d16"],"alphabet":["a16","b16"],"start_state":"s16","final_states":["f16"],"transitions":[["s16",null,"m16"],["s16",null,"d16"],["m16","a16","m16"],["m16","b16","f16"]],"seed_states":["s16"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a16\",\"b16\"],\"final_states\":[\"f16\"],\"seed_states\":[\"s16\"],\"start_state\":\"s16\",\"states\":[\"d16\",\"f16\",\"m16\",\"s16\"],\"transitions\":[[\"m16\",\"a16\",\"m16\"],[\"m16\",\"b16\",\"f16\"],[\"s16\",null,\"d16\"],[\"s16\",null,\"m16\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0043","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s17\",\"m17\",\"f17\",\"d17\"],\"alphabet\":[\"a17\",\"b17\"],\"start_state\":\"s17\",\"final_states\":[\"f17\"],\"transitions\":[[\"s17\",null,\"m17\"],[\"s17\",null,\"d17\"],[\"m17\",\"a17\",\"m17\"],[\"m17\",\"b17\",\"f17\"]],\"seed_states\":[\"s17\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s17], [d17, m17, s17], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s17], [d17, m17, s17], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117043,"parameters":{"states":["s17","m17","f17","d17"],"alphabet":["a17","b17"],"start_state":"s17","final_states":["f17"],"transitions":[["s17",null,"m17"],["s17",null,"d17"],["m17","a17","m17"],["m17","b17","f17"]],"seed_states":["s17"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a17\",\"b17\"],\"final_states\":[\"f17\"],\"seed_states\":[\"s17\"],\"start_state\":\"s17\",\"states\":[\"d17\",\"f17\",\"m17\",\"s17\"],\"transitions\":[[\"m17\",\"a17\",\"m17\"],[\"m17\",\"b17\",\"f17\"],[\"s17\",null,\"d17\"],[\"s17\",null,\"m17\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0044","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s18\",\"m18\",\"f18\",\"d18\"],\"alphabet\":[\"a18\",\"b18\"],\"start_state\":\"s18\",\"final_states\":[\"f18\"],\"transitions\":[[\"s18\",null,\"m18\"],[\"s18\",null,\"d18\"],[\"m18\",\"a18\",\"m18\"],[\"m18\",\"b18\",\"f18\"]],\"seed_states\":[\"s18\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s18], [d18, m18, s18], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s18], [d18, m18, s18], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117044,"parameters":{"states":["s18","m18","f18","d18"],"alphabet":["a18","b18"],"start_state":"s18","final_states":["f18"],"transitions":[["s18",null,"m18"],["s18",null,"d18"],["m18","a18","m18"],["m18","b18","f18"]],"seed_states":["s18"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a18\",\"b18\"],\"final_states\":[\"f18\"],\"seed_states\":[\"s18\"],\"start_state\":\"s18\",\"states\":[\"d18\",\"f18\",\"m18\",\"s18\"],\"transitions\":[[\"m18\",\"a18\",\"m18\"],[\"m18\",\"b18\",\"f18\"],[\"s18\",null,\"d18\"],[\"s18\",null,\"m18\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0045","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s19\",\"m19\",\"f19\",\"d19\"],\"alphabet\":[\"a19\",\"b19\"],\"start_state\":\"s19\",\"final_states\":[\"f19\"],\"transitions\":[[\"s19\",null,\"m19\"],[\"s19\",null,\"d19\"],[\"m19\",\"a19\",\"m19\"],[\"m19\",\"b19\",\"f19\"]],\"seed_states\":[\"s19\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s19], [d19, m19, s19], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s19], [d19, m19, s19], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117045,"parameters":{"states":["s19","m19","f19","d19"],"alphabet":["a19","b19"],"start_state":"s19","final_states":["f19"],"transitions":[["s19",null,"m19"],["s19",null,"d19"],["m19","a19","m19"],["m19","b19","f19"]],"seed_states":["s19"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a19\",\"b19\"],\"final_states\":[\"f19\"],\"seed_states\":[\"s19\"],\"start_state\":\"s19\",\"states\":[\"d19\",\"f19\",\"m19\",\"s19\"],\"transitions\":[[\"m19\",\"a19\",\"m19\"],[\"m19\",\"b19\",\"f19\"],[\"s19\",null,\"d19\"],[\"s19\",null,\"m19\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0046","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s20\",\"m20\",\"f20\",\"d20\"],\"alphabet\":[\"a20\",\"b20\"],\"start_state\":\"s20\",\"final_states\":[\"f20\"],\"transitions\":[[\"s20\",null,\"m20\"],[\"s20\",null,\"d20\"],[\"m20\",\"a20\",\"m20\"],[\"m20\",\"b20\",\"f20\"]],\"seed_states\":[\"s20\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s20], [d20, m20, s20], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s20], [d20, m20, s20], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117046,"parameters":{"states":["s20","m20","f20","d20"],"alphabet":["a20","b20"],"start_state":"s20","final_states":["f20"],"transitions":[["s20",null,"m20"],["s20",null,"d20"],["m20","a20","m20"],["m20","b20","f20"]],"seed_states":["s20"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a20\",\"b20\"],\"final_states\":[\"f20\"],\"seed_states\":[\"s20\"],\"start_state\":\"s20\",\"states\":[\"d20\",\"f20\",\"m20\",\"s20\"],\"transitions\":[[\"m20\",\"a20\",\"m20\"],[\"m20\",\"b20\",\"f20\"],[\"s20\",null,\"d20\"],[\"s20\",null,\"m20\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0047","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s21\",\"m21\",\"f21\",\"d21\"],\"alphabet\":[\"a21\",\"b21\"],\"start_state\":\"s21\",\"final_states\":[\"f21\"],\"transitions\":[[\"s21\",null,\"m21\"],[\"s21\",null,\"d21\"],[\"m21\",\"a21\",\"m21\"],[\"m21\",\"b21\",\"f21\"]],\"seed_states\":[\"s21\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s21], [d21, m21, s21], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s21], [d21, m21, s21], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117047,"parameters":{"states":["s21","m21","f21","d21"],"alphabet":["a21","b21"],"start_state":"s21","final_states":["f21"],"transitions":[["s21",null,"m21"],["s21",null,"d21"],["m21","a21","m21"],["m21","b21","f21"]],"seed_states":["s21"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a21\",\"b21\"],\"final_states\":[\"f21\"],\"seed_states\":[\"s21\"],\"start_state\":\"s21\",\"states\":[\"d21\",\"f21\",\"m21\",\"s21\"],\"transitions\":[[\"m21\",\"a21\",\"m21\"],[\"m21\",\"b21\",\"f21\"],[\"s21\",null,\"d21\"],[\"s21\",null,\"m21\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0048","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s22\",\"m22\",\"f22\",\"d22\"],\"alphabet\":[\"a22\",\"b22\"],\"start_state\":\"s22\",\"final_states\":[\"f22\"],\"transitions\":[[\"s22\",null,\"m22\"],[\"s22\",null,\"d22\"],[\"m22\",\"a22\",\"m22\"],[\"m22\",\"b22\",\"f22\"]],\"seed_states\":[\"s22\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s22], [d22, m22, s22], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s22], [d22, m22, s22], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117048,"parameters":{"states":["s22","m22","f22","d22"],"alphabet":["a22","b22"],"start_state":"s22","final_states":["f22"],"transitions":[["s22",null,"m22"],["s22",null,"d22"],["m22","a22","m22"],["m22","b22","f22"]],"seed_states":["s22"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a22\",\"b22\"],\"final_states\":[\"f22\"],\"seed_states\":[\"s22\"],\"start_state\":\"s22\",\"states\":[\"d22\",\"f22\",\"m22\",\"s22\"],\"transitions\":[[\"m22\",\"a22\",\"m22\"],[\"m22\",\"b22\",\"f22\"],[\"s22\",null,\"d22\"],[\"s22\",null,\"m22\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0049","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s23\",\"m23\",\"f23\",\"d23\"],\"alphabet\":[\"a23\",\"b23\"],\"start_state\":\"s23\",\"final_states\":[\"f23\"],\"transitions\":[[\"s23\",null,\"m23\"],[\"s23\",null,\"d23\"],[\"m23\",\"a23\",\"m23\"],[\"m23\",\"b23\",\"f23\"]],\"seed_states\":[\"s23\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s23], [d23, m23, s23], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s23], [d23, m23, s23], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117049,"parameters":{"states":["s23","m23","f23","d23"],"alphabet":["a23","b23"],"start_state":"s23","final_states":["f23"],"transitions":[["s23",null,"m23"],["s23",null,"d23"],["m23","a23","m23"],["m23","b23","f23"]],"seed_states":["s23"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a23\",\"b23\"],\"final_states\":[\"f23\"],\"seed_states\":[\"s23\"],\"start_state\":\"s23\",\"states\":[\"d23\",\"f23\",\"m23\",\"s23\"],\"transitions\":[[\"m23\",\"a23\",\"m23\"],[\"m23\",\"b23\",\"f23\"],[\"s23\",null,\"d23\"],[\"s23\",null,\"m23\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0050","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-epsilon-closure；資料={\"states\":[\"s24\",\"m24\",\"f24\",\"d24\"],\"alphabet\":[\"a24\",\"b24\"],\"start_state\":\"s24\",\"final_states\":[\"f24\"],\"transitions\":[[\"s24\",null,\"m24\"],[\"s24\",null,\"d24\"],[\"m24\",\"a24\",\"m24\"],[\"m24\",\"b24\",\"f24\"]],\"seed_states\":[\"s24\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([s24], [d24, m24, s24], 是, finite_epsilon_reachability_without_input_consumption)","explanation_zh":"Wave6第五層核對=([s24], [d24, m24, s24], 是, finite_epsilon_reachability_without_input_consumption)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-epsilon-closure","seed":202611117050,"parameters":{"states":["s24","m24","f24","d24"],"alphabet":["a24","b24"],"start_state":"s24","final_states":["f24"],"transitions":[["s24",null,"m24"],["s24",null,"d24"],["m24","a24","m24"],["m24","b24","f24"]],"seed_states":["s24"],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-epsilon-closure","semantic_template":"qf-mod42-nfa-epsilon-closure/{\"alphabet\":[\"a24\",\"b24\"],\"final_states\":[\"f24\"],\"seed_states\":[\"s24\"],\"start_state\":\"s24\",\"states\":[\"d24\",\"f24\",\"m24\",\"s24\"],\"transitions\":[[\"m24\",\"a24\",\"m24\"],[\"m24\",\"b24\",\"f24\"],[\"s24\",null,\"d24\"],[\"s24\",null,\"m24\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0051","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s0\",\"m0\",\"f0\",\"d0\"],\"alphabet\":[\"a0\",\"b0\"],\"start_state\":\"s0\",\"final_states\":[\"f0\"],\"transitions\":[[\"s0\",null,\"m0\"],[\"s0\",null,\"d0\"],[\"m0\",\"a0\",\"m0\"],[\"m0\",\"b0\",\"f0\"]],\"input\":[\"b0\"],\"path\":[[\"s0\",0],[\"m0\",0],[\"f0\",1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b0], [[s0, 0], [m0, 0], [f0, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([b0], [[s0, 0], [m0, 0], [f0, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117051,"parameters":{"states":["s0","m0","f0","d0"],"alphabet":["a0","b0"],"start_state":"s0","final_states":["f0"],"transitions":[["s0",null,"m0"],["s0",null,"d0"],["m0","a0","m0"],["m0","b0","f0"]],"input":["b0"],"path":[["s0",0],["m0",0],["f0",1]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a0\",\"b0\"],\"final_states\":[\"f0\"],\"input\":[\"b0\"],\"path\":[[\"s0\",0],[\"m0\",0],[\"f0\",1]],\"start_state\":\"s0\",\"states\":[\"d0\",\"f0\",\"m0\",\"s0\"],\"transitions\":[[\"m0\",\"a0\",\"m0\"],[\"m0\",\"b0\",\"f0\"],[\"s0\",null,\"d0\"],[\"s0\",null,\"m0\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0052","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s1\",\"m1\",\"f1\",\"d1\"],\"alphabet\":[\"a1\",\"b1\"],\"start_state\":\"s1\",\"final_states\":[\"f1\"],\"transitions\":[[\"s1\",null,\"m1\"],[\"s1\",null,\"d1\"],[\"m1\",\"a1\",\"m1\"],[\"m1\",\"b1\",\"f1\"]],\"input\":[\"a1\",\"b1\"],\"path\":[[\"s1\",0],[\"m1\",0],[\"m1\",1],[\"f1\",2]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a1, b1], [[s1, 0], [m1, 0], [m1, 1], [f1, 2]], [0, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a1, b1], [[s1, 0], [m1, 0], [m1, 1], [f1, 2]], [0, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117052,"parameters":{"states":["s1","m1","f1","d1"],"alphabet":["a1","b1"],"start_state":"s1","final_states":["f1"],"transitions":[["s1",null,"m1"],["s1",null,"d1"],["m1","a1","m1"],["m1","b1","f1"]],"input":["a1","b1"],"path":[["s1",0],["m1",0],["m1",1],["f1",2]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a1\",\"b1\"],\"final_states\":[\"f1\"],\"input\":[\"a1\",\"b1\"],\"path\":[[\"s1\",0],[\"m1\",0],[\"m1\",1],[\"f1\",2]],\"start_state\":\"s1\",\"states\":[\"d1\",\"f1\",\"m1\",\"s1\"],\"transitions\":[[\"m1\",\"a1\",\"m1\"],[\"m1\",\"b1\",\"f1\"],[\"s1\",null,\"d1\"],[\"s1\",null,\"m1\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0053","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s2\",\"m2\",\"f2\",\"d2\"],\"alphabet\":[\"a2\",\"b2\"],\"start_state\":\"s2\",\"final_states\":[\"f2\"],\"transitions\":[[\"s2\",null,\"m2\"],[\"s2\",null,\"d2\"],[\"m2\",\"a2\",\"m2\"],[\"m2\",\"b2\",\"f2\"]],\"input\":[\"a2\",\"a2\",\"b2\"],\"path\":[[\"s2\",0],[\"m2\",0],[\"m2\",1],[\"m2\",2],[\"f2\",3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a2, a2, b2], [[s2, 0], [m2, 0], [m2, 1], [m2, 2], [f2, 3]], [0, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a2, a2, b2], [[s2, 0], [m2, 0], [m2, 1], [m2, 2], [f2, 3]], [0, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117053,"parameters":{"states":["s2","m2","f2","d2"],"alphabet":["a2","b2"],"start_state":"s2","final_states":["f2"],"transitions":[["s2",null,"m2"],["s2",null,"d2"],["m2","a2","m2"],["m2","b2","f2"]],"input":["a2","a2","b2"],"path":[["s2",0],["m2",0],["m2",1],["m2",2],["f2",3]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a2\",\"b2\"],\"final_states\":[\"f2\"],\"input\":[\"a2\",\"a2\",\"b2\"],\"path\":[[\"s2\",0],[\"m2\",0],[\"m2\",1],[\"m2\",2],[\"f2\",3]],\"start_state\":\"s2\",\"states\":[\"d2\",\"f2\",\"m2\",\"s2\"],\"transitions\":[[\"m2\",\"a2\",\"m2\"],[\"m2\",\"b2\",\"f2\"],[\"s2\",null,\"d2\"],[\"s2\",null,\"m2\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0054","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s3\",\"m3\",\"f3\",\"d3\"],\"alphabet\":[\"a3\",\"b3\"],\"start_state\":\"s3\",\"final_states\":[\"f3\"],\"transitions\":[[\"s3\",null,\"m3\"],[\"s3\",null,\"d3\"],[\"m3\",\"a3\",\"m3\"],[\"m3\",\"b3\",\"f3\"]],\"input\":[\"a3\",\"a3\",\"a3\",\"b3\"],\"path\":[[\"s3\",0],[\"m3\",0],[\"m3\",1],[\"m3\",2],[\"m3\",3],[\"f3\",4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a3, a3, a3, b3], [[s3, 0], [m3, 0], [m3, 1], [m3, 2], [m3, 3], [f3, 4]], [0, 2, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a3, a3, a3, b3], [[s3, 0], [m3, 0], [m3, 1], [m3, 2], [m3, 3], [f3, 4]], [0, 2, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117054,"parameters":{"states":["s3","m3","f3","d3"],"alphabet":["a3","b3"],"start_state":"s3","final_states":["f3"],"transitions":[["s3",null,"m3"],["s3",null,"d3"],["m3","a3","m3"],["m3","b3","f3"]],"input":["a3","a3","a3","b3"],"path":[["s3",0],["m3",0],["m3",1],["m3",2],["m3",3],["f3",4]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a3\",\"b3\"],\"final_states\":[\"f3\"],\"input\":[\"a3\",\"a3\",\"a3\",\"b3\"],\"path\":[[\"s3\",0],[\"m3\",0],[\"m3\",1],[\"m3\",2],[\"m3\",3],[\"f3\",4]],\"start_state\":\"s3\",\"states\":[\"d3\",\"f3\",\"m3\",\"s3\"],\"transitions\":[[\"m3\",\"a3\",\"m3\"],[\"m3\",\"b3\",\"f3\"],[\"s3\",null,\"d3\"],[\"s3\",null,\"m3\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0055","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s4\",\"m4\",\"f4\",\"d4\"],\"alphabet\":[\"a4\",\"b4\"],\"start_state\":\"s4\",\"final_states\":[\"f4\"],\"transitions\":[[\"s4\",null,\"m4\"],[\"s4\",null,\"d4\"],[\"m4\",\"a4\",\"m4\"],[\"m4\",\"b4\",\"f4\"]],\"input\":[\"b4\"],\"path\":[[\"s4\",0],[\"m4\",0],[\"f4\",1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b4], [[s4, 0], [m4, 0], [f4, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([b4], [[s4, 0], [m4, 0], [f4, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117055,"parameters":{"states":["s4","m4","f4","d4"],"alphabet":["a4","b4"],"start_state":"s4","final_states":["f4"],"transitions":[["s4",null,"m4"],["s4",null,"d4"],["m4","a4","m4"],["m4","b4","f4"]],"input":["b4"],"path":[["s4",0],["m4",0],["f4",1]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a4\",\"b4\"],\"final_states\":[\"f4\"],\"input\":[\"b4\"],\"path\":[[\"s4\",0],[\"m4\",0],[\"f4\",1]],\"start_state\":\"s4\",\"states\":[\"d4\",\"f4\",\"m4\",\"s4\"],\"transitions\":[[\"m4\",\"a4\",\"m4\"],[\"m4\",\"b4\",\"f4\"],[\"s4\",null,\"d4\"],[\"s4\",null,\"m4\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0056","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s5\",\"m5\",\"f5\",\"d5\"],\"alphabet\":[\"a5\",\"b5\"],\"start_state\":\"s5\",\"final_states\":[\"f5\"],\"transitions\":[[\"s5\",null,\"m5\"],[\"s5\",null,\"d5\"],[\"m5\",\"a5\",\"m5\"],[\"m5\",\"b5\",\"f5\"]],\"input\":[\"a5\",\"b5\"],\"path\":[[\"s5\",0],[\"m5\",0],[\"m5\",1],[\"f5\",2]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a5, b5], [[s5, 0], [m5, 0], [m5, 1], [f5, 2]], [0, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a5, b5], [[s5, 0], [m5, 0], [m5, 1], [f5, 2]], [0, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117056,"parameters":{"states":["s5","m5","f5","d5"],"alphabet":["a5","b5"],"start_state":"s5","final_states":["f5"],"transitions":[["s5",null,"m5"],["s5",null,"d5"],["m5","a5","m5"],["m5","b5","f5"]],"input":["a5","b5"],"path":[["s5",0],["m5",0],["m5",1],["f5",2]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a5\",\"b5\"],\"final_states\":[\"f5\"],\"input\":[\"a5\",\"b5\"],\"path\":[[\"s5\",0],[\"m5\",0],[\"m5\",1],[\"f5\",2]],\"start_state\":\"s5\",\"states\":[\"d5\",\"f5\",\"m5\",\"s5\"],\"transitions\":[[\"m5\",\"a5\",\"m5\"],[\"m5\",\"b5\",\"f5\"],[\"s5\",null,\"d5\"],[\"s5\",null,\"m5\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0057","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s6\",\"m6\",\"f6\",\"d6\"],\"alphabet\":[\"a6\",\"b6\"],\"start_state\":\"s6\",\"final_states\":[\"f6\"],\"transitions\":[[\"s6\",null,\"m6\"],[\"s6\",null,\"d6\"],[\"m6\",\"a6\",\"m6\"],[\"m6\",\"b6\",\"f6\"]],\"input\":[\"a6\",\"a6\",\"b6\"],\"path\":[[\"s6\",0],[\"m6\",0],[\"m6\",1],[\"m6\",2],[\"f6\",3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a6, a6, b6], [[s6, 0], [m6, 0], [m6, 1], [m6, 2], [f6, 3]], [0, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a6, a6, b6], [[s6, 0], [m6, 0], [m6, 1], [m6, 2], [f6, 3]], [0, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117057,"parameters":{"states":["s6","m6","f6","d6"],"alphabet":["a6","b6"],"start_state":"s6","final_states":["f6"],"transitions":[["s6",null,"m6"],["s6",null,"d6"],["m6","a6","m6"],["m6","b6","f6"]],"input":["a6","a6","b6"],"path":[["s6",0],["m6",0],["m6",1],["m6",2],["f6",3]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a6\",\"b6\"],\"final_states\":[\"f6\"],\"input\":[\"a6\",\"a6\",\"b6\"],\"path\":[[\"s6\",0],[\"m6\",0],[\"m6\",1],[\"m6\",2],[\"f6\",3]],\"start_state\":\"s6\",\"states\":[\"d6\",\"f6\",\"m6\",\"s6\"],\"transitions\":[[\"m6\",\"a6\",\"m6\"],[\"m6\",\"b6\",\"f6\"],[\"s6\",null,\"d6\"],[\"s6\",null,\"m6\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0058","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s7\",\"m7\",\"f7\",\"d7\"],\"alphabet\":[\"a7\",\"b7\"],\"start_state\":\"s7\",\"final_states\":[\"f7\"],\"transitions\":[[\"s7\",null,\"m7\"],[\"s7\",null,\"d7\"],[\"m7\",\"a7\",\"m7\"],[\"m7\",\"b7\",\"f7\"]],\"input\":[\"a7\",\"a7\",\"a7\",\"b7\"],\"path\":[[\"s7\",0],[\"m7\",0],[\"m7\",1],[\"m7\",2],[\"m7\",3],[\"f7\",4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a7, a7, a7, b7], [[s7, 0], [m7, 0], [m7, 1], [m7, 2], [m7, 3], [f7, 4]], [0, 2, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a7, a7, a7, b7], [[s7, 0], [m7, 0], [m7, 1], [m7, 2], [m7, 3], [f7, 4]], [0, 2, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117058,"parameters":{"states":["s7","m7","f7","d7"],"alphabet":["a7","b7"],"start_state":"s7","final_states":["f7"],"transitions":[["s7",null,"m7"],["s7",null,"d7"],["m7","a7","m7"],["m7","b7","f7"]],"input":["a7","a7","a7","b7"],"path":[["s7",0],["m7",0],["m7",1],["m7",2],["m7",3],["f7",4]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a7\",\"b7\"],\"final_states\":[\"f7\"],\"input\":[\"a7\",\"a7\",\"a7\",\"b7\"],\"path\":[[\"s7\",0],[\"m7\",0],[\"m7\",1],[\"m7\",2],[\"m7\",3],[\"f7\",4]],\"start_state\":\"s7\",\"states\":[\"d7\",\"f7\",\"m7\",\"s7\"],\"transitions\":[[\"m7\",\"a7\",\"m7\"],[\"m7\",\"b7\",\"f7\"],[\"s7\",null,\"d7\"],[\"s7\",null,\"m7\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0059","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s8\",\"m8\",\"f8\",\"d8\"],\"alphabet\":[\"a8\",\"b8\"],\"start_state\":\"s8\",\"final_states\":[\"f8\"],\"transitions\":[[\"s8\",null,\"m8\"],[\"s8\",null,\"d8\"],[\"m8\",\"a8\",\"m8\"],[\"m8\",\"b8\",\"f8\"]],\"input\":[\"b8\"],\"path\":[[\"s8\",0],[\"m8\",0],[\"f8\",1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b8], [[s8, 0], [m8, 0], [f8, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([b8], [[s8, 0], [m8, 0], [f8, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117059,"parameters":{"states":["s8","m8","f8","d8"],"alphabet":["a8","b8"],"start_state":"s8","final_states":["f8"],"transitions":[["s8",null,"m8"],["s8",null,"d8"],["m8","a8","m8"],["m8","b8","f8"]],"input":["b8"],"path":[["s8",0],["m8",0],["f8",1]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a8\",\"b8\"],\"final_states\":[\"f8\"],\"input\":[\"b8\"],\"path\":[[\"s8\",0],[\"m8\",0],[\"f8\",1]],\"start_state\":\"s8\",\"states\":[\"d8\",\"f8\",\"m8\",\"s8\"],\"transitions\":[[\"m8\",\"a8\",\"m8\"],[\"m8\",\"b8\",\"f8\"],[\"s8\",null,\"d8\"],[\"s8\",null,\"m8\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0060","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s9\",\"m9\",\"f9\",\"d9\"],\"alphabet\":[\"a9\",\"b9\"],\"start_state\":\"s9\",\"final_states\":[\"f9\"],\"transitions\":[[\"s9\",null,\"m9\"],[\"s9\",null,\"d9\"],[\"m9\",\"a9\",\"m9\"],[\"m9\",\"b9\",\"f9\"]],\"input\":[\"a9\",\"b9\"],\"path\":[[\"s9\",0],[\"m9\",0],[\"m9\",1],[\"f9\",2]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a9, b9], [[s9, 0], [m9, 0], [m9, 1], [f9, 2]], [0, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a9, b9], [[s9, 0], [m9, 0], [m9, 1], [f9, 2]], [0, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117060,"parameters":{"states":["s9","m9","f9","d9"],"alphabet":["a9","b9"],"start_state":"s9","final_states":["f9"],"transitions":[["s9",null,"m9"],["s9",null,"d9"],["m9","a9","m9"],["m9","b9","f9"]],"input":["a9","b9"],"path":[["s9",0],["m9",0],["m9",1],["f9",2]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a9\",\"b9\"],\"final_states\":[\"f9\"],\"input\":[\"a9\",\"b9\"],\"path\":[[\"s9\",0],[\"m9\",0],[\"m9\",1],[\"f9\",2]],\"start_state\":\"s9\",\"states\":[\"d9\",\"f9\",\"m9\",\"s9\"],\"transitions\":[[\"m9\",\"a9\",\"m9\"],[\"m9\",\"b9\",\"f9\"],[\"s9\",null,\"d9\"],[\"s9\",null,\"m9\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0061","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s10\",\"m10\",\"f10\",\"d10\"],\"alphabet\":[\"a10\",\"b10\"],\"start_state\":\"s10\",\"final_states\":[\"f10\"],\"transitions\":[[\"s10\",null,\"m10\"],[\"s10\",null,\"d10\"],[\"m10\",\"a10\",\"m10\"],[\"m10\",\"b10\",\"f10\"]],\"input\":[\"a10\",\"a10\",\"b10\"],\"path\":[[\"s10\",0],[\"m10\",0],[\"m10\",1],[\"m10\",2],[\"f10\",3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a10, a10, b10], [[s10, 0], [m10, 0], [m10, 1], [m10, 2], [f10, 3]], [0, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a10, a10, b10], [[s10, 0], [m10, 0], [m10, 1], [m10, 2], [f10, 3]], [0, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117061,"parameters":{"states":["s10","m10","f10","d10"],"alphabet":["a10","b10"],"start_state":"s10","final_states":["f10"],"transitions":[["s10",null,"m10"],["s10",null,"d10"],["m10","a10","m10"],["m10","b10","f10"]],"input":["a10","a10","b10"],"path":[["s10",0],["m10",0],["m10",1],["m10",2],["f10",3]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a10\",\"b10\"],\"final_states\":[\"f10\"],\"input\":[\"a10\",\"a10\",\"b10\"],\"path\":[[\"s10\",0],[\"m10\",0],[\"m10\",1],[\"m10\",2],[\"f10\",3]],\"start_state\":\"s10\",\"states\":[\"d10\",\"f10\",\"m10\",\"s10\"],\"transitions\":[[\"m10\",\"a10\",\"m10\"],[\"m10\",\"b10\",\"f10\"],[\"s10\",null,\"d10\"],[\"s10\",null,\"m10\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0062","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s11\",\"m11\",\"f11\",\"d11\"],\"alphabet\":[\"a11\",\"b11\"],\"start_state\":\"s11\",\"final_states\":[\"f11\"],\"transitions\":[[\"s11\",null,\"m11\"],[\"s11\",null,\"d11\"],[\"m11\",\"a11\",\"m11\"],[\"m11\",\"b11\",\"f11\"]],\"input\":[\"a11\",\"a11\",\"a11\",\"b11\"],\"path\":[[\"s11\",0],[\"m11\",0],[\"m11\",1],[\"m11\",2],[\"m11\",3],[\"f11\",4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a11, a11, a11, b11], [[s11, 0], [m11, 0], [m11, 1], [m11, 2], [m11, 3], [f11, 4]], [0, 2, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a11, a11, a11, b11], [[s11, 0], [m11, 0], [m11, 1], [m11, 2], [m11, 3], [f11, 4]], [0, 2, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117062,"parameters":{"states":["s11","m11","f11","d11"],"alphabet":["a11","b11"],"start_state":"s11","final_states":["f11"],"transitions":[["s11",null,"m11"],["s11",null,"d11"],["m11","a11","m11"],["m11","b11","f11"]],"input":["a11","a11","a11","b11"],"path":[["s11",0],["m11",0],["m11",1],["m11",2],["m11",3],["f11",4]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a11\",\"b11\"],\"final_states\":[\"f11\"],\"input\":[\"a11\",\"a11\",\"a11\",\"b11\"],\"path\":[[\"s11\",0],[\"m11\",0],[\"m11\",1],[\"m11\",2],[\"m11\",3],[\"f11\",4]],\"start_state\":\"s11\",\"states\":[\"d11\",\"f11\",\"m11\",\"s11\"],\"transitions\":[[\"m11\",\"a11\",\"m11\"],[\"m11\",\"b11\",\"f11\"],[\"s11\",null,\"d11\"],[\"s11\",null,\"m11\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0063","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s12\",\"m12\",\"f12\",\"d12\"],\"alphabet\":[\"a12\",\"b12\"],\"start_state\":\"s12\",\"final_states\":[\"f12\"],\"transitions\":[[\"s12\",null,\"m12\"],[\"s12\",null,\"d12\"],[\"m12\",\"a12\",\"m12\"],[\"m12\",\"b12\",\"f12\"]],\"input\":[\"b12\"],\"path\":[[\"s12\",0],[\"m12\",0],[\"f12\",1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b12], [[s12, 0], [m12, 0], [f12, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([b12], [[s12, 0], [m12, 0], [f12, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117063,"parameters":{"states":["s12","m12","f12","d12"],"alphabet":["a12","b12"],"start_state":"s12","final_states":["f12"],"transitions":[["s12",null,"m12"],["s12",null,"d12"],["m12","a12","m12"],["m12","b12","f12"]],"input":["b12"],"path":[["s12",0],["m12",0],["f12",1]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a12\",\"b12\"],\"final_states\":[\"f12\"],\"input\":[\"b12\"],\"path\":[[\"s12\",0],[\"m12\",0],[\"f12\",1]],\"start_state\":\"s12\",\"states\":[\"d12\",\"f12\",\"m12\",\"s12\"],\"transitions\":[[\"m12\",\"a12\",\"m12\"],[\"m12\",\"b12\",\"f12\"],[\"s12\",null,\"d12\"],[\"s12\",null,\"m12\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0064","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s13\",\"m13\",\"f13\",\"d13\"],\"alphabet\":[\"a13\",\"b13\"],\"start_state\":\"s13\",\"final_states\":[\"f13\"],\"transitions\":[[\"s13\",null,\"m13\"],[\"s13\",null,\"d13\"],[\"m13\",\"a13\",\"m13\"],[\"m13\",\"b13\",\"f13\"]],\"input\":[\"a13\",\"b13\"],\"path\":[[\"s13\",0],[\"m13\",0],[\"m13\",1],[\"f13\",2]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a13, b13], [[s13, 0], [m13, 0], [m13, 1], [f13, 2]], [0, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a13, b13], [[s13, 0], [m13, 0], [m13, 1], [f13, 2]], [0, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117064,"parameters":{"states":["s13","m13","f13","d13"],"alphabet":["a13","b13"],"start_state":"s13","final_states":["f13"],"transitions":[["s13",null,"m13"],["s13",null,"d13"],["m13","a13","m13"],["m13","b13","f13"]],"input":["a13","b13"],"path":[["s13",0],["m13",0],["m13",1],["f13",2]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a13\",\"b13\"],\"final_states\":[\"f13\"],\"input\":[\"a13\",\"b13\"],\"path\":[[\"s13\",0],[\"m13\",0],[\"m13\",1],[\"f13\",2]],\"start_state\":\"s13\",\"states\":[\"d13\",\"f13\",\"m13\",\"s13\"],\"transitions\":[[\"m13\",\"a13\",\"m13\"],[\"m13\",\"b13\",\"f13\"],[\"s13\",null,\"d13\"],[\"s13\",null,\"m13\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0065","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s14\",\"m14\",\"f14\",\"d14\"],\"alphabet\":[\"a14\",\"b14\"],\"start_state\":\"s14\",\"final_states\":[\"f14\"],\"transitions\":[[\"s14\",null,\"m14\"],[\"s14\",null,\"d14\"],[\"m14\",\"a14\",\"m14\"],[\"m14\",\"b14\",\"f14\"]],\"input\":[\"a14\",\"a14\",\"b14\"],\"path\":[[\"s14\",0],[\"m14\",0],[\"m14\",1],[\"m14\",2],[\"f14\",3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a14, a14, b14], [[s14, 0], [m14, 0], [m14, 1], [m14, 2], [f14, 3]], [0, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a14, a14, b14], [[s14, 0], [m14, 0], [m14, 1], [m14, 2], [f14, 3]], [0, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117065,"parameters":{"states":["s14","m14","f14","d14"],"alphabet":["a14","b14"],"start_state":"s14","final_states":["f14"],"transitions":[["s14",null,"m14"],["s14",null,"d14"],["m14","a14","m14"],["m14","b14","f14"]],"input":["a14","a14","b14"],"path":[["s14",0],["m14",0],["m14",1],["m14",2],["f14",3]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a14\",\"b14\"],\"final_states\":[\"f14\"],\"input\":[\"a14\",\"a14\",\"b14\"],\"path\":[[\"s14\",0],[\"m14\",0],[\"m14\",1],[\"m14\",2],[\"f14\",3]],\"start_state\":\"s14\",\"states\":[\"d14\",\"f14\",\"m14\",\"s14\"],\"transitions\":[[\"m14\",\"a14\",\"m14\"],[\"m14\",\"b14\",\"f14\"],[\"s14\",null,\"d14\"],[\"s14\",null,\"m14\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0066","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s15\",\"m15\",\"f15\",\"d15\"],\"alphabet\":[\"a15\",\"b15\"],\"start_state\":\"s15\",\"final_states\":[\"f15\"],\"transitions\":[[\"s15\",null,\"m15\"],[\"s15\",null,\"d15\"],[\"m15\",\"a15\",\"m15\"],[\"m15\",\"b15\",\"f15\"]],\"input\":[\"a15\",\"a15\",\"a15\",\"b15\"],\"path\":[[\"s15\",0],[\"m15\",0],[\"m15\",1],[\"m15\",2],[\"m15\",3],[\"f15\",4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a15, a15, a15, b15], [[s15, 0], [m15, 0], [m15, 1], [m15, 2], [m15, 3], [f15, 4]], [0, 2, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a15, a15, a15, b15], [[s15, 0], [m15, 0], [m15, 1], [m15, 2], [m15, 3], [f15, 4]], [0, 2, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117066,"parameters":{"states":["s15","m15","f15","d15"],"alphabet":["a15","b15"],"start_state":"s15","final_states":["f15"],"transitions":[["s15",null,"m15"],["s15",null,"d15"],["m15","a15","m15"],["m15","b15","f15"]],"input":["a15","a15","a15","b15"],"path":[["s15",0],["m15",0],["m15",1],["m15",2],["m15",3],["f15",4]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a15\",\"b15\"],\"final_states\":[\"f15\"],\"input\":[\"a15\",\"a15\",\"a15\",\"b15\"],\"path\":[[\"s15\",0],[\"m15\",0],[\"m15\",1],[\"m15\",2],[\"m15\",3],[\"f15\",4]],\"start_state\":\"s15\",\"states\":[\"d15\",\"f15\",\"m15\",\"s15\"],\"transitions\":[[\"m15\",\"a15\",\"m15\"],[\"m15\",\"b15\",\"f15\"],[\"s15\",null,\"d15\"],[\"s15\",null,\"m15\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0067","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s16\",\"m16\",\"f16\",\"d16\"],\"alphabet\":[\"a16\",\"b16\"],\"start_state\":\"s16\",\"final_states\":[\"f16\"],\"transitions\":[[\"s16\",null,\"m16\"],[\"s16\",null,\"d16\"],[\"m16\",\"a16\",\"m16\"],[\"m16\",\"b16\",\"f16\"]],\"input\":[\"b16\"],\"path\":[[\"s16\",0],[\"m16\",0],[\"f16\",1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b16], [[s16, 0], [m16, 0], [f16, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([b16], [[s16, 0], [m16, 0], [f16, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117067,"parameters":{"states":["s16","m16","f16","d16"],"alphabet":["a16","b16"],"start_state":"s16","final_states":["f16"],"transitions":[["s16",null,"m16"],["s16",null,"d16"],["m16","a16","m16"],["m16","b16","f16"]],"input":["b16"],"path":[["s16",0],["m16",0],["f16",1]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a16\",\"b16\"],\"final_states\":[\"f16\"],\"input\":[\"b16\"],\"path\":[[\"s16\",0],[\"m16\",0],[\"f16\",1]],\"start_state\":\"s16\",\"states\":[\"d16\",\"f16\",\"m16\",\"s16\"],\"transitions\":[[\"m16\",\"a16\",\"m16\"],[\"m16\",\"b16\",\"f16\"],[\"s16\",null,\"d16\"],[\"s16\",null,\"m16\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0068","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s17\",\"m17\",\"f17\",\"d17\"],\"alphabet\":[\"a17\",\"b17\"],\"start_state\":\"s17\",\"final_states\":[\"f17\"],\"transitions\":[[\"s17\",null,\"m17\"],[\"s17\",null,\"d17\"],[\"m17\",\"a17\",\"m17\"],[\"m17\",\"b17\",\"f17\"]],\"input\":[\"a17\",\"b17\"],\"path\":[[\"s17\",0],[\"m17\",0],[\"m17\",1],[\"f17\",2]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a17, b17], [[s17, 0], [m17, 0], [m17, 1], [f17, 2]], [0, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a17, b17], [[s17, 0], [m17, 0], [m17, 1], [f17, 2]], [0, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117068,"parameters":{"states":["s17","m17","f17","d17"],"alphabet":["a17","b17"],"start_state":"s17","final_states":["f17"],"transitions":[["s17",null,"m17"],["s17",null,"d17"],["m17","a17","m17"],["m17","b17","f17"]],"input":["a17","b17"],"path":[["s17",0],["m17",0],["m17",1],["f17",2]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a17\",\"b17\"],\"final_states\":[\"f17\"],\"input\":[\"a17\",\"b17\"],\"path\":[[\"s17\",0],[\"m17\",0],[\"m17\",1],[\"f17\",2]],\"start_state\":\"s17\",\"states\":[\"d17\",\"f17\",\"m17\",\"s17\"],\"transitions\":[[\"m17\",\"a17\",\"m17\"],[\"m17\",\"b17\",\"f17\"],[\"s17\",null,\"d17\"],[\"s17\",null,\"m17\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0069","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s18\",\"m18\",\"f18\",\"d18\"],\"alphabet\":[\"a18\",\"b18\"],\"start_state\":\"s18\",\"final_states\":[\"f18\"],\"transitions\":[[\"s18\",null,\"m18\"],[\"s18\",null,\"d18\"],[\"m18\",\"a18\",\"m18\"],[\"m18\",\"b18\",\"f18\"]],\"input\":[\"a18\",\"a18\",\"b18\"],\"path\":[[\"s18\",0],[\"m18\",0],[\"m18\",1],[\"m18\",2],[\"f18\",3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a18, a18, b18], [[s18, 0], [m18, 0], [m18, 1], [m18, 2], [f18, 3]], [0, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a18, a18, b18], [[s18, 0], [m18, 0], [m18, 1], [m18, 2], [f18, 3]], [0, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117069,"parameters":{"states":["s18","m18","f18","d18"],"alphabet":["a18","b18"],"start_state":"s18","final_states":["f18"],"transitions":[["s18",null,"m18"],["s18",null,"d18"],["m18","a18","m18"],["m18","b18","f18"]],"input":["a18","a18","b18"],"path":[["s18",0],["m18",0],["m18",1],["m18",2],["f18",3]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a18\",\"b18\"],\"final_states\":[\"f18\"],\"input\":[\"a18\",\"a18\",\"b18\"],\"path\":[[\"s18\",0],[\"m18\",0],[\"m18\",1],[\"m18\",2],[\"f18\",3]],\"start_state\":\"s18\",\"states\":[\"d18\",\"f18\",\"m18\",\"s18\"],\"transitions\":[[\"m18\",\"a18\",\"m18\"],[\"m18\",\"b18\",\"f18\"],[\"s18\",null,\"d18\"],[\"s18\",null,\"m18\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0070","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s19\",\"m19\",\"f19\",\"d19\"],\"alphabet\":[\"a19\",\"b19\"],\"start_state\":\"s19\",\"final_states\":[\"f19\"],\"transitions\":[[\"s19\",null,\"m19\"],[\"s19\",null,\"d19\"],[\"m19\",\"a19\",\"m19\"],[\"m19\",\"b19\",\"f19\"]],\"input\":[\"a19\",\"a19\",\"a19\",\"b19\"],\"path\":[[\"s19\",0],[\"m19\",0],[\"m19\",1],[\"m19\",2],[\"m19\",3],[\"f19\",4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a19, a19, a19, b19], [[s19, 0], [m19, 0], [m19, 1], [m19, 2], [m19, 3], [f19, 4]], [0, 2, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a19, a19, a19, b19], [[s19, 0], [m19, 0], [m19, 1], [m19, 2], [m19, 3], [f19, 4]], [0, 2, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117070,"parameters":{"states":["s19","m19","f19","d19"],"alphabet":["a19","b19"],"start_state":"s19","final_states":["f19"],"transitions":[["s19",null,"m19"],["s19",null,"d19"],["m19","a19","m19"],["m19","b19","f19"]],"input":["a19","a19","a19","b19"],"path":[["s19",0],["m19",0],["m19",1],["m19",2],["m19",3],["f19",4]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a19\",\"b19\"],\"final_states\":[\"f19\"],\"input\":[\"a19\",\"a19\",\"a19\",\"b19\"],\"path\":[[\"s19\",0],[\"m19\",0],[\"m19\",1],[\"m19\",2],[\"m19\",3],[\"f19\",4]],\"start_state\":\"s19\",\"states\":[\"d19\",\"f19\",\"m19\",\"s19\"],\"transitions\":[[\"m19\",\"a19\",\"m19\"],[\"m19\",\"b19\",\"f19\"],[\"s19\",null,\"d19\"],[\"s19\",null,\"m19\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0071","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s20\",\"m20\",\"f20\",\"d20\"],\"alphabet\":[\"a20\",\"b20\"],\"start_state\":\"s20\",\"final_states\":[\"f20\"],\"transitions\":[[\"s20\",null,\"m20\"],[\"s20\",null,\"d20\"],[\"m20\",\"a20\",\"m20\"],[\"m20\",\"b20\",\"f20\"]],\"input\":[\"b20\"],\"path\":[[\"s20\",0],[\"m20\",0],[\"f20\",1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b20], [[s20, 0], [m20, 0], [f20, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([b20], [[s20, 0], [m20, 0], [f20, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117071,"parameters":{"states":["s20","m20","f20","d20"],"alphabet":["a20","b20"],"start_state":"s20","final_states":["f20"],"transitions":[["s20",null,"m20"],["s20",null,"d20"],["m20","a20","m20"],["m20","b20","f20"]],"input":["b20"],"path":[["s20",0],["m20",0],["f20",1]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a20\",\"b20\"],\"final_states\":[\"f20\"],\"input\":[\"b20\"],\"path\":[[\"s20\",0],[\"m20\",0],[\"f20\",1]],\"start_state\":\"s20\",\"states\":[\"d20\",\"f20\",\"m20\",\"s20\"],\"transitions\":[[\"m20\",\"a20\",\"m20\"],[\"m20\",\"b20\",\"f20\"],[\"s20\",null,\"d20\"],[\"s20\",null,\"m20\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0072","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s21\",\"m21\",\"f21\",\"d21\"],\"alphabet\":[\"a21\",\"b21\"],\"start_state\":\"s21\",\"final_states\":[\"f21\"],\"transitions\":[[\"s21\",null,\"m21\"],[\"s21\",null,\"d21\"],[\"m21\",\"a21\",\"m21\"],[\"m21\",\"b21\",\"f21\"]],\"input\":[\"a21\",\"b21\"],\"path\":[[\"s21\",0],[\"m21\",0],[\"m21\",1],[\"f21\",2]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a21, b21], [[s21, 0], [m21, 0], [m21, 1], [f21, 2]], [0, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a21, b21], [[s21, 0], [m21, 0], [m21, 1], [f21, 2]], [0, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117072,"parameters":{"states":["s21","m21","f21","d21"],"alphabet":["a21","b21"],"start_state":"s21","final_states":["f21"],"transitions":[["s21",null,"m21"],["s21",null,"d21"],["m21","a21","m21"],["m21","b21","f21"]],"input":["a21","b21"],"path":[["s21",0],["m21",0],["m21",1],["f21",2]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a21\",\"b21\"],\"final_states\":[\"f21\"],\"input\":[\"a21\",\"b21\"],\"path\":[[\"s21\",0],[\"m21\",0],[\"m21\",1],[\"f21\",2]],\"start_state\":\"s21\",\"states\":[\"d21\",\"f21\",\"m21\",\"s21\"],\"transitions\":[[\"m21\",\"a21\",\"m21\"],[\"m21\",\"b21\",\"f21\"],[\"s21\",null,\"d21\"],[\"s21\",null,\"m21\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0073","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s22\",\"m22\",\"f22\",\"d22\"],\"alphabet\":[\"a22\",\"b22\"],\"start_state\":\"s22\",\"final_states\":[\"f22\"],\"transitions\":[[\"s22\",null,\"m22\"],[\"s22\",null,\"d22\"],[\"m22\",\"a22\",\"m22\"],[\"m22\",\"b22\",\"f22\"]],\"input\":[\"a22\",\"a22\",\"b22\"],\"path\":[[\"s22\",0],[\"m22\",0],[\"m22\",1],[\"m22\",2],[\"f22\",3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a22, a22, b22], [[s22, 0], [m22, 0], [m22, 1], [m22, 2], [f22, 3]], [0, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a22, a22, b22], [[s22, 0], [m22, 0], [m22, 1], [m22, 2], [f22, 3]], [0, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117073,"parameters":{"states":["s22","m22","f22","d22"],"alphabet":["a22","b22"],"start_state":"s22","final_states":["f22"],"transitions":[["s22",null,"m22"],["s22",null,"d22"],["m22","a22","m22"],["m22","b22","f22"]],"input":["a22","a22","b22"],"path":[["s22",0],["m22",0],["m22",1],["m22",2],["f22",3]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a22\",\"b22\"],\"final_states\":[\"f22\"],\"input\":[\"a22\",\"a22\",\"b22\"],\"path\":[[\"s22\",0],[\"m22\",0],[\"m22\",1],[\"m22\",2],[\"f22\",3]],\"start_state\":\"s22\",\"states\":[\"d22\",\"f22\",\"m22\",\"s22\"],\"transitions\":[[\"m22\",\"a22\",\"m22\"],[\"m22\",\"b22\",\"f22\"],[\"s22\",null,\"d22\"],[\"s22\",null,\"m22\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0074","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s23\",\"m23\",\"f23\",\"d23\"],\"alphabet\":[\"a23\",\"b23\"],\"start_state\":\"s23\",\"final_states\":[\"f23\"],\"transitions\":[[\"s23\",null,\"m23\"],[\"s23\",null,\"d23\"],[\"m23\",\"a23\",\"m23\"],[\"m23\",\"b23\",\"f23\"]],\"input\":[\"a23\",\"a23\",\"a23\",\"b23\"],\"path\":[[\"s23\",0],[\"m23\",0],[\"m23\",1],[\"m23\",2],[\"m23\",3],[\"f23\",4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a23, a23, a23, b23], [[s23, 0], [m23, 0], [m23, 1], [m23, 2], [m23, 3], [f23, 4]], [0, 2, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([a23, a23, a23, b23], [[s23, 0], [m23, 0], [m23, 1], [m23, 2], [m23, 3], [f23, 4]], [0, 2, 2, 2, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117074,"parameters":{"states":["s23","m23","f23","d23"],"alphabet":["a23","b23"],"start_state":"s23","final_states":["f23"],"transitions":[["s23",null,"m23"],["s23",null,"d23"],["m23","a23","m23"],["m23","b23","f23"]],"input":["a23","a23","a23","b23"],"path":[["s23",0],["m23",0],["m23",1],["m23",2],["m23",3],["f23",4]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a23\",\"b23\"],\"final_states\":[\"f23\"],\"input\":[\"a23\",\"a23\",\"a23\",\"b23\"],\"path\":[[\"s23\",0],[\"m23\",0],[\"m23\",1],[\"m23\",2],[\"m23\",3],[\"f23\",4]],\"start_state\":\"s23\",\"states\":[\"d23\",\"f23\",\"m23\",\"s23\"],\"transitions\":[[\"m23\",\"a23\",\"m23\"],[\"m23\",\"b23\",\"f23\"],[\"s23\",null,\"d23\"],[\"s23\",null,\"m23\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0075","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-accepting-path-witness；資料={\"states\":[\"s24\",\"m24\",\"f24\",\"d24\"],\"alphabet\":[\"a24\",\"b24\"],\"start_state\":\"s24\",\"final_states\":[\"f24\"],\"transitions\":[[\"s24\",null,\"m24\"],[\"s24\",null,\"d24\"],[\"m24\",\"a24\",\"m24\"],[\"m24\",\"b24\",\"f24\"]],\"input\":[\"b24\"],\"path\":[[\"s24\",0],[\"m24\",0],[\"f24\",1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b24], [[s24, 0], [m24, 0], [f24, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)","explanation_zh":"Wave6第五層核對=([b24], [[s24, 0], [m24, 0], [f24, 1]], [0, 3], 是, 是, one_finite_path_consuming_full_input_and_ending_final_proves_membership)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-accepting-path-witness","seed":202611117075,"parameters":{"states":["s24","m24","f24","d24"],"alphabet":["a24","b24"],"start_state":"s24","final_states":["f24"],"transitions":[["s24",null,"m24"],["s24",null,"d24"],["m24","a24","m24"],["m24","b24","f24"]],"input":["b24"],"path":[["s24",0],["m24",0],["f24",1]],"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-accepting-path-witness","semantic_template":"qf-mod42-nfa-accepting-path-witness/{\"alphabet\":[\"a24\",\"b24\"],\"final_states\":[\"f24\"],\"input\":[\"b24\"],\"path\":[[\"s24\",0],[\"m24\",0],[\"f24\",1]],\"start_state\":\"s24\",\"states\":[\"d24\",\"f24\",\"m24\",\"s24\"],\"transitions\":[[\"m24\",\"a24\",\"m24\"],[\"m24\",\"b24\",\"f24\"],[\"s24\",null,\"d24\"],[\"s24\",null,\"m24\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0076","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s0\",\"m0\",\"f0\",\"d0\"],\"alphabet\":[\"a0\",\"b0\"],\"start_state\":\"s0\",\"final_states\":[\"f0\"],\"transitions\":[[\"s0\",null,\"m0\"],[\"s0\",null,\"d0\"],[\"m0\",\"a0\",\"m0\"],[\"m0\",\"b0\",\"f0\"]],\"input\":[\"b0\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b0], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([b0], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117076,"parameters":{"states":["s0","m0","f0","d0"],"alphabet":["a0","b0"],"start_state":"s0","final_states":["f0"],"transitions":[["s0",null,"m0"],["s0",null,"d0"],["m0","a0","m0"],["m0","b0","f0"]],"input":["b0"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a0\",\"b0\"],\"final_states\":[\"f0\"],\"input\":[\"b0\"],\"max_steps\":1,\"start_state\":\"s0\",\"states\":[\"d0\",\"f0\",\"m0\",\"s0\"],\"transitions\":[[\"m0\",\"a0\",\"m0\"],[\"m0\",\"b0\",\"f0\"],[\"s0\",null,\"d0\"],[\"s0\",null,\"m0\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0077","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s1\",\"m1\",\"f1\",\"d1\"],\"alphabet\":[\"a1\",\"b1\"],\"start_state\":\"s1\",\"final_states\":[\"f1\"],\"transitions\":[[\"s1\",null,\"m1\"],[\"s1\",null,\"d1\"],[\"m1\",\"a1\",\"m1\"],[\"m1\",\"b1\",\"f1\"]],\"input\":[\"a1\",\"b1\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a1, b1], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a1, b1], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117077,"parameters":{"states":["s1","m1","f1","d1"],"alphabet":["a1","b1"],"start_state":"s1","final_states":["f1"],"transitions":[["s1",null,"m1"],["s1",null,"d1"],["m1","a1","m1"],["m1","b1","f1"]],"input":["a1","b1"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a1\",\"b1\"],\"final_states\":[\"f1\"],\"input\":[\"a1\",\"b1\"],\"max_steps\":1,\"start_state\":\"s1\",\"states\":[\"d1\",\"f1\",\"m1\",\"s1\"],\"transitions\":[[\"m1\",\"a1\",\"m1\"],[\"m1\",\"b1\",\"f1\"],[\"s1\",null,\"d1\"],[\"s1\",null,\"m1\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0078","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s2\",\"m2\",\"f2\",\"d2\"],\"alphabet\":[\"a2\",\"b2\"],\"start_state\":\"s2\",\"final_states\":[\"f2\"],\"transitions\":[[\"s2\",null,\"m2\"],[\"s2\",null,\"d2\"],[\"m2\",\"a2\",\"m2\"],[\"m2\",\"b2\",\"f2\"]],\"input\":[\"a2\",\"a2\",\"b2\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a2, a2, b2], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a2, a2, b2], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117078,"parameters":{"states":["s2","m2","f2","d2"],"alphabet":["a2","b2"],"start_state":"s2","final_states":["f2"],"transitions":[["s2",null,"m2"],["s2",null,"d2"],["m2","a2","m2"],["m2","b2","f2"]],"input":["a2","a2","b2"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a2\",\"b2\"],\"final_states\":[\"f2\"],\"input\":[\"a2\",\"a2\",\"b2\"],\"max_steps\":1,\"start_state\":\"s2\",\"states\":[\"d2\",\"f2\",\"m2\",\"s2\"],\"transitions\":[[\"m2\",\"a2\",\"m2\"],[\"m2\",\"b2\",\"f2\"],[\"s2\",null,\"d2\"],[\"s2\",null,\"m2\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0079","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s3\",\"m3\",\"f3\",\"d3\"],\"alphabet\":[\"a3\",\"b3\"],\"start_state\":\"s3\",\"final_states\":[\"f3\"],\"transitions\":[[\"s3\",null,\"m3\"],[\"s3\",null,\"d3\"],[\"m3\",\"a3\",\"m3\"],[\"m3\",\"b3\",\"f3\"]],\"input\":[\"a3\",\"a3\",\"a3\",\"b3\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a3, a3, a3, b3], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a3, a3, a3, b3], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117079,"parameters":{"states":["s3","m3","f3","d3"],"alphabet":["a3","b3"],"start_state":"s3","final_states":["f3"],"transitions":[["s3",null,"m3"],["s3",null,"d3"],["m3","a3","m3"],["m3","b3","f3"]],"input":["a3","a3","a3","b3"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a3\",\"b3\"],\"final_states\":[\"f3\"],\"input\":[\"a3\",\"a3\",\"a3\",\"b3\"],\"max_steps\":1,\"start_state\":\"s3\",\"states\":[\"d3\",\"f3\",\"m3\",\"s3\"],\"transitions\":[[\"m3\",\"a3\",\"m3\"],[\"m3\",\"b3\",\"f3\"],[\"s3\",null,\"d3\"],[\"s3\",null,\"m3\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0080","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s4\",\"m4\",\"f4\",\"d4\"],\"alphabet\":[\"a4\",\"b4\"],\"start_state\":\"s4\",\"final_states\":[\"f4\"],\"transitions\":[[\"s4\",null,\"m4\"],[\"s4\",null,\"d4\"],[\"m4\",\"a4\",\"m4\"],[\"m4\",\"b4\",\"f4\"]],\"input\":[\"b4\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b4], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([b4], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117080,"parameters":{"states":["s4","m4","f4","d4"],"alphabet":["a4","b4"],"start_state":"s4","final_states":["f4"],"transitions":[["s4",null,"m4"],["s4",null,"d4"],["m4","a4","m4"],["m4","b4","f4"]],"input":["b4"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a4\",\"b4\"],\"final_states\":[\"f4\"],\"input\":[\"b4\"],\"max_steps\":1,\"start_state\":\"s4\",\"states\":[\"d4\",\"f4\",\"m4\",\"s4\"],\"transitions\":[[\"m4\",\"a4\",\"m4\"],[\"m4\",\"b4\",\"f4\"],[\"s4\",null,\"d4\"],[\"s4\",null,\"m4\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0081","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s5\",\"m5\",\"f5\",\"d5\"],\"alphabet\":[\"a5\",\"b5\"],\"start_state\":\"s5\",\"final_states\":[\"f5\"],\"transitions\":[[\"s5\",null,\"m5\"],[\"s5\",null,\"d5\"],[\"m5\",\"a5\",\"m5\"],[\"m5\",\"b5\",\"f5\"]],\"input\":[\"a5\",\"b5\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a5, b5], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a5, b5], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117081,"parameters":{"states":["s5","m5","f5","d5"],"alphabet":["a5","b5"],"start_state":"s5","final_states":["f5"],"transitions":[["s5",null,"m5"],["s5",null,"d5"],["m5","a5","m5"],["m5","b5","f5"]],"input":["a5","b5"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a5\",\"b5\"],\"final_states\":[\"f5\"],\"input\":[\"a5\",\"b5\"],\"max_steps\":1,\"start_state\":\"s5\",\"states\":[\"d5\",\"f5\",\"m5\",\"s5\"],\"transitions\":[[\"m5\",\"a5\",\"m5\"],[\"m5\",\"b5\",\"f5\"],[\"s5\",null,\"d5\"],[\"s5\",null,\"m5\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0082","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s6\",\"m6\",\"f6\",\"d6\"],\"alphabet\":[\"a6\",\"b6\"],\"start_state\":\"s6\",\"final_states\":[\"f6\"],\"transitions\":[[\"s6\",null,\"m6\"],[\"s6\",null,\"d6\"],[\"m6\",\"a6\",\"m6\"],[\"m6\",\"b6\",\"f6\"]],\"input\":[\"a6\",\"a6\",\"b6\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a6, a6, b6], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a6, a6, b6], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117082,"parameters":{"states":["s6","m6","f6","d6"],"alphabet":["a6","b6"],"start_state":"s6","final_states":["f6"],"transitions":[["s6",null,"m6"],["s6",null,"d6"],["m6","a6","m6"],["m6","b6","f6"]],"input":["a6","a6","b6"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a6\",\"b6\"],\"final_states\":[\"f6\"],\"input\":[\"a6\",\"a6\",\"b6\"],\"max_steps\":1,\"start_state\":\"s6\",\"states\":[\"d6\",\"f6\",\"m6\",\"s6\"],\"transitions\":[[\"m6\",\"a6\",\"m6\"],[\"m6\",\"b6\",\"f6\"],[\"s6\",null,\"d6\"],[\"s6\",null,\"m6\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0083","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s7\",\"m7\",\"f7\",\"d7\"],\"alphabet\":[\"a7\",\"b7\"],\"start_state\":\"s7\",\"final_states\":[\"f7\"],\"transitions\":[[\"s7\",null,\"m7\"],[\"s7\",null,\"d7\"],[\"m7\",\"a7\",\"m7\"],[\"m7\",\"b7\",\"f7\"]],\"input\":[\"a7\",\"a7\",\"a7\",\"b7\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a7, a7, a7, b7], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a7, a7, a7, b7], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117083,"parameters":{"states":["s7","m7","f7","d7"],"alphabet":["a7","b7"],"start_state":"s7","final_states":["f7"],"transitions":[["s7",null,"m7"],["s7",null,"d7"],["m7","a7","m7"],["m7","b7","f7"]],"input":["a7","a7","a7","b7"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a7\",\"b7\"],\"final_states\":[\"f7\"],\"input\":[\"a7\",\"a7\",\"a7\",\"b7\"],\"max_steps\":1,\"start_state\":\"s7\",\"states\":[\"d7\",\"f7\",\"m7\",\"s7\"],\"transitions\":[[\"m7\",\"a7\",\"m7\"],[\"m7\",\"b7\",\"f7\"],[\"s7\",null,\"d7\"],[\"s7\",null,\"m7\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0084","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s8\",\"m8\",\"f8\",\"d8\"],\"alphabet\":[\"a8\",\"b8\"],\"start_state\":\"s8\",\"final_states\":[\"f8\"],\"transitions\":[[\"s8\",null,\"m8\"],[\"s8\",null,\"d8\"],[\"m8\",\"a8\",\"m8\"],[\"m8\",\"b8\",\"f8\"]],\"input\":[\"b8\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b8], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([b8], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117084,"parameters":{"states":["s8","m8","f8","d8"],"alphabet":["a8","b8"],"start_state":"s8","final_states":["f8"],"transitions":[["s8",null,"m8"],["s8",null,"d8"],["m8","a8","m8"],["m8","b8","f8"]],"input":["b8"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a8\",\"b8\"],\"final_states\":[\"f8\"],\"input\":[\"b8\"],\"max_steps\":1,\"start_state\":\"s8\",\"states\":[\"d8\",\"f8\",\"m8\",\"s8\"],\"transitions\":[[\"m8\",\"a8\",\"m8\"],[\"m8\",\"b8\",\"f8\"],[\"s8\",null,\"d8\"],[\"s8\",null,\"m8\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0085","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s9\",\"m9\",\"f9\",\"d9\"],\"alphabet\":[\"a9\",\"b9\"],\"start_state\":\"s9\",\"final_states\":[\"f9\"],\"transitions\":[[\"s9\",null,\"m9\"],[\"s9\",null,\"d9\"],[\"m9\",\"a9\",\"m9\"],[\"m9\",\"b9\",\"f9\"]],\"input\":[\"a9\",\"b9\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a9, b9], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a9, b9], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117085,"parameters":{"states":["s9","m9","f9","d9"],"alphabet":["a9","b9"],"start_state":"s9","final_states":["f9"],"transitions":[["s9",null,"m9"],["s9",null,"d9"],["m9","a9","m9"],["m9","b9","f9"]],"input":["a9","b9"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a9\",\"b9\"],\"final_states\":[\"f9\"],\"input\":[\"a9\",\"b9\"],\"max_steps\":1,\"start_state\":\"s9\",\"states\":[\"d9\",\"f9\",\"m9\",\"s9\"],\"transitions\":[[\"m9\",\"a9\",\"m9\"],[\"m9\",\"b9\",\"f9\"],[\"s9\",null,\"d9\"],[\"s9\",null,\"m9\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0086","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s10\",\"m10\",\"f10\",\"d10\"],\"alphabet\":[\"a10\",\"b10\"],\"start_state\":\"s10\",\"final_states\":[\"f10\"],\"transitions\":[[\"s10\",null,\"m10\"],[\"s10\",null,\"d10\"],[\"m10\",\"a10\",\"m10\"],[\"m10\",\"b10\",\"f10\"]],\"input\":[\"a10\",\"a10\",\"b10\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a10, a10, b10], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a10, a10, b10], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117086,"parameters":{"states":["s10","m10","f10","d10"],"alphabet":["a10","b10"],"start_state":"s10","final_states":["f10"],"transitions":[["s10",null,"m10"],["s10",null,"d10"],["m10","a10","m10"],["m10","b10","f10"]],"input":["a10","a10","b10"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a10\",\"b10\"],\"final_states\":[\"f10\"],\"input\":[\"a10\",\"a10\",\"b10\"],\"max_steps\":1,\"start_state\":\"s10\",\"states\":[\"d10\",\"f10\",\"m10\",\"s10\"],\"transitions\":[[\"m10\",\"a10\",\"m10\"],[\"m10\",\"b10\",\"f10\"],[\"s10\",null,\"d10\"],[\"s10\",null,\"m10\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0087","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s11\",\"m11\",\"f11\",\"d11\"],\"alphabet\":[\"a11\",\"b11\"],\"start_state\":\"s11\",\"final_states\":[\"f11\"],\"transitions\":[[\"s11\",null,\"m11\"],[\"s11\",null,\"d11\"],[\"m11\",\"a11\",\"m11\"],[\"m11\",\"b11\",\"f11\"]],\"input\":[\"a11\",\"a11\",\"a11\",\"b11\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a11, a11, a11, b11], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a11, a11, a11, b11], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117087,"parameters":{"states":["s11","m11","f11","d11"],"alphabet":["a11","b11"],"start_state":"s11","final_states":["f11"],"transitions":[["s11",null,"m11"],["s11",null,"d11"],["m11","a11","m11"],["m11","b11","f11"]],"input":["a11","a11","a11","b11"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a11\",\"b11\"],\"final_states\":[\"f11\"],\"input\":[\"a11\",\"a11\",\"a11\",\"b11\"],\"max_steps\":1,\"start_state\":\"s11\",\"states\":[\"d11\",\"f11\",\"m11\",\"s11\"],\"transitions\":[[\"m11\",\"a11\",\"m11\"],[\"m11\",\"b11\",\"f11\"],[\"s11\",null,\"d11\"],[\"s11\",null,\"m11\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0088","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s12\",\"m12\",\"f12\",\"d12\"],\"alphabet\":[\"a12\",\"b12\"],\"start_state\":\"s12\",\"final_states\":[\"f12\"],\"transitions\":[[\"s12\",null,\"m12\"],[\"s12\",null,\"d12\"],[\"m12\",\"a12\",\"m12\"],[\"m12\",\"b12\",\"f12\"]],\"input\":[\"b12\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b12], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([b12], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117088,"parameters":{"states":["s12","m12","f12","d12"],"alphabet":["a12","b12"],"start_state":"s12","final_states":["f12"],"transitions":[["s12",null,"m12"],["s12",null,"d12"],["m12","a12","m12"],["m12","b12","f12"]],"input":["b12"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a12\",\"b12\"],\"final_states\":[\"f12\"],\"input\":[\"b12\"],\"max_steps\":1,\"start_state\":\"s12\",\"states\":[\"d12\",\"f12\",\"m12\",\"s12\"],\"transitions\":[[\"m12\",\"a12\",\"m12\"],[\"m12\",\"b12\",\"f12\"],[\"s12\",null,\"d12\"],[\"s12\",null,\"m12\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0089","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s13\",\"m13\",\"f13\",\"d13\"],\"alphabet\":[\"a13\",\"b13\"],\"start_state\":\"s13\",\"final_states\":[\"f13\"],\"transitions\":[[\"s13\",null,\"m13\"],[\"s13\",null,\"d13\"],[\"m13\",\"a13\",\"m13\"],[\"m13\",\"b13\",\"f13\"]],\"input\":[\"a13\",\"b13\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a13, b13], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a13, b13], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117089,"parameters":{"states":["s13","m13","f13","d13"],"alphabet":["a13","b13"],"start_state":"s13","final_states":["f13"],"transitions":[["s13",null,"m13"],["s13",null,"d13"],["m13","a13","m13"],["m13","b13","f13"]],"input":["a13","b13"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a13\",\"b13\"],\"final_states\":[\"f13\"],\"input\":[\"a13\",\"b13\"],\"max_steps\":1,\"start_state\":\"s13\",\"states\":[\"d13\",\"f13\",\"m13\",\"s13\"],\"transitions\":[[\"m13\",\"a13\",\"m13\"],[\"m13\",\"b13\",\"f13\"],[\"s13\",null,\"d13\"],[\"s13\",null,\"m13\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0090","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s14\",\"m14\",\"f14\",\"d14\"],\"alphabet\":[\"a14\",\"b14\"],\"start_state\":\"s14\",\"final_states\":[\"f14\"],\"transitions\":[[\"s14\",null,\"m14\"],[\"s14\",null,\"d14\"],[\"m14\",\"a14\",\"m14\"],[\"m14\",\"b14\",\"f14\"]],\"input\":[\"a14\",\"a14\",\"b14\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a14, a14, b14], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a14, a14, b14], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117090,"parameters":{"states":["s14","m14","f14","d14"],"alphabet":["a14","b14"],"start_state":"s14","final_states":["f14"],"transitions":[["s14",null,"m14"],["s14",null,"d14"],["m14","a14","m14"],["m14","b14","f14"]],"input":["a14","a14","b14"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a14\",\"b14\"],\"final_states\":[\"f14\"],\"input\":[\"a14\",\"a14\",\"b14\"],\"max_steps\":1,\"start_state\":\"s14\",\"states\":[\"d14\",\"f14\",\"m14\",\"s14\"],\"transitions\":[[\"m14\",\"a14\",\"m14\"],[\"m14\",\"b14\",\"f14\"],[\"s14\",null,\"d14\"],[\"s14\",null,\"m14\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0091","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s15\",\"m15\",\"f15\",\"d15\"],\"alphabet\":[\"a15\",\"b15\"],\"start_state\":\"s15\",\"final_states\":[\"f15\"],\"transitions\":[[\"s15\",null,\"m15\"],[\"s15\",null,\"d15\"],[\"m15\",\"a15\",\"m15\"],[\"m15\",\"b15\",\"f15\"]],\"input\":[\"a15\",\"a15\",\"a15\",\"b15\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a15, a15, a15, b15], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a15, a15, a15, b15], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117091,"parameters":{"states":["s15","m15","f15","d15"],"alphabet":["a15","b15"],"start_state":"s15","final_states":["f15"],"transitions":[["s15",null,"m15"],["s15",null,"d15"],["m15","a15","m15"],["m15","b15","f15"]],"input":["a15","a15","a15","b15"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a15\",\"b15\"],\"final_states\":[\"f15\"],\"input\":[\"a15\",\"a15\",\"a15\",\"b15\"],\"max_steps\":1,\"start_state\":\"s15\",\"states\":[\"d15\",\"f15\",\"m15\",\"s15\"],\"transitions\":[[\"m15\",\"a15\",\"m15\"],[\"m15\",\"b15\",\"f15\"],[\"s15\",null,\"d15\"],[\"s15\",null,\"m15\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0092","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s16\",\"m16\",\"f16\",\"d16\"],\"alphabet\":[\"a16\",\"b16\"],\"start_state\":\"s16\",\"final_states\":[\"f16\"],\"transitions\":[[\"s16\",null,\"m16\"],[\"s16\",null,\"d16\"],[\"m16\",\"a16\",\"m16\"],[\"m16\",\"b16\",\"f16\"]],\"input\":[\"b16\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b16], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([b16], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117092,"parameters":{"states":["s16","m16","f16","d16"],"alphabet":["a16","b16"],"start_state":"s16","final_states":["f16"],"transitions":[["s16",null,"m16"],["s16",null,"d16"],["m16","a16","m16"],["m16","b16","f16"]],"input":["b16"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a16\",\"b16\"],\"final_states\":[\"f16\"],\"input\":[\"b16\"],\"max_steps\":1,\"start_state\":\"s16\",\"states\":[\"d16\",\"f16\",\"m16\",\"s16\"],\"transitions\":[[\"m16\",\"a16\",\"m16\"],[\"m16\",\"b16\",\"f16\"],[\"s16\",null,\"d16\"],[\"s16\",null,\"m16\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0093","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s17\",\"m17\",\"f17\",\"d17\"],\"alphabet\":[\"a17\",\"b17\"],\"start_state\":\"s17\",\"final_states\":[\"f17\"],\"transitions\":[[\"s17\",null,\"m17\"],[\"s17\",null,\"d17\"],[\"m17\",\"a17\",\"m17\"],[\"m17\",\"b17\",\"f17\"]],\"input\":[\"a17\",\"b17\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a17, b17], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a17, b17], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117093,"parameters":{"states":["s17","m17","f17","d17"],"alphabet":["a17","b17"],"start_state":"s17","final_states":["f17"],"transitions":[["s17",null,"m17"],["s17",null,"d17"],["m17","a17","m17"],["m17","b17","f17"]],"input":["a17","b17"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a17\",\"b17\"],\"final_states\":[\"f17\"],\"input\":[\"a17\",\"b17\"],\"max_steps\":1,\"start_state\":\"s17\",\"states\":[\"d17\",\"f17\",\"m17\",\"s17\"],\"transitions\":[[\"m17\",\"a17\",\"m17\"],[\"m17\",\"b17\",\"f17\"],[\"s17\",null,\"d17\"],[\"s17\",null,\"m17\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0094","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s18\",\"m18\",\"f18\",\"d18\"],\"alphabet\":[\"a18\",\"b18\"],\"start_state\":\"s18\",\"final_states\":[\"f18\"],\"transitions\":[[\"s18\",null,\"m18\"],[\"s18\",null,\"d18\"],[\"m18\",\"a18\",\"m18\"],[\"m18\",\"b18\",\"f18\"]],\"input\":[\"a18\",\"a18\",\"b18\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a18, a18, b18], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a18, a18, b18], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117094,"parameters":{"states":["s18","m18","f18","d18"],"alphabet":["a18","b18"],"start_state":"s18","final_states":["f18"],"transitions":[["s18",null,"m18"],["s18",null,"d18"],["m18","a18","m18"],["m18","b18","f18"]],"input":["a18","a18","b18"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a18\",\"b18\"],\"final_states\":[\"f18\"],\"input\":[\"a18\",\"a18\",\"b18\"],\"max_steps\":1,\"start_state\":\"s18\",\"states\":[\"d18\",\"f18\",\"m18\",\"s18\"],\"transitions\":[[\"m18\",\"a18\",\"m18\"],[\"m18\",\"b18\",\"f18\"],[\"s18\",null,\"d18\"],[\"s18\",null,\"m18\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0095","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s19\",\"m19\",\"f19\",\"d19\"],\"alphabet\":[\"a19\",\"b19\"],\"start_state\":\"s19\",\"final_states\":[\"f19\"],\"transitions\":[[\"s19\",null,\"m19\"],[\"s19\",null,\"d19\"],[\"m19\",\"a19\",\"m19\"],[\"m19\",\"b19\",\"f19\"]],\"input\":[\"a19\",\"a19\",\"a19\",\"b19\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a19, a19, a19, b19], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a19, a19, a19, b19], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117095,"parameters":{"states":["s19","m19","f19","d19"],"alphabet":["a19","b19"],"start_state":"s19","final_states":["f19"],"transitions":[["s19",null,"m19"],["s19",null,"d19"],["m19","a19","m19"],["m19","b19","f19"]],"input":["a19","a19","a19","b19"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a19\",\"b19\"],\"final_states\":[\"f19\"],\"input\":[\"a19\",\"a19\",\"a19\",\"b19\"],\"max_steps\":1,\"start_state\":\"s19\",\"states\":[\"d19\",\"f19\",\"m19\",\"s19\"],\"transitions\":[[\"m19\",\"a19\",\"m19\"],[\"m19\",\"b19\",\"f19\"],[\"s19\",null,\"d19\"],[\"s19\",null,\"m19\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0096","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s20\",\"m20\",\"f20\",\"d20\"],\"alphabet\":[\"a20\",\"b20\"],\"start_state\":\"s20\",\"final_states\":[\"f20\"],\"transitions\":[[\"s20\",null,\"m20\"],[\"s20\",null,\"d20\"],[\"m20\",\"a20\",\"m20\"],[\"m20\",\"b20\",\"f20\"]],\"input\":[\"b20\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b20], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([b20], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117096,"parameters":{"states":["s20","m20","f20","d20"],"alphabet":["a20","b20"],"start_state":"s20","final_states":["f20"],"transitions":[["s20",null,"m20"],["s20",null,"d20"],["m20","a20","m20"],["m20","b20","f20"]],"input":["b20"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a20\",\"b20\"],\"final_states\":[\"f20\"],\"input\":[\"b20\"],\"max_steps\":1,\"start_state\":\"s20\",\"states\":[\"d20\",\"f20\",\"m20\",\"s20\"],\"transitions\":[[\"m20\",\"a20\",\"m20\"],[\"m20\",\"b20\",\"f20\"],[\"s20\",null,\"d20\"],[\"s20\",null,\"m20\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0097","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s21\",\"m21\",\"f21\",\"d21\"],\"alphabet\":[\"a21\",\"b21\"],\"start_state\":\"s21\",\"final_states\":[\"f21\"],\"transitions\":[[\"s21\",null,\"m21\"],[\"s21\",null,\"d21\"],[\"m21\",\"a21\",\"m21\"],[\"m21\",\"b21\",\"f21\"]],\"input\":[\"a21\",\"b21\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a21, b21], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a21, b21], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117097,"parameters":{"states":["s21","m21","f21","d21"],"alphabet":["a21","b21"],"start_state":"s21","final_states":["f21"],"transitions":[["s21",null,"m21"],["s21",null,"d21"],["m21","a21","m21"],["m21","b21","f21"]],"input":["a21","b21"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a21\",\"b21\"],\"final_states\":[\"f21\"],\"input\":[\"a21\",\"b21\"],\"max_steps\":1,\"start_state\":\"s21\",\"states\":[\"d21\",\"f21\",\"m21\",\"s21\"],\"transitions\":[[\"m21\",\"a21\",\"m21\"],[\"m21\",\"b21\",\"f21\"],[\"s21\",null,\"d21\"],[\"s21\",null,\"m21\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0098","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s22\",\"m22\",\"f22\",\"d22\"],\"alphabet\":[\"a22\",\"b22\"],\"start_state\":\"s22\",\"final_states\":[\"f22\"],\"transitions\":[[\"s22\",null,\"m22\"],[\"s22\",null,\"d22\"],[\"m22\",\"a22\",\"m22\"],[\"m22\",\"b22\",\"f22\"]],\"input\":[\"a22\",\"a22\",\"b22\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a22, a22, b22], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a22, a22, b22], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117098,"parameters":{"states":["s22","m22","f22","d22"],"alphabet":["a22","b22"],"start_state":"s22","final_states":["f22"],"transitions":[["s22",null,"m22"],["s22",null,"d22"],["m22","a22","m22"],["m22","b22","f22"]],"input":["a22","a22","b22"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a22\",\"b22\"],\"final_states\":[\"f22\"],\"input\":[\"a22\",\"a22\",\"b22\"],\"max_steps\":1,\"start_state\":\"s22\",\"states\":[\"d22\",\"f22\",\"m22\",\"s22\"],\"transitions\":[[\"m22\",\"a22\",\"m22\"],[\"m22\",\"b22\",\"f22\"],[\"s22\",null,\"d22\"],[\"s22\",null,\"m22\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0099","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s23\",\"m23\",\"f23\",\"d23\"],\"alphabet\":[\"a23\",\"b23\"],\"start_state\":\"s23\",\"final_states\":[\"f23\"],\"transitions\":[[\"s23\",null,\"m23\"],[\"s23\",null,\"d23\"],[\"m23\",\"a23\",\"m23\"],[\"m23\",\"b23\",\"f23\"]],\"input\":[\"a23\",\"a23\",\"a23\",\"b23\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a23, a23, a23, b23], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([a23, a23, a23, b23], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117099,"parameters":{"states":["s23","m23","f23","d23"],"alphabet":["a23","b23"],"start_state":"s23","final_states":["f23"],"transitions":[["s23",null,"m23"],["s23",null,"d23"],["m23","a23","m23"],["m23","b23","f23"]],"input":["a23","a23","a23","b23"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a23\",\"b23\"],\"final_states\":[\"f23\"],\"input\":[\"a23\",\"a23\",\"a23\",\"b23\"],\"max_steps\":1,\"start_state\":\"s23\",\"states\":[\"d23\",\"f23\",\"m23\",\"s23\"],\"transitions\":[[\"m23\",\"a23\",\"m23\"],[\"m23\",\"b23\",\"f23\"],[\"s23\",null,\"d23\"],[\"s23\",null,\"m23\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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-20261111-r07-nondeterministic-finite-automaton-0100","batch_id":"batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-nondeterministic-finite-automaton"],"title_zh":"非確定有限自動機","stem_zh":"transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-bounded-search-boundary；資料={\"states\":[\"s24\",\"m24\",\"f24\",\"d24\"],\"alphabet\":[\"a24\",\"b24\"],\"start_state\":\"s24\",\"final_states\":[\"f24\"],\"transitions\":[[\"s24\",null,\"m24\"],[\"s24\",null,\"d24\"],[\"m24\",\"a24\",\"m24\"],[\"m24\",\"b24\",\"f24\"]],\"input\":[\"b24\"],\"max_steps\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b24], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)","explanation_zh":"Wave6第五層核對=([b24], 1, 否, 否, bounded_search_failure_cannot_prove_rejection_and_epsilon_cycles_are_not_infinite_accepting_runs)；依完整明示資料獨立重算；null epsilon不消耗input、transition relation可empty或multi-valued且一條finite full-input final path即可證membership；empty final set合法且辨識空語言；bounded search failure不證rejection，epsilon cycle本身不接受。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非確定有限自動機"]},"variant":{"family_id":"qf-mod42-nfa-bounded-search-boundary","seed":202611117100,"parameters":{"states":["s24","m24","f24","d24"],"alphabet":["a24","b24"],"start_state":"s24","final_states":["f24"],"transitions":[["s24",null,"m24"],["s24",null,"d24"],["m24","a24","m24"],["m24","b24","f24"]],"input":["b24"],"max_steps":1,"domain":"Finite_epsilon_NFA_existential_acceptance","operation":"nfa-bounded-search-boundary","semantic_template":"qf-mod42-nfa-bounded-search-boundary/{\"alphabet\":[\"a24\",\"b24\"],\"final_states\":[\"f24\"],\"input\":[\"b24\"],\"max_steps\":1,\"start_state\":\"s24\",\"states\":[\"d24\",\"f24\",\"m24\",\"s24\"],\"transitions\":[[\"m24\",\"a24\",\"m24\"],[\"m24\",\"b24\",\"f24\"],[\"s24\",null,\"d24\"],[\"s24\",null,\"m24\"]]}"}},"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、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA 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"}}