{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-0001","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s0\",\"m0\",\"f0\",\"e10\",\"e20\",\"d0\"],\"alphabet\":[\"a0\",\"b0\"],\"start_state\":\"s0\",\"final_states\":[\"f0\"],\"transitions\":[[\"s0\",null,\"m0\"],[\"s0\",null,\"d0\"],[\"m0\",\"a0\",\"m0\"],[\"m0\",\"b0\",\"f0\"],[\"f0\",null,\"e10\"],[\"e10\",null,\"e20\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s0, [d0, m0, s0], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s0, [d0, m0, s0], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127001,"parameters":{"states":["s0","m0","f0","e10","e20","d0"],"alphabet":["a0","b0"],"start_state":"s0","final_states":["f0"],"transitions":[["s0",null,"m0"],["s0",null,"d0"],["m0","a0","m0"],["m0","b0","f0"],["f0",null,"e10"],["e10",null,"e20"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a0\",\"b0\"],\"final_states\":[\"f0\"],\"start_state\":\"s0\",\"states\":[\"d0\",\"e10\",\"e20\",\"f0\",\"m0\",\"s0\"],\"transitions\":[[\"e10\",null,\"e20\"],[\"f0\",null,\"e10\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0002","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s1\",\"m1\",\"f1\",\"e11\",\"e21\",\"d1\"],\"alphabet\":[\"a1\",\"b1\"],\"start_state\":\"s1\",\"final_states\":[\"f1\"],\"transitions\":[[\"s1\",null,\"m1\"],[\"s1\",null,\"d1\"],[\"m1\",\"a1\",\"m1\"],[\"m1\",\"b1\",\"f1\"],[\"f1\",null,\"e11\"],[\"e11\",null,\"e21\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s1, [d1, m1, s1], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s1, [d1, m1, s1], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127002,"parameters":{"states":["s1","m1","f1","e11","e21","d1"],"alphabet":["a1","b1"],"start_state":"s1","final_states":["f1"],"transitions":[["s1",null,"m1"],["s1",null,"d1"],["m1","a1","m1"],["m1","b1","f1"],["f1",null,"e11"],["e11",null,"e21"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a1\",\"b1\"],\"final_states\":[\"f1\"],\"start_state\":\"s1\",\"states\":[\"d1\",\"e11\",\"e21\",\"f1\",\"m1\",\"s1\"],\"transitions\":[[\"e11\",null,\"e21\"],[\"f1\",null,\"e11\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0003","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s2\",\"m2\",\"f2\",\"e12\",\"e22\",\"d2\"],\"alphabet\":[\"a2\",\"b2\"],\"start_state\":\"s2\",\"final_states\":[\"f2\"],\"transitions\":[[\"s2\",null,\"m2\"],[\"s2\",null,\"d2\"],[\"m2\",\"a2\",\"m2\"],[\"m2\",\"b2\",\"f2\"],[\"f2\",null,\"e12\"],[\"e12\",null,\"e22\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s2, [d2, m2, s2], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s2, [d2, m2, s2], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127003,"parameters":{"states":["s2","m2","f2","e12","e22","d2"],"alphabet":["a2","b2"],"start_state":"s2","final_states":["f2"],"transitions":[["s2",null,"m2"],["s2",null,"d2"],["m2","a2","m2"],["m2","b2","f2"],["f2",null,"e12"],["e12",null,"e22"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a2\",\"b2\"],\"final_states\":[\"f2\"],\"start_state\":\"s2\",\"states\":[\"d2\",\"e12\",\"e22\",\"f2\",\"m2\",\"s2\"],\"transitions\":[[\"e12\",null,\"e22\"],[\"f2\",null,\"e12\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0004","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s3\",\"m3\",\"f3\",\"e13\",\"e23\",\"d3\"],\"alphabet\":[\"a3\",\"b3\"],\"start_state\":\"s3\",\"final_states\":[\"f3\"],\"transitions\":[[\"s3\",null,\"m3\"],[\"s3\",null,\"d3\"],[\"m3\",\"a3\",\"m3\"],[\"m3\",\"b3\",\"f3\"],[\"f3\",null,\"e13\"],[\"e13\",null,\"e23\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s3, [d3, m3, s3], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s3, [d3, m3, s3], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127004,"parameters":{"states":["s3","m3","f3","e13","e23","d3"],"alphabet":["a3","b3"],"start_state":"s3","final_states":["f3"],"transitions":[["s3",null,"m3"],["s3",null,"d3"],["m3","a3","m3"],["m3","b3","f3"],["f3",null,"e13"],["e13",null,"e23"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a3\",\"b3\"],\"final_states\":[\"f3\"],\"start_state\":\"s3\",\"states\":[\"d3\",\"e13\",\"e23\",\"f3\",\"m3\",\"s3\"],\"transitions\":[[\"e13\",null,\"e23\"],[\"f3\",null,\"e13\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0005","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s4\",\"m4\",\"f4\",\"e14\",\"e24\",\"d4\"],\"alphabet\":[\"a4\",\"b4\"],\"start_state\":\"s4\",\"final_states\":[\"f4\"],\"transitions\":[[\"s4\",null,\"m4\"],[\"s4\",null,\"d4\"],[\"m4\",\"a4\",\"m4\"],[\"m4\",\"b4\",\"f4\"],[\"f4\",null,\"e14\"],[\"e14\",null,\"e24\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s4, [d4, m4, s4], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s4, [d4, m4, s4], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127005,"parameters":{"states":["s4","m4","f4","e14","e24","d4"],"alphabet":["a4","b4"],"start_state":"s4","final_states":["f4"],"transitions":[["s4",null,"m4"],["s4",null,"d4"],["m4","a4","m4"],["m4","b4","f4"],["f4",null,"e14"],["e14",null,"e24"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a4\",\"b4\"],\"final_states\":[\"f4\"],\"start_state\":\"s4\",\"states\":[\"d4\",\"e14\",\"e24\",\"f4\",\"m4\",\"s4\"],\"transitions\":[[\"e14\",null,\"e24\"],[\"f4\",null,\"e14\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0006","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s5\",\"m5\",\"f5\",\"e15\",\"e25\",\"d5\"],\"alphabet\":[\"a5\",\"b5\"],\"start_state\":\"s5\",\"final_states\":[\"f5\"],\"transitions\":[[\"s5\",null,\"m5\"],[\"s5\",null,\"d5\"],[\"m5\",\"a5\",\"m5\"],[\"m5\",\"b5\",\"f5\"],[\"f5\",null,\"e15\"],[\"e15\",null,\"e25\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s5, [d5, m5, s5], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s5, [d5, m5, s5], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127006,"parameters":{"states":["s5","m5","f5","e15","e25","d5"],"alphabet":["a5","b5"],"start_state":"s5","final_states":["f5"],"transitions":[["s5",null,"m5"],["s5",null,"d5"],["m5","a5","m5"],["m5","b5","f5"],["f5",null,"e15"],["e15",null,"e25"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a5\",\"b5\"],\"final_states\":[\"f5\"],\"start_state\":\"s5\",\"states\":[\"d5\",\"e15\",\"e25\",\"f5\",\"m5\",\"s5\"],\"transitions\":[[\"e15\",null,\"e25\"],[\"f5\",null,\"e15\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0007","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s6\",\"m6\",\"f6\",\"e16\",\"e26\",\"d6\"],\"alphabet\":[\"a6\",\"b6\"],\"start_state\":\"s6\",\"final_states\":[\"f6\"],\"transitions\":[[\"s6\",null,\"m6\"],[\"s6\",null,\"d6\"],[\"m6\",\"a6\",\"m6\"],[\"m6\",\"b6\",\"f6\"],[\"f6\",null,\"e16\"],[\"e16\",null,\"e26\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s6, [d6, m6, s6], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s6, [d6, m6, s6], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127007,"parameters":{"states":["s6","m6","f6","e16","e26","d6"],"alphabet":["a6","b6"],"start_state":"s6","final_states":["f6"],"transitions":[["s6",null,"m6"],["s6",null,"d6"],["m6","a6","m6"],["m6","b6","f6"],["f6",null,"e16"],["e16",null,"e26"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a6\",\"b6\"],\"final_states\":[\"f6\"],\"start_state\":\"s6\",\"states\":[\"d6\",\"e16\",\"e26\",\"f6\",\"m6\",\"s6\"],\"transitions\":[[\"e16\",null,\"e26\"],[\"f6\",null,\"e16\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0008","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s7\",\"m7\",\"f7\",\"e17\",\"e27\",\"d7\"],\"alphabet\":[\"a7\",\"b7\"],\"start_state\":\"s7\",\"final_states\":[\"f7\"],\"transitions\":[[\"s7\",null,\"m7\"],[\"s7\",null,\"d7\"],[\"m7\",\"a7\",\"m7\"],[\"m7\",\"b7\",\"f7\"],[\"f7\",null,\"e17\"],[\"e17\",null,\"e27\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s7, [d7, m7, s7], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s7, [d7, m7, s7], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127008,"parameters":{"states":["s7","m7","f7","e17","e27","d7"],"alphabet":["a7","b7"],"start_state":"s7","final_states":["f7"],"transitions":[["s7",null,"m7"],["s7",null,"d7"],["m7","a7","m7"],["m7","b7","f7"],["f7",null,"e17"],["e17",null,"e27"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a7\",\"b7\"],\"final_states\":[\"f7\"],\"start_state\":\"s7\",\"states\":[\"d7\",\"e17\",\"e27\",\"f7\",\"m7\",\"s7\"],\"transitions\":[[\"e17\",null,\"e27\"],[\"f7\",null,\"e17\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0009","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s8\",\"m8\",\"f8\",\"e18\",\"e28\",\"d8\"],\"alphabet\":[\"a8\",\"b8\"],\"start_state\":\"s8\",\"final_states\":[\"f8\"],\"transitions\":[[\"s8\",null,\"m8\"],[\"s8\",null,\"d8\"],[\"m8\",\"a8\",\"m8\"],[\"m8\",\"b8\",\"f8\"],[\"f8\",null,\"e18\"],[\"e18\",null,\"e28\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s8, [d8, m8, s8], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s8, [d8, m8, s8], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127009,"parameters":{"states":["s8","m8","f8","e18","e28","d8"],"alphabet":["a8","b8"],"start_state":"s8","final_states":["f8"],"transitions":[["s8",null,"m8"],["s8",null,"d8"],["m8","a8","m8"],["m8","b8","f8"],["f8",null,"e18"],["e18",null,"e28"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a8\",\"b8\"],\"final_states\":[\"f8\"],\"start_state\":\"s8\",\"states\":[\"d8\",\"e18\",\"e28\",\"f8\",\"m8\",\"s8\"],\"transitions\":[[\"e18\",null,\"e28\"],[\"f8\",null,\"e18\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0010","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s9\",\"m9\",\"f9\",\"e19\",\"e29\",\"d9\"],\"alphabet\":[\"a9\",\"b9\"],\"start_state\":\"s9\",\"final_states\":[\"f9\"],\"transitions\":[[\"s9\",null,\"m9\"],[\"s9\",null,\"d9\"],[\"m9\",\"a9\",\"m9\"],[\"m9\",\"b9\",\"f9\"],[\"f9\",null,\"e19\"],[\"e19\",null,\"e29\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s9, [d9, m9, s9], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s9, [d9, m9, s9], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127010,"parameters":{"states":["s9","m9","f9","e19","e29","d9"],"alphabet":["a9","b9"],"start_state":"s9","final_states":["f9"],"transitions":[["s9",null,"m9"],["s9",null,"d9"],["m9","a9","m9"],["m9","b9","f9"],["f9",null,"e19"],["e19",null,"e29"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a9\",\"b9\"],\"final_states\":[\"f9\"],\"start_state\":\"s9\",\"states\":[\"d9\",\"e19\",\"e29\",\"f9\",\"m9\",\"s9\"],\"transitions\":[[\"e19\",null,\"e29\"],[\"f9\",null,\"e19\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0011","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s10\",\"m10\",\"f10\",\"e110\",\"e210\",\"d10\"],\"alphabet\":[\"a10\",\"b10\"],\"start_state\":\"s10\",\"final_states\":[\"f10\"],\"transitions\":[[\"s10\",null,\"m10\"],[\"s10\",null,\"d10\"],[\"m10\",\"a10\",\"m10\"],[\"m10\",\"b10\",\"f10\"],[\"f10\",null,\"e110\"],[\"e110\",null,\"e210\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s10, [d10, m10, s10], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s10, [d10, m10, s10], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127011,"parameters":{"states":["s10","m10","f10","e110","e210","d10"],"alphabet":["a10","b10"],"start_state":"s10","final_states":["f10"],"transitions":[["s10",null,"m10"],["s10",null,"d10"],["m10","a10","m10"],["m10","b10","f10"],["f10",null,"e110"],["e110",null,"e210"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a10\",\"b10\"],\"final_states\":[\"f10\"],\"start_state\":\"s10\",\"states\":[\"d10\",\"e110\",\"e210\",\"f10\",\"m10\",\"s10\"],\"transitions\":[[\"e110\",null,\"e210\"],[\"f10\",null,\"e110\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0012","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s11\",\"m11\",\"f11\",\"e111\",\"e211\",\"d11\"],\"alphabet\":[\"a11\",\"b11\"],\"start_state\":\"s11\",\"final_states\":[\"f11\"],\"transitions\":[[\"s11\",null,\"m11\"],[\"s11\",null,\"d11\"],[\"m11\",\"a11\",\"m11\"],[\"m11\",\"b11\",\"f11\"],[\"f11\",null,\"e111\"],[\"e111\",null,\"e211\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s11, [d11, m11, s11], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s11, [d11, m11, s11], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127012,"parameters":{"states":["s11","m11","f11","e111","e211","d11"],"alphabet":["a11","b11"],"start_state":"s11","final_states":["f11"],"transitions":[["s11",null,"m11"],["s11",null,"d11"],["m11","a11","m11"],["m11","b11","f11"],["f11",null,"e111"],["e111",null,"e211"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a11\",\"b11\"],\"final_states\":[\"f11\"],\"start_state\":\"s11\",\"states\":[\"d11\",\"e111\",\"e211\",\"f11\",\"m11\",\"s11\"],\"transitions\":[[\"e111\",null,\"e211\"],[\"f11\",null,\"e111\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0013","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s12\",\"m12\",\"f12\",\"e112\",\"e212\",\"d12\"],\"alphabet\":[\"a12\",\"b12\"],\"start_state\":\"s12\",\"final_states\":[\"f12\"],\"transitions\":[[\"s12\",null,\"m12\"],[\"s12\",null,\"d12\"],[\"m12\",\"a12\",\"m12\"],[\"m12\",\"b12\",\"f12\"],[\"f12\",null,\"e112\"],[\"e112\",null,\"e212\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s12, [d12, m12, s12], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s12, [d12, m12, s12], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127013,"parameters":{"states":["s12","m12","f12","e112","e212","d12"],"alphabet":["a12","b12"],"start_state":"s12","final_states":["f12"],"transitions":[["s12",null,"m12"],["s12",null,"d12"],["m12","a12","m12"],["m12","b12","f12"],["f12",null,"e112"],["e112",null,"e212"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a12\",\"b12\"],\"final_states\":[\"f12\"],\"start_state\":\"s12\",\"states\":[\"d12\",\"e112\",\"e212\",\"f12\",\"m12\",\"s12\"],\"transitions\":[[\"e112\",null,\"e212\"],[\"f12\",null,\"e112\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0014","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s13\",\"m13\",\"f13\",\"e113\",\"e213\",\"d13\"],\"alphabet\":[\"a13\",\"b13\"],\"start_state\":\"s13\",\"final_states\":[\"f13\"],\"transitions\":[[\"s13\",null,\"m13\"],[\"s13\",null,\"d13\"],[\"m13\",\"a13\",\"m13\"],[\"m13\",\"b13\",\"f13\"],[\"f13\",null,\"e113\"],[\"e113\",null,\"e213\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s13, [d13, m13, s13], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s13, [d13, m13, s13], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127014,"parameters":{"states":["s13","m13","f13","e113","e213","d13"],"alphabet":["a13","b13"],"start_state":"s13","final_states":["f13"],"transitions":[["s13",null,"m13"],["s13",null,"d13"],["m13","a13","m13"],["m13","b13","f13"],["f13",null,"e113"],["e113",null,"e213"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a13\",\"b13\"],\"final_states\":[\"f13\"],\"start_state\":\"s13\",\"states\":[\"d13\",\"e113\",\"e213\",\"f13\",\"m13\",\"s13\"],\"transitions\":[[\"e113\",null,\"e213\"],[\"f13\",null,\"e113\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0015","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s14\",\"m14\",\"f14\",\"e114\",\"e214\",\"d14\"],\"alphabet\":[\"a14\",\"b14\"],\"start_state\":\"s14\",\"final_states\":[\"f14\"],\"transitions\":[[\"s14\",null,\"m14\"],[\"s14\",null,\"d14\"],[\"m14\",\"a14\",\"m14\"],[\"m14\",\"b14\",\"f14\"],[\"f14\",null,\"e114\"],[\"e114\",null,\"e214\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s14, [d14, m14, s14], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s14, [d14, m14, s14], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127015,"parameters":{"states":["s14","m14","f14","e114","e214","d14"],"alphabet":["a14","b14"],"start_state":"s14","final_states":["f14"],"transitions":[["s14",null,"m14"],["s14",null,"d14"],["m14","a14","m14"],["m14","b14","f14"],["f14",null,"e114"],["e114",null,"e214"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a14\",\"b14\"],\"final_states\":[\"f14\"],\"start_state\":\"s14\",\"states\":[\"d14\",\"e114\",\"e214\",\"f14\",\"m14\",\"s14\"],\"transitions\":[[\"e114\",null,\"e214\"],[\"f14\",null,\"e114\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0016","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s15\",\"m15\",\"f15\",\"e115\",\"e215\",\"d15\"],\"alphabet\":[\"a15\",\"b15\"],\"start_state\":\"s15\",\"final_states\":[\"f15\"],\"transitions\":[[\"s15\",null,\"m15\"],[\"s15\",null,\"d15\"],[\"m15\",\"a15\",\"m15\"],[\"m15\",\"b15\",\"f15\"],[\"f15\",null,\"e115\"],[\"e115\",null,\"e215\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s15, [d15, m15, s15], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s15, [d15, m15, s15], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127016,"parameters":{"states":["s15","m15","f15","e115","e215","d15"],"alphabet":["a15","b15"],"start_state":"s15","final_states":["f15"],"transitions":[["s15",null,"m15"],["s15",null,"d15"],["m15","a15","m15"],["m15","b15","f15"],["f15",null,"e115"],["e115",null,"e215"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a15\",\"b15\"],\"final_states\":[\"f15\"],\"start_state\":\"s15\",\"states\":[\"d15\",\"e115\",\"e215\",\"f15\",\"m15\",\"s15\"],\"transitions\":[[\"e115\",null,\"e215\"],[\"f15\",null,\"e115\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0017","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s16\",\"m16\",\"f16\",\"e116\",\"e216\",\"d16\"],\"alphabet\":[\"a16\",\"b16\"],\"start_state\":\"s16\",\"final_states\":[\"f16\"],\"transitions\":[[\"s16\",null,\"m16\"],[\"s16\",null,\"d16\"],[\"m16\",\"a16\",\"m16\"],[\"m16\",\"b16\",\"f16\"],[\"f16\",null,\"e116\"],[\"e116\",null,\"e216\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s16, [d16, m16, s16], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s16, [d16, m16, s16], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127017,"parameters":{"states":["s16","m16","f16","e116","e216","d16"],"alphabet":["a16","b16"],"start_state":"s16","final_states":["f16"],"transitions":[["s16",null,"m16"],["s16",null,"d16"],["m16","a16","m16"],["m16","b16","f16"],["f16",null,"e116"],["e116",null,"e216"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a16\",\"b16\"],\"final_states\":[\"f16\"],\"start_state\":\"s16\",\"states\":[\"d16\",\"e116\",\"e216\",\"f16\",\"m16\",\"s16\"],\"transitions\":[[\"e116\",null,\"e216\"],[\"f16\",null,\"e116\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0018","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s17\",\"m17\",\"f17\",\"e117\",\"e217\",\"d17\"],\"alphabet\":[\"a17\",\"b17\"],\"start_state\":\"s17\",\"final_states\":[\"f17\"],\"transitions\":[[\"s17\",null,\"m17\"],[\"s17\",null,\"d17\"],[\"m17\",\"a17\",\"m17\"],[\"m17\",\"b17\",\"f17\"],[\"f17\",null,\"e117\"],[\"e117\",null,\"e217\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s17, [d17, m17, s17], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s17, [d17, m17, s17], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127018,"parameters":{"states":["s17","m17","f17","e117","e217","d17"],"alphabet":["a17","b17"],"start_state":"s17","final_states":["f17"],"transitions":[["s17",null,"m17"],["s17",null,"d17"],["m17","a17","m17"],["m17","b17","f17"],["f17",null,"e117"],["e117",null,"e217"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a17\",\"b17\"],\"final_states\":[\"f17\"],\"start_state\":\"s17\",\"states\":[\"d17\",\"e117\",\"e217\",\"f17\",\"m17\",\"s17\"],\"transitions\":[[\"e117\",null,\"e217\"],[\"f17\",null,\"e117\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0019","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s18\",\"m18\",\"f18\",\"e118\",\"e218\",\"d18\"],\"alphabet\":[\"a18\",\"b18\"],\"start_state\":\"s18\",\"final_states\":[\"f18\"],\"transitions\":[[\"s18\",null,\"m18\"],[\"s18\",null,\"d18\"],[\"m18\",\"a18\",\"m18\"],[\"m18\",\"b18\",\"f18\"],[\"f18\",null,\"e118\"],[\"e118\",null,\"e218\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s18, [d18, m18, s18], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s18, [d18, m18, s18], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127019,"parameters":{"states":["s18","m18","f18","e118","e218","d18"],"alphabet":["a18","b18"],"start_state":"s18","final_states":["f18"],"transitions":[["s18",null,"m18"],["s18",null,"d18"],["m18","a18","m18"],["m18","b18","f18"],["f18",null,"e118"],["e118",null,"e218"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a18\",\"b18\"],\"final_states\":[\"f18\"],\"start_state\":\"s18\",\"states\":[\"d18\",\"e118\",\"e218\",\"f18\",\"m18\",\"s18\"],\"transitions\":[[\"e118\",null,\"e218\"],[\"f18\",null,\"e118\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0020","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s19\",\"m19\",\"f19\",\"e119\",\"e219\",\"d19\"],\"alphabet\":[\"a19\",\"b19\"],\"start_state\":\"s19\",\"final_states\":[\"f19\"],\"transitions\":[[\"s19\",null,\"m19\"],[\"s19\",null,\"d19\"],[\"m19\",\"a19\",\"m19\"],[\"m19\",\"b19\",\"f19\"],[\"f19\",null,\"e119\"],[\"e119\",null,\"e219\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s19, [d19, m19, s19], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s19, [d19, m19, s19], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127020,"parameters":{"states":["s19","m19","f19","e119","e219","d19"],"alphabet":["a19","b19"],"start_state":"s19","final_states":["f19"],"transitions":[["s19",null,"m19"],["s19",null,"d19"],["m19","a19","m19"],["m19","b19","f19"],["f19",null,"e119"],["e119",null,"e219"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a19\",\"b19\"],\"final_states\":[\"f19\"],\"start_state\":\"s19\",\"states\":[\"d19\",\"e119\",\"e219\",\"f19\",\"m19\",\"s19\"],\"transitions\":[[\"e119\",null,\"e219\"],[\"f19\",null,\"e119\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0021","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s20\",\"m20\",\"f20\",\"e120\",\"e220\",\"d20\"],\"alphabet\":[\"a20\",\"b20\"],\"start_state\":\"s20\",\"final_states\":[\"f20\"],\"transitions\":[[\"s20\",null,\"m20\"],[\"s20\",null,\"d20\"],[\"m20\",\"a20\",\"m20\"],[\"m20\",\"b20\",\"f20\"],[\"f20\",null,\"e120\"],[\"e120\",null,\"e220\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s20, [d20, m20, s20], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s20, [d20, m20, s20], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127021,"parameters":{"states":["s20","m20","f20","e120","e220","d20"],"alphabet":["a20","b20"],"start_state":"s20","final_states":["f20"],"transitions":[["s20",null,"m20"],["s20",null,"d20"],["m20","a20","m20"],["m20","b20","f20"],["f20",null,"e120"],["e120",null,"e220"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a20\",\"b20\"],\"final_states\":[\"f20\"],\"start_state\":\"s20\",\"states\":[\"d20\",\"e120\",\"e220\",\"f20\",\"m20\",\"s20\"],\"transitions\":[[\"e120\",null,\"e220\"],[\"f20\",null,\"e120\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0022","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s21\",\"m21\",\"f21\",\"e121\",\"e221\",\"d21\"],\"alphabet\":[\"a21\",\"b21\"],\"start_state\":\"s21\",\"final_states\":[\"f21\"],\"transitions\":[[\"s21\",null,\"m21\"],[\"s21\",null,\"d21\"],[\"m21\",\"a21\",\"m21\"],[\"m21\",\"b21\",\"f21\"],[\"f21\",null,\"e121\"],[\"e121\",null,\"e221\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s21, [d21, m21, s21], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s21, [d21, m21, s21], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127022,"parameters":{"states":["s21","m21","f21","e121","e221","d21"],"alphabet":["a21","b21"],"start_state":"s21","final_states":["f21"],"transitions":[["s21",null,"m21"],["s21",null,"d21"],["m21","a21","m21"],["m21","b21","f21"],["f21",null,"e121"],["e121",null,"e221"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a21\",\"b21\"],\"final_states\":[\"f21\"],\"start_state\":\"s21\",\"states\":[\"d21\",\"e121\",\"e221\",\"f21\",\"m21\",\"s21\"],\"transitions\":[[\"e121\",null,\"e221\"],[\"f21\",null,\"e121\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0023","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s22\",\"m22\",\"f22\",\"e122\",\"e222\",\"d22\"],\"alphabet\":[\"a22\",\"b22\"],\"start_state\":\"s22\",\"final_states\":[\"f22\"],\"transitions\":[[\"s22\",null,\"m22\"],[\"s22\",null,\"d22\"],[\"m22\",\"a22\",\"m22\"],[\"m22\",\"b22\",\"f22\"],[\"f22\",null,\"e122\"],[\"e122\",null,\"e222\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s22, [d22, m22, s22], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s22, [d22, m22, s22], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127023,"parameters":{"states":["s22","m22","f22","e122","e222","d22"],"alphabet":["a22","b22"],"start_state":"s22","final_states":["f22"],"transitions":[["s22",null,"m22"],["s22",null,"d22"],["m22","a22","m22"],["m22","b22","f22"],["f22",null,"e122"],["e122",null,"e222"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a22\",\"b22\"],\"final_states\":[\"f22\"],\"start_state\":\"s22\",\"states\":[\"d22\",\"e122\",\"e222\",\"f22\",\"m22\",\"s22\"],\"transitions\":[[\"e122\",null,\"e222\"],[\"f22\",null,\"e122\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0024","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s23\",\"m23\",\"f23\",\"e123\",\"e223\",\"d23\"],\"alphabet\":[\"a23\",\"b23\"],\"start_state\":\"s23\",\"final_states\":[\"f23\"],\"transitions\":[[\"s23\",null,\"m23\"],[\"s23\",null,\"d23\"],[\"m23\",\"a23\",\"m23\"],[\"m23\",\"b23\",\"f23\"],[\"f23\",null,\"e123\"],[\"e123\",null,\"e223\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s23, [d23, m23, s23], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s23, [d23, m23, s23], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127024,"parameters":{"states":["s23","m23","f23","e123","e223","d23"],"alphabet":["a23","b23"],"start_state":"s23","final_states":["f23"],"transitions":[["s23",null,"m23"],["s23",null,"d23"],["m23","a23","m23"],["m23","b23","f23"],["f23",null,"e123"],["e123",null,"e223"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a23\",\"b23\"],\"final_states\":[\"f23\"],\"start_state\":\"s23\",\"states\":[\"d23\",\"e123\",\"e223\",\"f23\",\"m23\",\"s23\"],\"transitions\":[[\"e123\",null,\"e223\"],[\"f23\",null,\"e123\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0025","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={\"states\":[\"s24\",\"m24\",\"f24\",\"e124\",\"e224\",\"d24\"],\"alphabet\":[\"a24\",\"b24\"],\"start_state\":\"s24\",\"final_states\":[\"f24\"],\"transitions\":[[\"s24\",null,\"m24\"],[\"s24\",null,\"d24\"],[\"m24\",\"a24\",\"m24\"],[\"m24\",\"b24\",\"f24\"],[\"f24\",null,\"e124\"],[\"e124\",null,\"e224\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(s24, [d24, m24, s24], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)","explanation_zh":"Wave6第六層核對=(s24, [d24, m24, s24], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-epsilon-start","seed":202611127025,"parameters":{"states":["s24","m24","f24","e124","e224","d24"],"alphabet":["a24","b24"],"start_state":"s24","final_states":["f24"],"transitions":[["s24",null,"m24"],["s24",null,"d24"],["m24","a24","m24"],["m24","b24","f24"],["f24",null,"e124"],["e124",null,"e224"]],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-epsilon-start","semantic_template":"qf-mod43-subsetdfa-epsilon-start/{\"alphabet\":[\"a24\",\"b24\"],\"final_states\":[\"f24\"],\"start_state\":\"s24\",\"states\":[\"d24\",\"e124\",\"e224\",\"f24\",\"m24\",\"s24\"],\"transitions\":[[\"e124\",null,\"e224\"],[\"f24\",null,\"e124\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0026","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s0\",\"m0\",\"f0\",\"e10\",\"e20\",\"d0\"],\"alphabet\":[\"a0\",\"b0\"],\"start_state\":\"s0\",\"final_states\":[\"f0\"],\"transitions\":[[\"s0\",null,\"m0\"],[\"s0\",null,\"d0\"],[\"m0\",\"a0\",\"m0\"],[\"m0\",\"b0\",\"f0\"],[\"f0\",null,\"e10\"],[\"e10\",null,\"e20\"]],\"subset\":[\"s0\",\"m0\",\"d0\"],\"symbol\":\"a0\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d0, m0, s0], a0, [m0], [m0], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d0, m0, s0], a0, [m0], [m0], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127026,"parameters":{"states":["s0","m0","f0","e10","e20","d0"],"alphabet":["a0","b0"],"start_state":"s0","final_states":["f0"],"transitions":[["s0",null,"m0"],["s0",null,"d0"],["m0","a0","m0"],["m0","b0","f0"],["f0",null,"e10"],["e10",null,"e20"]],"subset":["s0","m0","d0"],"symbol":"a0","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a0\",\"b0\"],\"final_states\":[\"f0\"],\"start_state\":\"s0\",\"states\":[\"d0\",\"e10\",\"e20\",\"f0\",\"m0\",\"s0\"],\"subset\":[\"d0\",\"m0\",\"s0\"],\"symbol\":\"a0\",\"transitions\":[[\"e10\",null,\"e20\"],[\"f0\",null,\"e10\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0027","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s1\",\"m1\",\"f1\",\"e11\",\"e21\",\"d1\"],\"alphabet\":[\"a1\",\"b1\"],\"start_state\":\"s1\",\"final_states\":[\"f1\"],\"transitions\":[[\"s1\",null,\"m1\"],[\"s1\",null,\"d1\"],[\"m1\",\"a1\",\"m1\"],[\"m1\",\"b1\",\"f1\"],[\"f1\",null,\"e11\"],[\"e11\",null,\"e21\"]],\"subset\":[\"s1\",\"m1\",\"d1\"],\"symbol\":\"b1\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d1, m1, s1], b1, [f1], [e11, e21, f1], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d1, m1, s1], b1, [f1], [e11, e21, f1], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127027,"parameters":{"states":["s1","m1","f1","e11","e21","d1"],"alphabet":["a1","b1"],"start_state":"s1","final_states":["f1"],"transitions":[["s1",null,"m1"],["s1",null,"d1"],["m1","a1","m1"],["m1","b1","f1"],["f1",null,"e11"],["e11",null,"e21"]],"subset":["s1","m1","d1"],"symbol":"b1","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a1\",\"b1\"],\"final_states\":[\"f1\"],\"start_state\":\"s1\",\"states\":[\"d1\",\"e11\",\"e21\",\"f1\",\"m1\",\"s1\"],\"subset\":[\"d1\",\"m1\",\"s1\"],\"symbol\":\"b1\",\"transitions\":[[\"e11\",null,\"e21\"],[\"f1\",null,\"e11\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0028","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s2\",\"m2\",\"f2\",\"e12\",\"e22\",\"d2\"],\"alphabet\":[\"a2\",\"b2\"],\"start_state\":\"s2\",\"final_states\":[\"f2\"],\"transitions\":[[\"s2\",null,\"m2\"],[\"s2\",null,\"d2\"],[\"m2\",\"a2\",\"m2\"],[\"m2\",\"b2\",\"f2\"],[\"f2\",null,\"e12\"],[\"e12\",null,\"e22\"]],\"subset\":[\"s2\",\"m2\",\"d2\"],\"symbol\":\"a2\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d2, m2, s2], a2, [m2], [m2], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d2, m2, s2], a2, [m2], [m2], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127028,"parameters":{"states":["s2","m2","f2","e12","e22","d2"],"alphabet":["a2","b2"],"start_state":"s2","final_states":["f2"],"transitions":[["s2",null,"m2"],["s2",null,"d2"],["m2","a2","m2"],["m2","b2","f2"],["f2",null,"e12"],["e12",null,"e22"]],"subset":["s2","m2","d2"],"symbol":"a2","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a2\",\"b2\"],\"final_states\":[\"f2\"],\"start_state\":\"s2\",\"states\":[\"d2\",\"e12\",\"e22\",\"f2\",\"m2\",\"s2\"],\"subset\":[\"d2\",\"m2\",\"s2\"],\"symbol\":\"a2\",\"transitions\":[[\"e12\",null,\"e22\"],[\"f2\",null,\"e12\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0029","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s3\",\"m3\",\"f3\",\"e13\",\"e23\",\"d3\"],\"alphabet\":[\"a3\",\"b3\"],\"start_state\":\"s3\",\"final_states\":[\"f3\"],\"transitions\":[[\"s3\",null,\"m3\"],[\"s3\",null,\"d3\"],[\"m3\",\"a3\",\"m3\"],[\"m3\",\"b3\",\"f3\"],[\"f3\",null,\"e13\"],[\"e13\",null,\"e23\"]],\"subset\":[\"s3\",\"m3\",\"d3\"],\"symbol\":\"b3\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d3, m3, s3], b3, [f3], [e13, e23, f3], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d3, m3, s3], b3, [f3], [e13, e23, f3], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127029,"parameters":{"states":["s3","m3","f3","e13","e23","d3"],"alphabet":["a3","b3"],"start_state":"s3","final_states":["f3"],"transitions":[["s3",null,"m3"],["s3",null,"d3"],["m3","a3","m3"],["m3","b3","f3"],["f3",null,"e13"],["e13",null,"e23"]],"subset":["s3","m3","d3"],"symbol":"b3","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a3\",\"b3\"],\"final_states\":[\"f3\"],\"start_state\":\"s3\",\"states\":[\"d3\",\"e13\",\"e23\",\"f3\",\"m3\",\"s3\"],\"subset\":[\"d3\",\"m3\",\"s3\"],\"symbol\":\"b3\",\"transitions\":[[\"e13\",null,\"e23\"],[\"f3\",null,\"e13\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0030","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s4\",\"m4\",\"f4\",\"e14\",\"e24\",\"d4\"],\"alphabet\":[\"a4\",\"b4\"],\"start_state\":\"s4\",\"final_states\":[\"f4\"],\"transitions\":[[\"s4\",null,\"m4\"],[\"s4\",null,\"d4\"],[\"m4\",\"a4\",\"m4\"],[\"m4\",\"b4\",\"f4\"],[\"f4\",null,\"e14\"],[\"e14\",null,\"e24\"]],\"subset\":[\"s4\",\"m4\",\"d4\"],\"symbol\":\"a4\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d4, m4, s4], a4, [m4], [m4], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d4, m4, s4], a4, [m4], [m4], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127030,"parameters":{"states":["s4","m4","f4","e14","e24","d4"],"alphabet":["a4","b4"],"start_state":"s4","final_states":["f4"],"transitions":[["s4",null,"m4"],["s4",null,"d4"],["m4","a4","m4"],["m4","b4","f4"],["f4",null,"e14"],["e14",null,"e24"]],"subset":["s4","m4","d4"],"symbol":"a4","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a4\",\"b4\"],\"final_states\":[\"f4\"],\"start_state\":\"s4\",\"states\":[\"d4\",\"e14\",\"e24\",\"f4\",\"m4\",\"s4\"],\"subset\":[\"d4\",\"m4\",\"s4\"],\"symbol\":\"a4\",\"transitions\":[[\"e14\",null,\"e24\"],[\"f4\",null,\"e14\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0031","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s5\",\"m5\",\"f5\",\"e15\",\"e25\",\"d5\"],\"alphabet\":[\"a5\",\"b5\"],\"start_state\":\"s5\",\"final_states\":[\"f5\"],\"transitions\":[[\"s5\",null,\"m5\"],[\"s5\",null,\"d5\"],[\"m5\",\"a5\",\"m5\"],[\"m5\",\"b5\",\"f5\"],[\"f5\",null,\"e15\"],[\"e15\",null,\"e25\"]],\"subset\":[\"s5\",\"m5\",\"d5\"],\"symbol\":\"b5\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d5, m5, s5], b5, [f5], [e15, e25, f5], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d5, m5, s5], b5, [f5], [e15, e25, f5], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127031,"parameters":{"states":["s5","m5","f5","e15","e25","d5"],"alphabet":["a5","b5"],"start_state":"s5","final_states":["f5"],"transitions":[["s5",null,"m5"],["s5",null,"d5"],["m5","a5","m5"],["m5","b5","f5"],["f5",null,"e15"],["e15",null,"e25"]],"subset":["s5","m5","d5"],"symbol":"b5","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a5\",\"b5\"],\"final_states\":[\"f5\"],\"start_state\":\"s5\",\"states\":[\"d5\",\"e15\",\"e25\",\"f5\",\"m5\",\"s5\"],\"subset\":[\"d5\",\"m5\",\"s5\"],\"symbol\":\"b5\",\"transitions\":[[\"e15\",null,\"e25\"],[\"f5\",null,\"e15\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0032","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s6\",\"m6\",\"f6\",\"e16\",\"e26\",\"d6\"],\"alphabet\":[\"a6\",\"b6\"],\"start_state\":\"s6\",\"final_states\":[\"f6\"],\"transitions\":[[\"s6\",null,\"m6\"],[\"s6\",null,\"d6\"],[\"m6\",\"a6\",\"m6\"],[\"m6\",\"b6\",\"f6\"],[\"f6\",null,\"e16\"],[\"e16\",null,\"e26\"]],\"subset\":[\"s6\",\"m6\",\"d6\"],\"symbol\":\"a6\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d6, m6, s6], a6, [m6], [m6], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d6, m6, s6], a6, [m6], [m6], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127032,"parameters":{"states":["s6","m6","f6","e16","e26","d6"],"alphabet":["a6","b6"],"start_state":"s6","final_states":["f6"],"transitions":[["s6",null,"m6"],["s6",null,"d6"],["m6","a6","m6"],["m6","b6","f6"],["f6",null,"e16"],["e16",null,"e26"]],"subset":["s6","m6","d6"],"symbol":"a6","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a6\",\"b6\"],\"final_states\":[\"f6\"],\"start_state\":\"s6\",\"states\":[\"d6\",\"e16\",\"e26\",\"f6\",\"m6\",\"s6\"],\"subset\":[\"d6\",\"m6\",\"s6\"],\"symbol\":\"a6\",\"transitions\":[[\"e16\",null,\"e26\"],[\"f6\",null,\"e16\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0033","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s7\",\"m7\",\"f7\",\"e17\",\"e27\",\"d7\"],\"alphabet\":[\"a7\",\"b7\"],\"start_state\":\"s7\",\"final_states\":[\"f7\"],\"transitions\":[[\"s7\",null,\"m7\"],[\"s7\",null,\"d7\"],[\"m7\",\"a7\",\"m7\"],[\"m7\",\"b7\",\"f7\"],[\"f7\",null,\"e17\"],[\"e17\",null,\"e27\"]],\"subset\":[\"s7\",\"m7\",\"d7\"],\"symbol\":\"b7\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d7, m7, s7], b7, [f7], [e17, e27, f7], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d7, m7, s7], b7, [f7], [e17, e27, f7], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127033,"parameters":{"states":["s7","m7","f7","e17","e27","d7"],"alphabet":["a7","b7"],"start_state":"s7","final_states":["f7"],"transitions":[["s7",null,"m7"],["s7",null,"d7"],["m7","a7","m7"],["m7","b7","f7"],["f7",null,"e17"],["e17",null,"e27"]],"subset":["s7","m7","d7"],"symbol":"b7","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a7\",\"b7\"],\"final_states\":[\"f7\"],\"start_state\":\"s7\",\"states\":[\"d7\",\"e17\",\"e27\",\"f7\",\"m7\",\"s7\"],\"subset\":[\"d7\",\"m7\",\"s7\"],\"symbol\":\"b7\",\"transitions\":[[\"e17\",null,\"e27\"],[\"f7\",null,\"e17\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0034","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s8\",\"m8\",\"f8\",\"e18\",\"e28\",\"d8\"],\"alphabet\":[\"a8\",\"b8\"],\"start_state\":\"s8\",\"final_states\":[\"f8\"],\"transitions\":[[\"s8\",null,\"m8\"],[\"s8\",null,\"d8\"],[\"m8\",\"a8\",\"m8\"],[\"m8\",\"b8\",\"f8\"],[\"f8\",null,\"e18\"],[\"e18\",null,\"e28\"]],\"subset\":[\"s8\",\"m8\",\"d8\"],\"symbol\":\"a8\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d8, m8, s8], a8, [m8], [m8], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d8, m8, s8], a8, [m8], [m8], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127034,"parameters":{"states":["s8","m8","f8","e18","e28","d8"],"alphabet":["a8","b8"],"start_state":"s8","final_states":["f8"],"transitions":[["s8",null,"m8"],["s8",null,"d8"],["m8","a8","m8"],["m8","b8","f8"],["f8",null,"e18"],["e18",null,"e28"]],"subset":["s8","m8","d8"],"symbol":"a8","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a8\",\"b8\"],\"final_states\":[\"f8\"],\"start_state\":\"s8\",\"states\":[\"d8\",\"e18\",\"e28\",\"f8\",\"m8\",\"s8\"],\"subset\":[\"d8\",\"m8\",\"s8\"],\"symbol\":\"a8\",\"transitions\":[[\"e18\",null,\"e28\"],[\"f8\",null,\"e18\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0035","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s9\",\"m9\",\"f9\",\"e19\",\"e29\",\"d9\"],\"alphabet\":[\"a9\",\"b9\"],\"start_state\":\"s9\",\"final_states\":[\"f9\"],\"transitions\":[[\"s9\",null,\"m9\"],[\"s9\",null,\"d9\"],[\"m9\",\"a9\",\"m9\"],[\"m9\",\"b9\",\"f9\"],[\"f9\",null,\"e19\"],[\"e19\",null,\"e29\"]],\"subset\":[\"s9\",\"m9\",\"d9\"],\"symbol\":\"b9\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d9, m9, s9], b9, [f9], [e19, e29, f9], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d9, m9, s9], b9, [f9], [e19, e29, f9], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127035,"parameters":{"states":["s9","m9","f9","e19","e29","d9"],"alphabet":["a9","b9"],"start_state":"s9","final_states":["f9"],"transitions":[["s9",null,"m9"],["s9",null,"d9"],["m9","a9","m9"],["m9","b9","f9"],["f9",null,"e19"],["e19",null,"e29"]],"subset":["s9","m9","d9"],"symbol":"b9","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a9\",\"b9\"],\"final_states\":[\"f9\"],\"start_state\":\"s9\",\"states\":[\"d9\",\"e19\",\"e29\",\"f9\",\"m9\",\"s9\"],\"subset\":[\"d9\",\"m9\",\"s9\"],\"symbol\":\"b9\",\"transitions\":[[\"e19\",null,\"e29\"],[\"f9\",null,\"e19\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0036","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s10\",\"m10\",\"f10\",\"e110\",\"e210\",\"d10\"],\"alphabet\":[\"a10\",\"b10\"],\"start_state\":\"s10\",\"final_states\":[\"f10\"],\"transitions\":[[\"s10\",null,\"m10\"],[\"s10\",null,\"d10\"],[\"m10\",\"a10\",\"m10\"],[\"m10\",\"b10\",\"f10\"],[\"f10\",null,\"e110\"],[\"e110\",null,\"e210\"]],\"subset\":[\"s10\",\"m10\",\"d10\"],\"symbol\":\"a10\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d10, m10, s10], a10, [m10], [m10], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d10, m10, s10], a10, [m10], [m10], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127036,"parameters":{"states":["s10","m10","f10","e110","e210","d10"],"alphabet":["a10","b10"],"start_state":"s10","final_states":["f10"],"transitions":[["s10",null,"m10"],["s10",null,"d10"],["m10","a10","m10"],["m10","b10","f10"],["f10",null,"e110"],["e110",null,"e210"]],"subset":["s10","m10","d10"],"symbol":"a10","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a10\",\"b10\"],\"final_states\":[\"f10\"],\"start_state\":\"s10\",\"states\":[\"d10\",\"e110\",\"e210\",\"f10\",\"m10\",\"s10\"],\"subset\":[\"d10\",\"m10\",\"s10\"],\"symbol\":\"a10\",\"transitions\":[[\"e110\",null,\"e210\"],[\"f10\",null,\"e110\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0037","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s11\",\"m11\",\"f11\",\"e111\",\"e211\",\"d11\"],\"alphabet\":[\"a11\",\"b11\"],\"start_state\":\"s11\",\"final_states\":[\"f11\"],\"transitions\":[[\"s11\",null,\"m11\"],[\"s11\",null,\"d11\"],[\"m11\",\"a11\",\"m11\"],[\"m11\",\"b11\",\"f11\"],[\"f11\",null,\"e111\"],[\"e111\",null,\"e211\"]],\"subset\":[\"s11\",\"m11\",\"d11\"],\"symbol\":\"b11\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d11, m11, s11], b11, [f11], [e111, e211, f11], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d11, m11, s11], b11, [f11], [e111, e211, f11], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127037,"parameters":{"states":["s11","m11","f11","e111","e211","d11"],"alphabet":["a11","b11"],"start_state":"s11","final_states":["f11"],"transitions":[["s11",null,"m11"],["s11",null,"d11"],["m11","a11","m11"],["m11","b11","f11"],["f11",null,"e111"],["e111",null,"e211"]],"subset":["s11","m11","d11"],"symbol":"b11","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a11\",\"b11\"],\"final_states\":[\"f11\"],\"start_state\":\"s11\",\"states\":[\"d11\",\"e111\",\"e211\",\"f11\",\"m11\",\"s11\"],\"subset\":[\"d11\",\"m11\",\"s11\"],\"symbol\":\"b11\",\"transitions\":[[\"e111\",null,\"e211\"],[\"f11\",null,\"e111\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0038","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s12\",\"m12\",\"f12\",\"e112\",\"e212\",\"d12\"],\"alphabet\":[\"a12\",\"b12\"],\"start_state\":\"s12\",\"final_states\":[\"f12\"],\"transitions\":[[\"s12\",null,\"m12\"],[\"s12\",null,\"d12\"],[\"m12\",\"a12\",\"m12\"],[\"m12\",\"b12\",\"f12\"],[\"f12\",null,\"e112\"],[\"e112\",null,\"e212\"]],\"subset\":[\"s12\",\"m12\",\"d12\"],\"symbol\":\"a12\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d12, m12, s12], a12, [m12], [m12], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d12, m12, s12], a12, [m12], [m12], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127038,"parameters":{"states":["s12","m12","f12","e112","e212","d12"],"alphabet":["a12","b12"],"start_state":"s12","final_states":["f12"],"transitions":[["s12",null,"m12"],["s12",null,"d12"],["m12","a12","m12"],["m12","b12","f12"],["f12",null,"e112"],["e112",null,"e212"]],"subset":["s12","m12","d12"],"symbol":"a12","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a12\",\"b12\"],\"final_states\":[\"f12\"],\"start_state\":\"s12\",\"states\":[\"d12\",\"e112\",\"e212\",\"f12\",\"m12\",\"s12\"],\"subset\":[\"d12\",\"m12\",\"s12\"],\"symbol\":\"a12\",\"transitions\":[[\"e112\",null,\"e212\"],[\"f12\",null,\"e112\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0039","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s13\",\"m13\",\"f13\",\"e113\",\"e213\",\"d13\"],\"alphabet\":[\"a13\",\"b13\"],\"start_state\":\"s13\",\"final_states\":[\"f13\"],\"transitions\":[[\"s13\",null,\"m13\"],[\"s13\",null,\"d13\"],[\"m13\",\"a13\",\"m13\"],[\"m13\",\"b13\",\"f13\"],[\"f13\",null,\"e113\"],[\"e113\",null,\"e213\"]],\"subset\":[\"s13\",\"m13\",\"d13\"],\"symbol\":\"b13\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d13, m13, s13], b13, [f13], [e113, e213, f13], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d13, m13, s13], b13, [f13], [e113, e213, f13], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127039,"parameters":{"states":["s13","m13","f13","e113","e213","d13"],"alphabet":["a13","b13"],"start_state":"s13","final_states":["f13"],"transitions":[["s13",null,"m13"],["s13",null,"d13"],["m13","a13","m13"],["m13","b13","f13"],["f13",null,"e113"],["e113",null,"e213"]],"subset":["s13","m13","d13"],"symbol":"b13","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a13\",\"b13\"],\"final_states\":[\"f13\"],\"start_state\":\"s13\",\"states\":[\"d13\",\"e113\",\"e213\",\"f13\",\"m13\",\"s13\"],\"subset\":[\"d13\",\"m13\",\"s13\"],\"symbol\":\"b13\",\"transitions\":[[\"e113\",null,\"e213\"],[\"f13\",null,\"e113\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0040","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s14\",\"m14\",\"f14\",\"e114\",\"e214\",\"d14\"],\"alphabet\":[\"a14\",\"b14\"],\"start_state\":\"s14\",\"final_states\":[\"f14\"],\"transitions\":[[\"s14\",null,\"m14\"],[\"s14\",null,\"d14\"],[\"m14\",\"a14\",\"m14\"],[\"m14\",\"b14\",\"f14\"],[\"f14\",null,\"e114\"],[\"e114\",null,\"e214\"]],\"subset\":[\"s14\",\"m14\",\"d14\"],\"symbol\":\"a14\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d14, m14, s14], a14, [m14], [m14], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d14, m14, s14], a14, [m14], [m14], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127040,"parameters":{"states":["s14","m14","f14","e114","e214","d14"],"alphabet":["a14","b14"],"start_state":"s14","final_states":["f14"],"transitions":[["s14",null,"m14"],["s14",null,"d14"],["m14","a14","m14"],["m14","b14","f14"],["f14",null,"e114"],["e114",null,"e214"]],"subset":["s14","m14","d14"],"symbol":"a14","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a14\",\"b14\"],\"final_states\":[\"f14\"],\"start_state\":\"s14\",\"states\":[\"d14\",\"e114\",\"e214\",\"f14\",\"m14\",\"s14\"],\"subset\":[\"d14\",\"m14\",\"s14\"],\"symbol\":\"a14\",\"transitions\":[[\"e114\",null,\"e214\"],[\"f14\",null,\"e114\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0041","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s15\",\"m15\",\"f15\",\"e115\",\"e215\",\"d15\"],\"alphabet\":[\"a15\",\"b15\"],\"start_state\":\"s15\",\"final_states\":[\"f15\"],\"transitions\":[[\"s15\",null,\"m15\"],[\"s15\",null,\"d15\"],[\"m15\",\"a15\",\"m15\"],[\"m15\",\"b15\",\"f15\"],[\"f15\",null,\"e115\"],[\"e115\",null,\"e215\"]],\"subset\":[\"s15\",\"m15\",\"d15\"],\"symbol\":\"b15\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d15, m15, s15], b15, [f15], [e115, e215, f15], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d15, m15, s15], b15, [f15], [e115, e215, f15], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127041,"parameters":{"states":["s15","m15","f15","e115","e215","d15"],"alphabet":["a15","b15"],"start_state":"s15","final_states":["f15"],"transitions":[["s15",null,"m15"],["s15",null,"d15"],["m15","a15","m15"],["m15","b15","f15"],["f15",null,"e115"],["e115",null,"e215"]],"subset":["s15","m15","d15"],"symbol":"b15","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a15\",\"b15\"],\"final_states\":[\"f15\"],\"start_state\":\"s15\",\"states\":[\"d15\",\"e115\",\"e215\",\"f15\",\"m15\",\"s15\"],\"subset\":[\"d15\",\"m15\",\"s15\"],\"symbol\":\"b15\",\"transitions\":[[\"e115\",null,\"e215\"],[\"f15\",null,\"e115\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0042","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s16\",\"m16\",\"f16\",\"e116\",\"e216\",\"d16\"],\"alphabet\":[\"a16\",\"b16\"],\"start_state\":\"s16\",\"final_states\":[\"f16\"],\"transitions\":[[\"s16\",null,\"m16\"],[\"s16\",null,\"d16\"],[\"m16\",\"a16\",\"m16\"],[\"m16\",\"b16\",\"f16\"],[\"f16\",null,\"e116\"],[\"e116\",null,\"e216\"]],\"subset\":[\"s16\",\"m16\",\"d16\"],\"symbol\":\"a16\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d16, m16, s16], a16, [m16], [m16], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d16, m16, s16], a16, [m16], [m16], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127042,"parameters":{"states":["s16","m16","f16","e116","e216","d16"],"alphabet":["a16","b16"],"start_state":"s16","final_states":["f16"],"transitions":[["s16",null,"m16"],["s16",null,"d16"],["m16","a16","m16"],["m16","b16","f16"],["f16",null,"e116"],["e116",null,"e216"]],"subset":["s16","m16","d16"],"symbol":"a16","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a16\",\"b16\"],\"final_states\":[\"f16\"],\"start_state\":\"s16\",\"states\":[\"d16\",\"e116\",\"e216\",\"f16\",\"m16\",\"s16\"],\"subset\":[\"d16\",\"m16\",\"s16\"],\"symbol\":\"a16\",\"transitions\":[[\"e116\",null,\"e216\"],[\"f16\",null,\"e116\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0043","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s17\",\"m17\",\"f17\",\"e117\",\"e217\",\"d17\"],\"alphabet\":[\"a17\",\"b17\"],\"start_state\":\"s17\",\"final_states\":[\"f17\"],\"transitions\":[[\"s17\",null,\"m17\"],[\"s17\",null,\"d17\"],[\"m17\",\"a17\",\"m17\"],[\"m17\",\"b17\",\"f17\"],[\"f17\",null,\"e117\"],[\"e117\",null,\"e217\"]],\"subset\":[\"s17\",\"m17\",\"d17\"],\"symbol\":\"b17\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d17, m17, s17], b17, [f17], [e117, e217, f17], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d17, m17, s17], b17, [f17], [e117, e217, f17], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127043,"parameters":{"states":["s17","m17","f17","e117","e217","d17"],"alphabet":["a17","b17"],"start_state":"s17","final_states":["f17"],"transitions":[["s17",null,"m17"],["s17",null,"d17"],["m17","a17","m17"],["m17","b17","f17"],["f17",null,"e117"],["e117",null,"e217"]],"subset":["s17","m17","d17"],"symbol":"b17","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a17\",\"b17\"],\"final_states\":[\"f17\"],\"start_state\":\"s17\",\"states\":[\"d17\",\"e117\",\"e217\",\"f17\",\"m17\",\"s17\"],\"subset\":[\"d17\",\"m17\",\"s17\"],\"symbol\":\"b17\",\"transitions\":[[\"e117\",null,\"e217\"],[\"f17\",null,\"e117\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0044","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s18\",\"m18\",\"f18\",\"e118\",\"e218\",\"d18\"],\"alphabet\":[\"a18\",\"b18\"],\"start_state\":\"s18\",\"final_states\":[\"f18\"],\"transitions\":[[\"s18\",null,\"m18\"],[\"s18\",null,\"d18\"],[\"m18\",\"a18\",\"m18\"],[\"m18\",\"b18\",\"f18\"],[\"f18\",null,\"e118\"],[\"e118\",null,\"e218\"]],\"subset\":[\"s18\",\"m18\",\"d18\"],\"symbol\":\"a18\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d18, m18, s18], a18, [m18], [m18], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d18, m18, s18], a18, [m18], [m18], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127044,"parameters":{"states":["s18","m18","f18","e118","e218","d18"],"alphabet":["a18","b18"],"start_state":"s18","final_states":["f18"],"transitions":[["s18",null,"m18"],["s18",null,"d18"],["m18","a18","m18"],["m18","b18","f18"],["f18",null,"e118"],["e118",null,"e218"]],"subset":["s18","m18","d18"],"symbol":"a18","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a18\",\"b18\"],\"final_states\":[\"f18\"],\"start_state\":\"s18\",\"states\":[\"d18\",\"e118\",\"e218\",\"f18\",\"m18\",\"s18\"],\"subset\":[\"d18\",\"m18\",\"s18\"],\"symbol\":\"a18\",\"transitions\":[[\"e118\",null,\"e218\"],[\"f18\",null,\"e118\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0045","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s19\",\"m19\",\"f19\",\"e119\",\"e219\",\"d19\"],\"alphabet\":[\"a19\",\"b19\"],\"start_state\":\"s19\",\"final_states\":[\"f19\"],\"transitions\":[[\"s19\",null,\"m19\"],[\"s19\",null,\"d19\"],[\"m19\",\"a19\",\"m19\"],[\"m19\",\"b19\",\"f19\"],[\"f19\",null,\"e119\"],[\"e119\",null,\"e219\"]],\"subset\":[\"s19\",\"m19\",\"d19\"],\"symbol\":\"b19\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d19, m19, s19], b19, [f19], [e119, e219, f19], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d19, m19, s19], b19, [f19], [e119, e219, f19], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127045,"parameters":{"states":["s19","m19","f19","e119","e219","d19"],"alphabet":["a19","b19"],"start_state":"s19","final_states":["f19"],"transitions":[["s19",null,"m19"],["s19",null,"d19"],["m19","a19","m19"],["m19","b19","f19"],["f19",null,"e119"],["e119",null,"e219"]],"subset":["s19","m19","d19"],"symbol":"b19","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a19\",\"b19\"],\"final_states\":[\"f19\"],\"start_state\":\"s19\",\"states\":[\"d19\",\"e119\",\"e219\",\"f19\",\"m19\",\"s19\"],\"subset\":[\"d19\",\"m19\",\"s19\"],\"symbol\":\"b19\",\"transitions\":[[\"e119\",null,\"e219\"],[\"f19\",null,\"e119\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0046","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s20\",\"m20\",\"f20\",\"e120\",\"e220\",\"d20\"],\"alphabet\":[\"a20\",\"b20\"],\"start_state\":\"s20\",\"final_states\":[\"f20\"],\"transitions\":[[\"s20\",null,\"m20\"],[\"s20\",null,\"d20\"],[\"m20\",\"a20\",\"m20\"],[\"m20\",\"b20\",\"f20\"],[\"f20\",null,\"e120\"],[\"e120\",null,\"e220\"]],\"subset\":[\"s20\",\"m20\",\"d20\"],\"symbol\":\"a20\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d20, m20, s20], a20, [m20], [m20], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d20, m20, s20], a20, [m20], [m20], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127046,"parameters":{"states":["s20","m20","f20","e120","e220","d20"],"alphabet":["a20","b20"],"start_state":"s20","final_states":["f20"],"transitions":[["s20",null,"m20"],["s20",null,"d20"],["m20","a20","m20"],["m20","b20","f20"],["f20",null,"e120"],["e120",null,"e220"]],"subset":["s20","m20","d20"],"symbol":"a20","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a20\",\"b20\"],\"final_states\":[\"f20\"],\"start_state\":\"s20\",\"states\":[\"d20\",\"e120\",\"e220\",\"f20\",\"m20\",\"s20\"],\"subset\":[\"d20\",\"m20\",\"s20\"],\"symbol\":\"a20\",\"transitions\":[[\"e120\",null,\"e220\"],[\"f20\",null,\"e120\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0047","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s21\",\"m21\",\"f21\",\"e121\",\"e221\",\"d21\"],\"alphabet\":[\"a21\",\"b21\"],\"start_state\":\"s21\",\"final_states\":[\"f21\"],\"transitions\":[[\"s21\",null,\"m21\"],[\"s21\",null,\"d21\"],[\"m21\",\"a21\",\"m21\"],[\"m21\",\"b21\",\"f21\"],[\"f21\",null,\"e121\"],[\"e121\",null,\"e221\"]],\"subset\":[\"s21\",\"m21\",\"d21\"],\"symbol\":\"b21\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d21, m21, s21], b21, [f21], [e121, e221, f21], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d21, m21, s21], b21, [f21], [e121, e221, f21], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127047,"parameters":{"states":["s21","m21","f21","e121","e221","d21"],"alphabet":["a21","b21"],"start_state":"s21","final_states":["f21"],"transitions":[["s21",null,"m21"],["s21",null,"d21"],["m21","a21","m21"],["m21","b21","f21"],["f21",null,"e121"],["e121",null,"e221"]],"subset":["s21","m21","d21"],"symbol":"b21","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a21\",\"b21\"],\"final_states\":[\"f21\"],\"start_state\":\"s21\",\"states\":[\"d21\",\"e121\",\"e221\",\"f21\",\"m21\",\"s21\"],\"subset\":[\"d21\",\"m21\",\"s21\"],\"symbol\":\"b21\",\"transitions\":[[\"e121\",null,\"e221\"],[\"f21\",null,\"e121\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0048","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s22\",\"m22\",\"f22\",\"e122\",\"e222\",\"d22\"],\"alphabet\":[\"a22\",\"b22\"],\"start_state\":\"s22\",\"final_states\":[\"f22\"],\"transitions\":[[\"s22\",null,\"m22\"],[\"s22\",null,\"d22\"],[\"m22\",\"a22\",\"m22\"],[\"m22\",\"b22\",\"f22\"],[\"f22\",null,\"e122\"],[\"e122\",null,\"e222\"]],\"subset\":[\"s22\",\"m22\",\"d22\"],\"symbol\":\"a22\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d22, m22, s22], a22, [m22], [m22], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d22, m22, s22], a22, [m22], [m22], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127048,"parameters":{"states":["s22","m22","f22","e122","e222","d22"],"alphabet":["a22","b22"],"start_state":"s22","final_states":["f22"],"transitions":[["s22",null,"m22"],["s22",null,"d22"],["m22","a22","m22"],["m22","b22","f22"],["f22",null,"e122"],["e122",null,"e222"]],"subset":["s22","m22","d22"],"symbol":"a22","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a22\",\"b22\"],\"final_states\":[\"f22\"],\"start_state\":\"s22\",\"states\":[\"d22\",\"e122\",\"e222\",\"f22\",\"m22\",\"s22\"],\"subset\":[\"d22\",\"m22\",\"s22\"],\"symbol\":\"a22\",\"transitions\":[[\"e122\",null,\"e222\"],[\"f22\",null,\"e122\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0049","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s23\",\"m23\",\"f23\",\"e123\",\"e223\",\"d23\"],\"alphabet\":[\"a23\",\"b23\"],\"start_state\":\"s23\",\"final_states\":[\"f23\"],\"transitions\":[[\"s23\",null,\"m23\"],[\"s23\",null,\"d23\"],[\"m23\",\"a23\",\"m23\"],[\"m23\",\"b23\",\"f23\"],[\"f23\",null,\"e123\"],[\"e123\",null,\"e223\"]],\"subset\":[\"s23\",\"m23\",\"d23\"],\"symbol\":\"b23\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d23, m23, s23], b23, [f23], [e123, e223, f23], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d23, m23, s23], b23, [f23], [e123, e223, f23], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127049,"parameters":{"states":["s23","m23","f23","e123","e223","d23"],"alphabet":["a23","b23"],"start_state":"s23","final_states":["f23"],"transitions":[["s23",null,"m23"],["s23",null,"d23"],["m23","a23","m23"],["m23","b23","f23"],["f23",null,"e123"],["e123",null,"e223"]],"subset":["s23","m23","d23"],"symbol":"b23","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a23\",\"b23\"],\"final_states\":[\"f23\"],\"start_state\":\"s23\",\"states\":[\"d23\",\"e123\",\"e223\",\"f23\",\"m23\",\"s23\"],\"subset\":[\"d23\",\"m23\",\"s23\"],\"symbol\":\"b23\",\"transitions\":[[\"e123\",null,\"e223\"],[\"f23\",null,\"e123\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0050","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={\"states\":[\"s24\",\"m24\",\"f24\",\"e124\",\"e224\",\"d24\"],\"alphabet\":[\"a24\",\"b24\"],\"start_state\":\"s24\",\"final_states\":[\"f24\"],\"transitions\":[[\"s24\",null,\"m24\"],[\"s24\",null,\"d24\"],[\"m24\",\"a24\",\"m24\"],[\"m24\",\"b24\",\"f24\"],[\"f24\",null,\"e124\"],[\"e124\",null,\"e224\"]],\"subset\":[\"s24\",\"m24\",\"d24\"],\"symbol\":\"a24\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d24, m24, s24], a24, [m24], [m24], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)","explanation_zh":"Wave6第六層核對=([d24, m24, s24], a24, [m24], [m24], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-symbol-transition","seed":202611127050,"parameters":{"states":["s24","m24","f24","e124","e224","d24"],"alphabet":["a24","b24"],"start_state":"s24","final_states":["f24"],"transitions":[["s24",null,"m24"],["s24",null,"d24"],["m24","a24","m24"],["m24","b24","f24"],["f24",null,"e124"],["e124",null,"e224"]],"subset":["s24","m24","d24"],"symbol":"a24","domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-symbol-transition","semantic_template":"qf-mod43-subsetdfa-symbol-transition/{\"alphabet\":[\"a24\",\"b24\"],\"final_states\":[\"f24\"],\"start_state\":\"s24\",\"states\":[\"d24\",\"e124\",\"e224\",\"f24\",\"m24\",\"s24\"],\"subset\":[\"d24\",\"m24\",\"s24\"],\"symbol\":\"a24\",\"transitions\":[[\"e124\",null,\"e224\"],[\"f24\",null,\"e124\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0051","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s0\",\"m0\",\"f0\",\"e10\",\"e20\",\"d0\"],\"alphabet\":[\"a0\",\"b0\"],\"start_state\":\"s0\",\"final_states\":[\"f0\"],\"transitions\":[[\"s0\",null,\"m0\"],[\"s0\",null,\"d0\"],[\"m0\",\"a0\",\"m0\"],[\"m0\",\"b0\",\"f0\"],[\"f0\",null,\"e10\"],[\"e10\",null,\"e20\"]],\"subset\":[\"f0\",\"m0\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f0, m0], [f0], [f0], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f0, m0], [f0], [f0], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127051,"parameters":{"states":["s0","m0","f0","e10","e20","d0"],"alphabet":["a0","b0"],"start_state":"s0","final_states":["f0"],"transitions":[["s0",null,"m0"],["s0",null,"d0"],["m0","a0","m0"],["m0","b0","f0"],["f0",null,"e10"],["e10",null,"e20"]],"subset":["f0","m0"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a0\",\"b0\"],\"final_states\":[\"f0\"],\"start_state\":\"s0\",\"states\":[\"d0\",\"e10\",\"e20\",\"f0\",\"m0\",\"s0\"],\"subset\":[\"f0\",\"m0\"],\"transitions\":[[\"e10\",null,\"e20\"],[\"f0\",null,\"e10\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0052","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s1\",\"m1\",\"f1\",\"e11\",\"e21\",\"d1\"],\"alphabet\":[\"a1\",\"b1\"],\"start_state\":\"s1\",\"final_states\":[\"f1\"],\"transitions\":[[\"s1\",null,\"m1\"],[\"s1\",null,\"d1\"],[\"m1\",\"a1\",\"m1\"],[\"m1\",\"b1\",\"f1\"],[\"f1\",null,\"e11\"],[\"e11\",null,\"e21\"]],\"subset\":[\"m1\",\"d1\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d1, m1], [f1], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([d1, m1], [f1], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127052,"parameters":{"states":["s1","m1","f1","e11","e21","d1"],"alphabet":["a1","b1"],"start_state":"s1","final_states":["f1"],"transitions":[["s1",null,"m1"],["s1",null,"d1"],["m1","a1","m1"],["m1","b1","f1"],["f1",null,"e11"],["e11",null,"e21"]],"subset":["m1","d1"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a1\",\"b1\"],\"final_states\":[\"f1\"],\"start_state\":\"s1\",\"states\":[\"d1\",\"e11\",\"e21\",\"f1\",\"m1\",\"s1\"],\"subset\":[\"d1\",\"m1\"],\"transitions\":[[\"e11\",null,\"e21\"],[\"f1\",null,\"e11\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0053","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s2\",\"m2\",\"f2\",\"e12\",\"e22\",\"d2\"],\"alphabet\":[\"a2\",\"b2\"],\"start_state\":\"s2\",\"final_states\":[\"f2\"],\"transitions\":[[\"s2\",null,\"m2\"],[\"s2\",null,\"d2\"],[\"m2\",\"a2\",\"m2\"],[\"m2\",\"b2\",\"f2\"],[\"f2\",null,\"e12\"],[\"e12\",null,\"e22\"]],\"subset\":[\"f2\",\"m2\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f2, m2], [f2], [f2], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f2, m2], [f2], [f2], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127053,"parameters":{"states":["s2","m2","f2","e12","e22","d2"],"alphabet":["a2","b2"],"start_state":"s2","final_states":["f2"],"transitions":[["s2",null,"m2"],["s2",null,"d2"],["m2","a2","m2"],["m2","b2","f2"],["f2",null,"e12"],["e12",null,"e22"]],"subset":["f2","m2"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a2\",\"b2\"],\"final_states\":[\"f2\"],\"start_state\":\"s2\",\"states\":[\"d2\",\"e12\",\"e22\",\"f2\",\"m2\",\"s2\"],\"subset\":[\"f2\",\"m2\"],\"transitions\":[[\"e12\",null,\"e22\"],[\"f2\",null,\"e12\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0054","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s3\",\"m3\",\"f3\",\"e13\",\"e23\",\"d3\"],\"alphabet\":[\"a3\",\"b3\"],\"start_state\":\"s3\",\"final_states\":[\"f3\"],\"transitions\":[[\"s3\",null,\"m3\"],[\"s3\",null,\"d3\"],[\"m3\",\"a3\",\"m3\"],[\"m3\",\"b3\",\"f3\"],[\"f3\",null,\"e13\"],[\"e13\",null,\"e23\"]],\"subset\":[\"m3\",\"d3\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d3, m3], [f3], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([d3, m3], [f3], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127054,"parameters":{"states":["s3","m3","f3","e13","e23","d3"],"alphabet":["a3","b3"],"start_state":"s3","final_states":["f3"],"transitions":[["s3",null,"m3"],["s3",null,"d3"],["m3","a3","m3"],["m3","b3","f3"],["f3",null,"e13"],["e13",null,"e23"]],"subset":["m3","d3"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a3\",\"b3\"],\"final_states\":[\"f3\"],\"start_state\":\"s3\",\"states\":[\"d3\",\"e13\",\"e23\",\"f3\",\"m3\",\"s3\"],\"subset\":[\"d3\",\"m3\"],\"transitions\":[[\"e13\",null,\"e23\"],[\"f3\",null,\"e13\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0055","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s4\",\"m4\",\"f4\",\"e14\",\"e24\",\"d4\"],\"alphabet\":[\"a4\",\"b4\"],\"start_state\":\"s4\",\"final_states\":[\"f4\"],\"transitions\":[[\"s4\",null,\"m4\"],[\"s4\",null,\"d4\"],[\"m4\",\"a4\",\"m4\"],[\"m4\",\"b4\",\"f4\"],[\"f4\",null,\"e14\"],[\"e14\",null,\"e24\"]],\"subset\":[\"f4\",\"m4\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f4, m4], [f4], [f4], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f4, m4], [f4], [f4], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127055,"parameters":{"states":["s4","m4","f4","e14","e24","d4"],"alphabet":["a4","b4"],"start_state":"s4","final_states":["f4"],"transitions":[["s4",null,"m4"],["s4",null,"d4"],["m4","a4","m4"],["m4","b4","f4"],["f4",null,"e14"],["e14",null,"e24"]],"subset":["f4","m4"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a4\",\"b4\"],\"final_states\":[\"f4\"],\"start_state\":\"s4\",\"states\":[\"d4\",\"e14\",\"e24\",\"f4\",\"m4\",\"s4\"],\"subset\":[\"f4\",\"m4\"],\"transitions\":[[\"e14\",null,\"e24\"],[\"f4\",null,\"e14\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0056","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s5\",\"m5\",\"f5\",\"e15\",\"e25\",\"d5\"],\"alphabet\":[\"a5\",\"b5\"],\"start_state\":\"s5\",\"final_states\":[\"f5\"],\"transitions\":[[\"s5\",null,\"m5\"],[\"s5\",null,\"d5\"],[\"m5\",\"a5\",\"m5\"],[\"m5\",\"b5\",\"f5\"],[\"f5\",null,\"e15\"],[\"e15\",null,\"e25\"]],\"subset\":[\"m5\",\"d5\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d5, m5], [f5], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([d5, m5], [f5], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127056,"parameters":{"states":["s5","m5","f5","e15","e25","d5"],"alphabet":["a5","b5"],"start_state":"s5","final_states":["f5"],"transitions":[["s5",null,"m5"],["s5",null,"d5"],["m5","a5","m5"],["m5","b5","f5"],["f5",null,"e15"],["e15",null,"e25"]],"subset":["m5","d5"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a5\",\"b5\"],\"final_states\":[\"f5\"],\"start_state\":\"s5\",\"states\":[\"d5\",\"e15\",\"e25\",\"f5\",\"m5\",\"s5\"],\"subset\":[\"d5\",\"m5\"],\"transitions\":[[\"e15\",null,\"e25\"],[\"f5\",null,\"e15\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0057","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s6\",\"m6\",\"f6\",\"e16\",\"e26\",\"d6\"],\"alphabet\":[\"a6\",\"b6\"],\"start_state\":\"s6\",\"final_states\":[\"f6\"],\"transitions\":[[\"s6\",null,\"m6\"],[\"s6\",null,\"d6\"],[\"m6\",\"a6\",\"m6\"],[\"m6\",\"b6\",\"f6\"],[\"f6\",null,\"e16\"],[\"e16\",null,\"e26\"]],\"subset\":[\"f6\",\"m6\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f6, m6], [f6], [f6], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f6, m6], [f6], [f6], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127057,"parameters":{"states":["s6","m6","f6","e16","e26","d6"],"alphabet":["a6","b6"],"start_state":"s6","final_states":["f6"],"transitions":[["s6",null,"m6"],["s6",null,"d6"],["m6","a6","m6"],["m6","b6","f6"],["f6",null,"e16"],["e16",null,"e26"]],"subset":["f6","m6"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a6\",\"b6\"],\"final_states\":[\"f6\"],\"start_state\":\"s6\",\"states\":[\"d6\",\"e16\",\"e26\",\"f6\",\"m6\",\"s6\"],\"subset\":[\"f6\",\"m6\"],\"transitions\":[[\"e16\",null,\"e26\"],[\"f6\",null,\"e16\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0058","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s7\",\"m7\",\"f7\",\"e17\",\"e27\",\"d7\"],\"alphabet\":[\"a7\",\"b7\"],\"start_state\":\"s7\",\"final_states\":[\"f7\"],\"transitions\":[[\"s7\",null,\"m7\"],[\"s7\",null,\"d7\"],[\"m7\",\"a7\",\"m7\"],[\"m7\",\"b7\",\"f7\"],[\"f7\",null,\"e17\"],[\"e17\",null,\"e27\"]],\"subset\":[\"m7\",\"d7\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d7, m7], [f7], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([d7, m7], [f7], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127058,"parameters":{"states":["s7","m7","f7","e17","e27","d7"],"alphabet":["a7","b7"],"start_state":"s7","final_states":["f7"],"transitions":[["s7",null,"m7"],["s7",null,"d7"],["m7","a7","m7"],["m7","b7","f7"],["f7",null,"e17"],["e17",null,"e27"]],"subset":["m7","d7"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a7\",\"b7\"],\"final_states\":[\"f7\"],\"start_state\":\"s7\",\"states\":[\"d7\",\"e17\",\"e27\",\"f7\",\"m7\",\"s7\"],\"subset\":[\"d7\",\"m7\"],\"transitions\":[[\"e17\",null,\"e27\"],[\"f7\",null,\"e17\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0059","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s8\",\"m8\",\"f8\",\"e18\",\"e28\",\"d8\"],\"alphabet\":[\"a8\",\"b8\"],\"start_state\":\"s8\",\"final_states\":[\"f8\"],\"transitions\":[[\"s8\",null,\"m8\"],[\"s8\",null,\"d8\"],[\"m8\",\"a8\",\"m8\"],[\"m8\",\"b8\",\"f8\"],[\"f8\",null,\"e18\"],[\"e18\",null,\"e28\"]],\"subset\":[\"f8\",\"m8\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f8, m8], [f8], [f8], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f8, m8], [f8], [f8], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127059,"parameters":{"states":["s8","m8","f8","e18","e28","d8"],"alphabet":["a8","b8"],"start_state":"s8","final_states":["f8"],"transitions":[["s8",null,"m8"],["s8",null,"d8"],["m8","a8","m8"],["m8","b8","f8"],["f8",null,"e18"],["e18",null,"e28"]],"subset":["f8","m8"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a8\",\"b8\"],\"final_states\":[\"f8\"],\"start_state\":\"s8\",\"states\":[\"d8\",\"e18\",\"e28\",\"f8\",\"m8\",\"s8\"],\"subset\":[\"f8\",\"m8\"],\"transitions\":[[\"e18\",null,\"e28\"],[\"f8\",null,\"e18\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0060","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s9\",\"m9\",\"f9\",\"e19\",\"e29\",\"d9\"],\"alphabet\":[\"a9\",\"b9\"],\"start_state\":\"s9\",\"final_states\":[\"f9\"],\"transitions\":[[\"s9\",null,\"m9\"],[\"s9\",null,\"d9\"],[\"m9\",\"a9\",\"m9\"],[\"m9\",\"b9\",\"f9\"],[\"f9\",null,\"e19\"],[\"e19\",null,\"e29\"]],\"subset\":[\"m9\",\"d9\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d9, m9], [f9], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([d9, m9], [f9], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127060,"parameters":{"states":["s9","m9","f9","e19","e29","d9"],"alphabet":["a9","b9"],"start_state":"s9","final_states":["f9"],"transitions":[["s9",null,"m9"],["s9",null,"d9"],["m9","a9","m9"],["m9","b9","f9"],["f9",null,"e19"],["e19",null,"e29"]],"subset":["m9","d9"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a9\",\"b9\"],\"final_states\":[\"f9\"],\"start_state\":\"s9\",\"states\":[\"d9\",\"e19\",\"e29\",\"f9\",\"m9\",\"s9\"],\"subset\":[\"d9\",\"m9\"],\"transitions\":[[\"e19\",null,\"e29\"],[\"f9\",null,\"e19\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0061","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s10\",\"m10\",\"f10\",\"e110\",\"e210\",\"d10\"],\"alphabet\":[\"a10\",\"b10\"],\"start_state\":\"s10\",\"final_states\":[\"f10\"],\"transitions\":[[\"s10\",null,\"m10\"],[\"s10\",null,\"d10\"],[\"m10\",\"a10\",\"m10\"],[\"m10\",\"b10\",\"f10\"],[\"f10\",null,\"e110\"],[\"e110\",null,\"e210\"]],\"subset\":[\"f10\",\"m10\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f10, m10], [f10], [f10], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f10, m10], [f10], [f10], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127061,"parameters":{"states":["s10","m10","f10","e110","e210","d10"],"alphabet":["a10","b10"],"start_state":"s10","final_states":["f10"],"transitions":[["s10",null,"m10"],["s10",null,"d10"],["m10","a10","m10"],["m10","b10","f10"],["f10",null,"e110"],["e110",null,"e210"]],"subset":["f10","m10"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a10\",\"b10\"],\"final_states\":[\"f10\"],\"start_state\":\"s10\",\"states\":[\"d10\",\"e110\",\"e210\",\"f10\",\"m10\",\"s10\"],\"subset\":[\"f10\",\"m10\"],\"transitions\":[[\"e110\",null,\"e210\"],[\"f10\",null,\"e110\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0062","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s11\",\"m11\",\"f11\",\"e111\",\"e211\",\"d11\"],\"alphabet\":[\"a11\",\"b11\"],\"start_state\":\"s11\",\"final_states\":[\"f11\"],\"transitions\":[[\"s11\",null,\"m11\"],[\"s11\",null,\"d11\"],[\"m11\",\"a11\",\"m11\"],[\"m11\",\"b11\",\"f11\"],[\"f11\",null,\"e111\"],[\"e111\",null,\"e211\"]],\"subset\":[\"m11\",\"d11\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d11, m11], [f11], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([d11, m11], [f11], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127062,"parameters":{"states":["s11","m11","f11","e111","e211","d11"],"alphabet":["a11","b11"],"start_state":"s11","final_states":["f11"],"transitions":[["s11",null,"m11"],["s11",null,"d11"],["m11","a11","m11"],["m11","b11","f11"],["f11",null,"e111"],["e111",null,"e211"]],"subset":["m11","d11"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a11\",\"b11\"],\"final_states\":[\"f11\"],\"start_state\":\"s11\",\"states\":[\"d11\",\"e111\",\"e211\",\"f11\",\"m11\",\"s11\"],\"subset\":[\"d11\",\"m11\"],\"transitions\":[[\"e111\",null,\"e211\"],[\"f11\",null,\"e111\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0063","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s12\",\"m12\",\"f12\",\"e112\",\"e212\",\"d12\"],\"alphabet\":[\"a12\",\"b12\"],\"start_state\":\"s12\",\"final_states\":[\"f12\"],\"transitions\":[[\"s12\",null,\"m12\"],[\"s12\",null,\"d12\"],[\"m12\",\"a12\",\"m12\"],[\"m12\",\"b12\",\"f12\"],[\"f12\",null,\"e112\"],[\"e112\",null,\"e212\"]],\"subset\":[\"f12\",\"m12\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f12, m12], [f12], [f12], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f12, m12], [f12], [f12], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127063,"parameters":{"states":["s12","m12","f12","e112","e212","d12"],"alphabet":["a12","b12"],"start_state":"s12","final_states":["f12"],"transitions":[["s12",null,"m12"],["s12",null,"d12"],["m12","a12","m12"],["m12","b12","f12"],["f12",null,"e112"],["e112",null,"e212"]],"subset":["f12","m12"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a12\",\"b12\"],\"final_states\":[\"f12\"],\"start_state\":\"s12\",\"states\":[\"d12\",\"e112\",\"e212\",\"f12\",\"m12\",\"s12\"],\"subset\":[\"f12\",\"m12\"],\"transitions\":[[\"e112\",null,\"e212\"],[\"f12\",null,\"e112\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0064","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s13\",\"m13\",\"f13\",\"e113\",\"e213\",\"d13\"],\"alphabet\":[\"a13\",\"b13\"],\"start_state\":\"s13\",\"final_states\":[\"f13\"],\"transitions\":[[\"s13\",null,\"m13\"],[\"s13\",null,\"d13\"],[\"m13\",\"a13\",\"m13\"],[\"m13\",\"b13\",\"f13\"],[\"f13\",null,\"e113\"],[\"e113\",null,\"e213\"]],\"subset\":[\"m13\",\"d13\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d13, m13], [f13], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([d13, m13], [f13], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127064,"parameters":{"states":["s13","m13","f13","e113","e213","d13"],"alphabet":["a13","b13"],"start_state":"s13","final_states":["f13"],"transitions":[["s13",null,"m13"],["s13",null,"d13"],["m13","a13","m13"],["m13","b13","f13"],["f13",null,"e113"],["e113",null,"e213"]],"subset":["m13","d13"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a13\",\"b13\"],\"final_states\":[\"f13\"],\"start_state\":\"s13\",\"states\":[\"d13\",\"e113\",\"e213\",\"f13\",\"m13\",\"s13\"],\"subset\":[\"d13\",\"m13\"],\"transitions\":[[\"e113\",null,\"e213\"],[\"f13\",null,\"e113\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0065","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s14\",\"m14\",\"f14\",\"e114\",\"e214\",\"d14\"],\"alphabet\":[\"a14\",\"b14\"],\"start_state\":\"s14\",\"final_states\":[\"f14\"],\"transitions\":[[\"s14\",null,\"m14\"],[\"s14\",null,\"d14\"],[\"m14\",\"a14\",\"m14\"],[\"m14\",\"b14\",\"f14\"],[\"f14\",null,\"e114\"],[\"e114\",null,\"e214\"]],\"subset\":[\"f14\",\"m14\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f14, m14], [f14], [f14], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f14, m14], [f14], [f14], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127065,"parameters":{"states":["s14","m14","f14","e114","e214","d14"],"alphabet":["a14","b14"],"start_state":"s14","final_states":["f14"],"transitions":[["s14",null,"m14"],["s14",null,"d14"],["m14","a14","m14"],["m14","b14","f14"],["f14",null,"e114"],["e114",null,"e214"]],"subset":["f14","m14"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a14\",\"b14\"],\"final_states\":[\"f14\"],\"start_state\":\"s14\",\"states\":[\"d14\",\"e114\",\"e214\",\"f14\",\"m14\",\"s14\"],\"subset\":[\"f14\",\"m14\"],\"transitions\":[[\"e114\",null,\"e214\"],[\"f14\",null,\"e114\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0066","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s15\",\"m15\",\"f15\",\"e115\",\"e215\",\"d15\"],\"alphabet\":[\"a15\",\"b15\"],\"start_state\":\"s15\",\"final_states\":[\"f15\"],\"transitions\":[[\"s15\",null,\"m15\"],[\"s15\",null,\"d15\"],[\"m15\",\"a15\",\"m15\"],[\"m15\",\"b15\",\"f15\"],[\"f15\",null,\"e115\"],[\"e115\",null,\"e215\"]],\"subset\":[\"m15\",\"d15\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d15, m15], [f15], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([d15, m15], [f15], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127066,"parameters":{"states":["s15","m15","f15","e115","e215","d15"],"alphabet":["a15","b15"],"start_state":"s15","final_states":["f15"],"transitions":[["s15",null,"m15"],["s15",null,"d15"],["m15","a15","m15"],["m15","b15","f15"],["f15",null,"e115"],["e115",null,"e215"]],"subset":["m15","d15"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a15\",\"b15\"],\"final_states\":[\"f15\"],\"start_state\":\"s15\",\"states\":[\"d15\",\"e115\",\"e215\",\"f15\",\"m15\",\"s15\"],\"subset\":[\"d15\",\"m15\"],\"transitions\":[[\"e115\",null,\"e215\"],[\"f15\",null,\"e115\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0067","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s16\",\"m16\",\"f16\",\"e116\",\"e216\",\"d16\"],\"alphabet\":[\"a16\",\"b16\"],\"start_state\":\"s16\",\"final_states\":[\"f16\"],\"transitions\":[[\"s16\",null,\"m16\"],[\"s16\",null,\"d16\"],[\"m16\",\"a16\",\"m16\"],[\"m16\",\"b16\",\"f16\"],[\"f16\",null,\"e116\"],[\"e116\",null,\"e216\"]],\"subset\":[\"f16\",\"m16\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f16, m16], [f16], [f16], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f16, m16], [f16], [f16], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127067,"parameters":{"states":["s16","m16","f16","e116","e216","d16"],"alphabet":["a16","b16"],"start_state":"s16","final_states":["f16"],"transitions":[["s16",null,"m16"],["s16",null,"d16"],["m16","a16","m16"],["m16","b16","f16"],["f16",null,"e116"],["e116",null,"e216"]],"subset":["f16","m16"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a16\",\"b16\"],\"final_states\":[\"f16\"],\"start_state\":\"s16\",\"states\":[\"d16\",\"e116\",\"e216\",\"f16\",\"m16\",\"s16\"],\"subset\":[\"f16\",\"m16\"],\"transitions\":[[\"e116\",null,\"e216\"],[\"f16\",null,\"e116\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0068","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s17\",\"m17\",\"f17\",\"e117\",\"e217\",\"d17\"],\"alphabet\":[\"a17\",\"b17\"],\"start_state\":\"s17\",\"final_states\":[\"f17\"],\"transitions\":[[\"s17\",null,\"m17\"],[\"s17\",null,\"d17\"],[\"m17\",\"a17\",\"m17\"],[\"m17\",\"b17\",\"f17\"],[\"f17\",null,\"e117\"],[\"e117\",null,\"e217\"]],\"subset\":[\"m17\",\"d17\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d17, m17], [f17], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([d17, m17], [f17], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127068,"parameters":{"states":["s17","m17","f17","e117","e217","d17"],"alphabet":["a17","b17"],"start_state":"s17","final_states":["f17"],"transitions":[["s17",null,"m17"],["s17",null,"d17"],["m17","a17","m17"],["m17","b17","f17"],["f17",null,"e117"],["e117",null,"e217"]],"subset":["m17","d17"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a17\",\"b17\"],\"final_states\":[\"f17\"],\"start_state\":\"s17\",\"states\":[\"d17\",\"e117\",\"e217\",\"f17\",\"m17\",\"s17\"],\"subset\":[\"d17\",\"m17\"],\"transitions\":[[\"e117\",null,\"e217\"],[\"f17\",null,\"e117\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0069","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s18\",\"m18\",\"f18\",\"e118\",\"e218\",\"d18\"],\"alphabet\":[\"a18\",\"b18\"],\"start_state\":\"s18\",\"final_states\":[\"f18\"],\"transitions\":[[\"s18\",null,\"m18\"],[\"s18\",null,\"d18\"],[\"m18\",\"a18\",\"m18\"],[\"m18\",\"b18\",\"f18\"],[\"f18\",null,\"e118\"],[\"e118\",null,\"e218\"]],\"subset\":[\"f18\",\"m18\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f18, m18], [f18], [f18], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f18, m18], [f18], [f18], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127069,"parameters":{"states":["s18","m18","f18","e118","e218","d18"],"alphabet":["a18","b18"],"start_state":"s18","final_states":["f18"],"transitions":[["s18",null,"m18"],["s18",null,"d18"],["m18","a18","m18"],["m18","b18","f18"],["f18",null,"e118"],["e118",null,"e218"]],"subset":["f18","m18"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a18\",\"b18\"],\"final_states\":[\"f18\"],\"start_state\":\"s18\",\"states\":[\"d18\",\"e118\",\"e218\",\"f18\",\"m18\",\"s18\"],\"subset\":[\"f18\",\"m18\"],\"transitions\":[[\"e118\",null,\"e218\"],[\"f18\",null,\"e118\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0070","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s19\",\"m19\",\"f19\",\"e119\",\"e219\",\"d19\"],\"alphabet\":[\"a19\",\"b19\"],\"start_state\":\"s19\",\"final_states\":[\"f19\"],\"transitions\":[[\"s19\",null,\"m19\"],[\"s19\",null,\"d19\"],[\"m19\",\"a19\",\"m19\"],[\"m19\",\"b19\",\"f19\"],[\"f19\",null,\"e119\"],[\"e119\",null,\"e219\"]],\"subset\":[\"m19\",\"d19\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d19, m19], [f19], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([d19, m19], [f19], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127070,"parameters":{"states":["s19","m19","f19","e119","e219","d19"],"alphabet":["a19","b19"],"start_state":"s19","final_states":["f19"],"transitions":[["s19",null,"m19"],["s19",null,"d19"],["m19","a19","m19"],["m19","b19","f19"],["f19",null,"e119"],["e119",null,"e219"]],"subset":["m19","d19"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a19\",\"b19\"],\"final_states\":[\"f19\"],\"start_state\":\"s19\",\"states\":[\"d19\",\"e119\",\"e219\",\"f19\",\"m19\",\"s19\"],\"subset\":[\"d19\",\"m19\"],\"transitions\":[[\"e119\",null,\"e219\"],[\"f19\",null,\"e119\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0071","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s20\",\"m20\",\"f20\",\"e120\",\"e220\",\"d20\"],\"alphabet\":[\"a20\",\"b20\"],\"start_state\":\"s20\",\"final_states\":[\"f20\"],\"transitions\":[[\"s20\",null,\"m20\"],[\"s20\",null,\"d20\"],[\"m20\",\"a20\",\"m20\"],[\"m20\",\"b20\",\"f20\"],[\"f20\",null,\"e120\"],[\"e120\",null,\"e220\"]],\"subset\":[\"f20\",\"m20\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f20, m20], [f20], [f20], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f20, m20], [f20], [f20], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127071,"parameters":{"states":["s20","m20","f20","e120","e220","d20"],"alphabet":["a20","b20"],"start_state":"s20","final_states":["f20"],"transitions":[["s20",null,"m20"],["s20",null,"d20"],["m20","a20","m20"],["m20","b20","f20"],["f20",null,"e120"],["e120",null,"e220"]],"subset":["f20","m20"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a20\",\"b20\"],\"final_states\":[\"f20\"],\"start_state\":\"s20\",\"states\":[\"d20\",\"e120\",\"e220\",\"f20\",\"m20\",\"s20\"],\"subset\":[\"f20\",\"m20\"],\"transitions\":[[\"e120\",null,\"e220\"],[\"f20\",null,\"e120\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0072","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s21\",\"m21\",\"f21\",\"e121\",\"e221\",\"d21\"],\"alphabet\":[\"a21\",\"b21\"],\"start_state\":\"s21\",\"final_states\":[\"f21\"],\"transitions\":[[\"s21\",null,\"m21\"],[\"s21\",null,\"d21\"],[\"m21\",\"a21\",\"m21\"],[\"m21\",\"b21\",\"f21\"],[\"f21\",null,\"e121\"],[\"e121\",null,\"e221\"]],\"subset\":[\"m21\",\"d21\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d21, m21], [f21], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([d21, m21], [f21], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127072,"parameters":{"states":["s21","m21","f21","e121","e221","d21"],"alphabet":["a21","b21"],"start_state":"s21","final_states":["f21"],"transitions":[["s21",null,"m21"],["s21",null,"d21"],["m21","a21","m21"],["m21","b21","f21"],["f21",null,"e121"],["e121",null,"e221"]],"subset":["m21","d21"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a21\",\"b21\"],\"final_states\":[\"f21\"],\"start_state\":\"s21\",\"states\":[\"d21\",\"e121\",\"e221\",\"f21\",\"m21\",\"s21\"],\"subset\":[\"d21\",\"m21\"],\"transitions\":[[\"e121\",null,\"e221\"],[\"f21\",null,\"e121\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0073","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s22\",\"m22\",\"f22\",\"e122\",\"e222\",\"d22\"],\"alphabet\":[\"a22\",\"b22\"],\"start_state\":\"s22\",\"final_states\":[\"f22\"],\"transitions\":[[\"s22\",null,\"m22\"],[\"s22\",null,\"d22\"],[\"m22\",\"a22\",\"m22\"],[\"m22\",\"b22\",\"f22\"],[\"f22\",null,\"e122\"],[\"e122\",null,\"e222\"]],\"subset\":[\"f22\",\"m22\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f22, m22], [f22], [f22], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f22, m22], [f22], [f22], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127073,"parameters":{"states":["s22","m22","f22","e122","e222","d22"],"alphabet":["a22","b22"],"start_state":"s22","final_states":["f22"],"transitions":[["s22",null,"m22"],["s22",null,"d22"],["m22","a22","m22"],["m22","b22","f22"],["f22",null,"e122"],["e122",null,"e222"]],"subset":["f22","m22"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a22\",\"b22\"],\"final_states\":[\"f22\"],\"start_state\":\"s22\",\"states\":[\"d22\",\"e122\",\"e222\",\"f22\",\"m22\",\"s22\"],\"subset\":[\"f22\",\"m22\"],\"transitions\":[[\"e122\",null,\"e222\"],[\"f22\",null,\"e122\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0074","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s23\",\"m23\",\"f23\",\"e123\",\"e223\",\"d23\"],\"alphabet\":[\"a23\",\"b23\"],\"start_state\":\"s23\",\"final_states\":[\"f23\"],\"transitions\":[[\"s23\",null,\"m23\"],[\"s23\",null,\"d23\"],[\"m23\",\"a23\",\"m23\"],[\"m23\",\"b23\",\"f23\"],[\"f23\",null,\"e123\"],[\"e123\",null,\"e223\"]],\"subset\":[\"m23\",\"d23\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([d23, m23], [f23], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([d23, m23], [f23], [], 否, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127074,"parameters":{"states":["s23","m23","f23","e123","e223","d23"],"alphabet":["a23","b23"],"start_state":"s23","final_states":["f23"],"transitions":[["s23",null,"m23"],["s23",null,"d23"],["m23","a23","m23"],["m23","b23","f23"],["f23",null,"e123"],["e123",null,"e223"]],"subset":["m23","d23"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a23\",\"b23\"],\"final_states\":[\"f23\"],\"start_state\":\"s23\",\"states\":[\"d23\",\"e123\",\"e223\",\"f23\",\"m23\",\"s23\"],\"subset\":[\"d23\",\"m23\"],\"transitions\":[[\"e123\",null,\"e223\"],[\"f23\",null,\"e123\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0075","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={\"states\":[\"s24\",\"m24\",\"f24\",\"e124\",\"e224\",\"d24\"],\"alphabet\":[\"a24\",\"b24\"],\"start_state\":\"s24\",\"final_states\":[\"f24\"],\"transitions\":[[\"s24\",null,\"m24\"],[\"s24\",null,\"d24\"],[\"m24\",\"a24\",\"m24\"],[\"m24\",\"b24\",\"f24\"],[\"f24\",null,\"e124\"],[\"e124\",null,\"e224\"]],\"subset\":[\"f24\",\"m24\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([f24, m24], [f24], [f24], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)","explanation_zh":"Wave6第六層核對=([f24, m24], [f24], [f24], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-accepting-subset","seed":202611127075,"parameters":{"states":["s24","m24","f24","e124","e224","d24"],"alphabet":["a24","b24"],"start_state":"s24","final_states":["f24"],"transitions":[["s24",null,"m24"],["s24",null,"d24"],["m24","a24","m24"],["m24","b24","f24"],["f24",null,"e124"],["e124",null,"e224"]],"subset":["f24","m24"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-accepting-subset","semantic_template":"qf-mod43-subsetdfa-accepting-subset/{\"alphabet\":[\"a24\",\"b24\"],\"final_states\":[\"f24\"],\"start_state\":\"s24\",\"states\":[\"d24\",\"e124\",\"e224\",\"f24\",\"m24\",\"s24\"],\"subset\":[\"f24\",\"m24\"],\"transitions\":[[\"e124\",null,\"e224\"],[\"f24\",null,\"e124\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0076","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s0\",\"m0\",\"f0\",\"e10\",\"e20\",\"d0\"],\"alphabet\":[\"a0\",\"b0\"],\"start_state\":\"s0\",\"final_states\":[\"f0\"],\"transitions\":[[\"s0\",null,\"m0\"],[\"s0\",null,\"d0\"],[\"m0\",\"a0\",\"m0\"],[\"m0\",\"b0\",\"f0\"],[\"f0\",null,\"e10\"],[\"e10\",null,\"e20\"]],\"input\":[\"b0\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b0], [[d0, m0, s0], [e10, e20, f0]], [[d0, m0, s0], [e10, e20, f0]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([b0], [[d0, m0, s0], [e10, e20, f0]], [[d0, m0, s0], [e10, e20, f0]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127076,"parameters":{"states":["s0","m0","f0","e10","e20","d0"],"alphabet":["a0","b0"],"start_state":"s0","final_states":["f0"],"transitions":[["s0",null,"m0"],["s0",null,"d0"],["m0","a0","m0"],["m0","b0","f0"],["f0",null,"e10"],["e10",null,"e20"]],"input":["b0"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a0\",\"b0\"],\"final_states\":[\"f0\"],\"input\":[\"b0\"],\"start_state\":\"s0\",\"states\":[\"d0\",\"e10\",\"e20\",\"f0\",\"m0\",\"s0\"],\"transitions\":[[\"e10\",null,\"e20\"],[\"f0\",null,\"e10\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0077","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s1\",\"m1\",\"f1\",\"e11\",\"e21\",\"d1\"],\"alphabet\":[\"a1\",\"b1\"],\"start_state\":\"s1\",\"final_states\":[\"f1\"],\"transitions\":[[\"s1\",null,\"m1\"],[\"s1\",null,\"d1\"],[\"m1\",\"a1\",\"m1\"],[\"m1\",\"b1\",\"f1\"],[\"f1\",null,\"e11\"],[\"e11\",null,\"e21\"]],\"input\":[\"a1\",\"b1\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a1, b1], [[d1, m1, s1], [m1], [e11, e21, f1]], [[d1, m1, s1], [m1], [e11, e21, f1]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a1, b1], [[d1, m1, s1], [m1], [e11, e21, f1]], [[d1, m1, s1], [m1], [e11, e21, f1]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127077,"parameters":{"states":["s1","m1","f1","e11","e21","d1"],"alphabet":["a1","b1"],"start_state":"s1","final_states":["f1"],"transitions":[["s1",null,"m1"],["s1",null,"d1"],["m1","a1","m1"],["m1","b1","f1"],["f1",null,"e11"],["e11",null,"e21"]],"input":["a1","b1"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a1\",\"b1\"],\"final_states\":[\"f1\"],\"input\":[\"a1\",\"b1\"],\"start_state\":\"s1\",\"states\":[\"d1\",\"e11\",\"e21\",\"f1\",\"m1\",\"s1\"],\"transitions\":[[\"e11\",null,\"e21\"],[\"f1\",null,\"e11\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0078","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s2\",\"m2\",\"f2\",\"e12\",\"e22\",\"d2\"],\"alphabet\":[\"a2\",\"b2\"],\"start_state\":\"s2\",\"final_states\":[\"f2\"],\"transitions\":[[\"s2\",null,\"m2\"],[\"s2\",null,\"d2\"],[\"m2\",\"a2\",\"m2\"],[\"m2\",\"b2\",\"f2\"],[\"f2\",null,\"e12\"],[\"e12\",null,\"e22\"]],\"input\":[\"a2\",\"a2\",\"b2\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a2, a2, b2], [[d2, m2, s2], [m2], [m2], [e12, e22, f2]], [[d2, m2, s2], [m2], [m2], [e12, e22, f2]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a2, a2, b2], [[d2, m2, s2], [m2], [m2], [e12, e22, f2]], [[d2, m2, s2], [m2], [m2], [e12, e22, f2]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127078,"parameters":{"states":["s2","m2","f2","e12","e22","d2"],"alphabet":["a2","b2"],"start_state":"s2","final_states":["f2"],"transitions":[["s2",null,"m2"],["s2",null,"d2"],["m2","a2","m2"],["m2","b2","f2"],["f2",null,"e12"],["e12",null,"e22"]],"input":["a2","a2","b2"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a2\",\"b2\"],\"final_states\":[\"f2\"],\"input\":[\"a2\",\"a2\",\"b2\"],\"start_state\":\"s2\",\"states\":[\"d2\",\"e12\",\"e22\",\"f2\",\"m2\",\"s2\"],\"transitions\":[[\"e12\",null,\"e22\"],[\"f2\",null,\"e12\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0079","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s3\",\"m3\",\"f3\",\"e13\",\"e23\",\"d3\"],\"alphabet\":[\"a3\",\"b3\"],\"start_state\":\"s3\",\"final_states\":[\"f3\"],\"transitions\":[[\"s3\",null,\"m3\"],[\"s3\",null,\"d3\"],[\"m3\",\"a3\",\"m3\"],[\"m3\",\"b3\",\"f3\"],[\"f3\",null,\"e13\"],[\"e13\",null,\"e23\"]],\"input\":[\"a3\",\"a3\",\"a3\",\"b3\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a3, a3, a3, b3], [[d3, m3, s3], [m3], [m3], [m3], [e13, e23, f3]], [[d3, m3, s3], [m3], [m3], [m3], [e13, e23, f3]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a3, a3, a3, b3], [[d3, m3, s3], [m3], [m3], [m3], [e13, e23, f3]], [[d3, m3, s3], [m3], [m3], [m3], [e13, e23, f3]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127079,"parameters":{"states":["s3","m3","f3","e13","e23","d3"],"alphabet":["a3","b3"],"start_state":"s3","final_states":["f3"],"transitions":[["s3",null,"m3"],["s3",null,"d3"],["m3","a3","m3"],["m3","b3","f3"],["f3",null,"e13"],["e13",null,"e23"]],"input":["a3","a3","a3","b3"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a3\",\"b3\"],\"final_states\":[\"f3\"],\"input\":[\"a3\",\"a3\",\"a3\",\"b3\"],\"start_state\":\"s3\",\"states\":[\"d3\",\"e13\",\"e23\",\"f3\",\"m3\",\"s3\"],\"transitions\":[[\"e13\",null,\"e23\"],[\"f3\",null,\"e13\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0080","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s4\",\"m4\",\"f4\",\"e14\",\"e24\",\"d4\"],\"alphabet\":[\"a4\",\"b4\"],\"start_state\":\"s4\",\"final_states\":[\"f4\"],\"transitions\":[[\"s4\",null,\"m4\"],[\"s4\",null,\"d4\"],[\"m4\",\"a4\",\"m4\"],[\"m4\",\"b4\",\"f4\"],[\"f4\",null,\"e14\"],[\"e14\",null,\"e24\"]],\"input\":[\"b4\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b4], [[d4, m4, s4], [e14, e24, f4]], [[d4, m4, s4], [e14, e24, f4]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([b4], [[d4, m4, s4], [e14, e24, f4]], [[d4, m4, s4], [e14, e24, f4]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127080,"parameters":{"states":["s4","m4","f4","e14","e24","d4"],"alphabet":["a4","b4"],"start_state":"s4","final_states":["f4"],"transitions":[["s4",null,"m4"],["s4",null,"d4"],["m4","a4","m4"],["m4","b4","f4"],["f4",null,"e14"],["e14",null,"e24"]],"input":["b4"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a4\",\"b4\"],\"final_states\":[\"f4\"],\"input\":[\"b4\"],\"start_state\":\"s4\",\"states\":[\"d4\",\"e14\",\"e24\",\"f4\",\"m4\",\"s4\"],\"transitions\":[[\"e14\",null,\"e24\"],[\"f4\",null,\"e14\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0081","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s5\",\"m5\",\"f5\",\"e15\",\"e25\",\"d5\"],\"alphabet\":[\"a5\",\"b5\"],\"start_state\":\"s5\",\"final_states\":[\"f5\"],\"transitions\":[[\"s5\",null,\"m5\"],[\"s5\",null,\"d5\"],[\"m5\",\"a5\",\"m5\"],[\"m5\",\"b5\",\"f5\"],[\"f5\",null,\"e15\"],[\"e15\",null,\"e25\"]],\"input\":[\"a5\",\"b5\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a5, b5], [[d5, m5, s5], [m5], [e15, e25, f5]], [[d5, m5, s5], [m5], [e15, e25, f5]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a5, b5], [[d5, m5, s5], [m5], [e15, e25, f5]], [[d5, m5, s5], [m5], [e15, e25, f5]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127081,"parameters":{"states":["s5","m5","f5","e15","e25","d5"],"alphabet":["a5","b5"],"start_state":"s5","final_states":["f5"],"transitions":[["s5",null,"m5"],["s5",null,"d5"],["m5","a5","m5"],["m5","b5","f5"],["f5",null,"e15"],["e15",null,"e25"]],"input":["a5","b5"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a5\",\"b5\"],\"final_states\":[\"f5\"],\"input\":[\"a5\",\"b5\"],\"start_state\":\"s5\",\"states\":[\"d5\",\"e15\",\"e25\",\"f5\",\"m5\",\"s5\"],\"transitions\":[[\"e15\",null,\"e25\"],[\"f5\",null,\"e15\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0082","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s6\",\"m6\",\"f6\",\"e16\",\"e26\",\"d6\"],\"alphabet\":[\"a6\",\"b6\"],\"start_state\":\"s6\",\"final_states\":[\"f6\"],\"transitions\":[[\"s6\",null,\"m6\"],[\"s6\",null,\"d6\"],[\"m6\",\"a6\",\"m6\"],[\"m6\",\"b6\",\"f6\"],[\"f6\",null,\"e16\"],[\"e16\",null,\"e26\"]],\"input\":[\"a6\",\"a6\",\"b6\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a6, a6, b6], [[d6, m6, s6], [m6], [m6], [e16, e26, f6]], [[d6, m6, s6], [m6], [m6], [e16, e26, f6]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a6, a6, b6], [[d6, m6, s6], [m6], [m6], [e16, e26, f6]], [[d6, m6, s6], [m6], [m6], [e16, e26, f6]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127082,"parameters":{"states":["s6","m6","f6","e16","e26","d6"],"alphabet":["a6","b6"],"start_state":"s6","final_states":["f6"],"transitions":[["s6",null,"m6"],["s6",null,"d6"],["m6","a6","m6"],["m6","b6","f6"],["f6",null,"e16"],["e16",null,"e26"]],"input":["a6","a6","b6"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a6\",\"b6\"],\"final_states\":[\"f6\"],\"input\":[\"a6\",\"a6\",\"b6\"],\"start_state\":\"s6\",\"states\":[\"d6\",\"e16\",\"e26\",\"f6\",\"m6\",\"s6\"],\"transitions\":[[\"e16\",null,\"e26\"],[\"f6\",null,\"e16\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0083","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s7\",\"m7\",\"f7\",\"e17\",\"e27\",\"d7\"],\"alphabet\":[\"a7\",\"b7\"],\"start_state\":\"s7\",\"final_states\":[\"f7\"],\"transitions\":[[\"s7\",null,\"m7\"],[\"s7\",null,\"d7\"],[\"m7\",\"a7\",\"m7\"],[\"m7\",\"b7\",\"f7\"],[\"f7\",null,\"e17\"],[\"e17\",null,\"e27\"]],\"input\":[\"a7\",\"a7\",\"a7\",\"b7\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a7, a7, a7, b7], [[d7, m7, s7], [m7], [m7], [m7], [e17, e27, f7]], [[d7, m7, s7], [m7], [m7], [m7], [e17, e27, f7]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a7, a7, a7, b7], [[d7, m7, s7], [m7], [m7], [m7], [e17, e27, f7]], [[d7, m7, s7], [m7], [m7], [m7], [e17, e27, f7]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127083,"parameters":{"states":["s7","m7","f7","e17","e27","d7"],"alphabet":["a7","b7"],"start_state":"s7","final_states":["f7"],"transitions":[["s7",null,"m7"],["s7",null,"d7"],["m7","a7","m7"],["m7","b7","f7"],["f7",null,"e17"],["e17",null,"e27"]],"input":["a7","a7","a7","b7"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a7\",\"b7\"],\"final_states\":[\"f7\"],\"input\":[\"a7\",\"a7\",\"a7\",\"b7\"],\"start_state\":\"s7\",\"states\":[\"d7\",\"e17\",\"e27\",\"f7\",\"m7\",\"s7\"],\"transitions\":[[\"e17\",null,\"e27\"],[\"f7\",null,\"e17\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0084","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s8\",\"m8\",\"f8\",\"e18\",\"e28\",\"d8\"],\"alphabet\":[\"a8\",\"b8\"],\"start_state\":\"s8\",\"final_states\":[\"f8\"],\"transitions\":[[\"s8\",null,\"m8\"],[\"s8\",null,\"d8\"],[\"m8\",\"a8\",\"m8\"],[\"m8\",\"b8\",\"f8\"],[\"f8\",null,\"e18\"],[\"e18\",null,\"e28\"]],\"input\":[\"b8\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b8], [[d8, m8, s8], [e18, e28, f8]], [[d8, m8, s8], [e18, e28, f8]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([b8], [[d8, m8, s8], [e18, e28, f8]], [[d8, m8, s8], [e18, e28, f8]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127084,"parameters":{"states":["s8","m8","f8","e18","e28","d8"],"alphabet":["a8","b8"],"start_state":"s8","final_states":["f8"],"transitions":[["s8",null,"m8"],["s8",null,"d8"],["m8","a8","m8"],["m8","b8","f8"],["f8",null,"e18"],["e18",null,"e28"]],"input":["b8"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a8\",\"b8\"],\"final_states\":[\"f8\"],\"input\":[\"b8\"],\"start_state\":\"s8\",\"states\":[\"d8\",\"e18\",\"e28\",\"f8\",\"m8\",\"s8\"],\"transitions\":[[\"e18\",null,\"e28\"],[\"f8\",null,\"e18\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0085","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s9\",\"m9\",\"f9\",\"e19\",\"e29\",\"d9\"],\"alphabet\":[\"a9\",\"b9\"],\"start_state\":\"s9\",\"final_states\":[\"f9\"],\"transitions\":[[\"s9\",null,\"m9\"],[\"s9\",null,\"d9\"],[\"m9\",\"a9\",\"m9\"],[\"m9\",\"b9\",\"f9\"],[\"f9\",null,\"e19\"],[\"e19\",null,\"e29\"]],\"input\":[\"a9\",\"b9\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a9, b9], [[d9, m9, s9], [m9], [e19, e29, f9]], [[d9, m9, s9], [m9], [e19, e29, f9]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a9, b9], [[d9, m9, s9], [m9], [e19, e29, f9]], [[d9, m9, s9], [m9], [e19, e29, f9]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127085,"parameters":{"states":["s9","m9","f9","e19","e29","d9"],"alphabet":["a9","b9"],"start_state":"s9","final_states":["f9"],"transitions":[["s9",null,"m9"],["s9",null,"d9"],["m9","a9","m9"],["m9","b9","f9"],["f9",null,"e19"],["e19",null,"e29"]],"input":["a9","b9"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a9\",\"b9\"],\"final_states\":[\"f9\"],\"input\":[\"a9\",\"b9\"],\"start_state\":\"s9\",\"states\":[\"d9\",\"e19\",\"e29\",\"f9\",\"m9\",\"s9\"],\"transitions\":[[\"e19\",null,\"e29\"],[\"f9\",null,\"e19\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0086","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s10\",\"m10\",\"f10\",\"e110\",\"e210\",\"d10\"],\"alphabet\":[\"a10\",\"b10\"],\"start_state\":\"s10\",\"final_states\":[\"f10\"],\"transitions\":[[\"s10\",null,\"m10\"],[\"s10\",null,\"d10\"],[\"m10\",\"a10\",\"m10\"],[\"m10\",\"b10\",\"f10\"],[\"f10\",null,\"e110\"],[\"e110\",null,\"e210\"]],\"input\":[\"a10\",\"a10\",\"b10\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a10, a10, b10], [[d10, m10, s10], [m10], [m10], [e110, e210, f10]], [[d10, m10, s10], [m10], [m10], [e110, e210, f10]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a10, a10, b10], [[d10, m10, s10], [m10], [m10], [e110, e210, f10]], [[d10, m10, s10], [m10], [m10], [e110, e210, f10]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127086,"parameters":{"states":["s10","m10","f10","e110","e210","d10"],"alphabet":["a10","b10"],"start_state":"s10","final_states":["f10"],"transitions":[["s10",null,"m10"],["s10",null,"d10"],["m10","a10","m10"],["m10","b10","f10"],["f10",null,"e110"],["e110",null,"e210"]],"input":["a10","a10","b10"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a10\",\"b10\"],\"final_states\":[\"f10\"],\"input\":[\"a10\",\"a10\",\"b10\"],\"start_state\":\"s10\",\"states\":[\"d10\",\"e110\",\"e210\",\"f10\",\"m10\",\"s10\"],\"transitions\":[[\"e110\",null,\"e210\"],[\"f10\",null,\"e110\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0087","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s11\",\"m11\",\"f11\",\"e111\",\"e211\",\"d11\"],\"alphabet\":[\"a11\",\"b11\"],\"start_state\":\"s11\",\"final_states\":[\"f11\"],\"transitions\":[[\"s11\",null,\"m11\"],[\"s11\",null,\"d11\"],[\"m11\",\"a11\",\"m11\"],[\"m11\",\"b11\",\"f11\"],[\"f11\",null,\"e111\"],[\"e111\",null,\"e211\"]],\"input\":[\"a11\",\"a11\",\"a11\",\"b11\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a11, a11, a11, b11], [[d11, m11, s11], [m11], [m11], [m11], [e111, e211, f11]], [[d11, m11, s11], [m11], [m11], [m11], [e111, e211, f11]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a11, a11, a11, b11], [[d11, m11, s11], [m11], [m11], [m11], [e111, e211, f11]], [[d11, m11, s11], [m11], [m11], [m11], [e111, e211, f11]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127087,"parameters":{"states":["s11","m11","f11","e111","e211","d11"],"alphabet":["a11","b11"],"start_state":"s11","final_states":["f11"],"transitions":[["s11",null,"m11"],["s11",null,"d11"],["m11","a11","m11"],["m11","b11","f11"],["f11",null,"e111"],["e111",null,"e211"]],"input":["a11","a11","a11","b11"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a11\",\"b11\"],\"final_states\":[\"f11\"],\"input\":[\"a11\",\"a11\",\"a11\",\"b11\"],\"start_state\":\"s11\",\"states\":[\"d11\",\"e111\",\"e211\",\"f11\",\"m11\",\"s11\"],\"transitions\":[[\"e111\",null,\"e211\"],[\"f11\",null,\"e111\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0088","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s12\",\"m12\",\"f12\",\"e112\",\"e212\",\"d12\"],\"alphabet\":[\"a12\",\"b12\"],\"start_state\":\"s12\",\"final_states\":[\"f12\"],\"transitions\":[[\"s12\",null,\"m12\"],[\"s12\",null,\"d12\"],[\"m12\",\"a12\",\"m12\"],[\"m12\",\"b12\",\"f12\"],[\"f12\",null,\"e112\"],[\"e112\",null,\"e212\"]],\"input\":[\"b12\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b12], [[d12, m12, s12], [e112, e212, f12]], [[d12, m12, s12], [e112, e212, f12]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([b12], [[d12, m12, s12], [e112, e212, f12]], [[d12, m12, s12], [e112, e212, f12]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127088,"parameters":{"states":["s12","m12","f12","e112","e212","d12"],"alphabet":["a12","b12"],"start_state":"s12","final_states":["f12"],"transitions":[["s12",null,"m12"],["s12",null,"d12"],["m12","a12","m12"],["m12","b12","f12"],["f12",null,"e112"],["e112",null,"e212"]],"input":["b12"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a12\",\"b12\"],\"final_states\":[\"f12\"],\"input\":[\"b12\"],\"start_state\":\"s12\",\"states\":[\"d12\",\"e112\",\"e212\",\"f12\",\"m12\",\"s12\"],\"transitions\":[[\"e112\",null,\"e212\"],[\"f12\",null,\"e112\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0089","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s13\",\"m13\",\"f13\",\"e113\",\"e213\",\"d13\"],\"alphabet\":[\"a13\",\"b13\"],\"start_state\":\"s13\",\"final_states\":[\"f13\"],\"transitions\":[[\"s13\",null,\"m13\"],[\"s13\",null,\"d13\"],[\"m13\",\"a13\",\"m13\"],[\"m13\",\"b13\",\"f13\"],[\"f13\",null,\"e113\"],[\"e113\",null,\"e213\"]],\"input\":[\"a13\",\"b13\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a13, b13], [[d13, m13, s13], [m13], [e113, e213, f13]], [[d13, m13, s13], [m13], [e113, e213, f13]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a13, b13], [[d13, m13, s13], [m13], [e113, e213, f13]], [[d13, m13, s13], [m13], [e113, e213, f13]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127089,"parameters":{"states":["s13","m13","f13","e113","e213","d13"],"alphabet":["a13","b13"],"start_state":"s13","final_states":["f13"],"transitions":[["s13",null,"m13"],["s13",null,"d13"],["m13","a13","m13"],["m13","b13","f13"],["f13",null,"e113"],["e113",null,"e213"]],"input":["a13","b13"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a13\",\"b13\"],\"final_states\":[\"f13\"],\"input\":[\"a13\",\"b13\"],\"start_state\":\"s13\",\"states\":[\"d13\",\"e113\",\"e213\",\"f13\",\"m13\",\"s13\"],\"transitions\":[[\"e113\",null,\"e213\"],[\"f13\",null,\"e113\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0090","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s14\",\"m14\",\"f14\",\"e114\",\"e214\",\"d14\"],\"alphabet\":[\"a14\",\"b14\"],\"start_state\":\"s14\",\"final_states\":[\"f14\"],\"transitions\":[[\"s14\",null,\"m14\"],[\"s14\",null,\"d14\"],[\"m14\",\"a14\",\"m14\"],[\"m14\",\"b14\",\"f14\"],[\"f14\",null,\"e114\"],[\"e114\",null,\"e214\"]],\"input\":[\"a14\",\"a14\",\"b14\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a14, a14, b14], [[d14, m14, s14], [m14], [m14], [e114, e214, f14]], [[d14, m14, s14], [m14], [m14], [e114, e214, f14]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a14, a14, b14], [[d14, m14, s14], [m14], [m14], [e114, e214, f14]], [[d14, m14, s14], [m14], [m14], [e114, e214, f14]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127090,"parameters":{"states":["s14","m14","f14","e114","e214","d14"],"alphabet":["a14","b14"],"start_state":"s14","final_states":["f14"],"transitions":[["s14",null,"m14"],["s14",null,"d14"],["m14","a14","m14"],["m14","b14","f14"],["f14",null,"e114"],["e114",null,"e214"]],"input":["a14","a14","b14"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a14\",\"b14\"],\"final_states\":[\"f14\"],\"input\":[\"a14\",\"a14\",\"b14\"],\"start_state\":\"s14\",\"states\":[\"d14\",\"e114\",\"e214\",\"f14\",\"m14\",\"s14\"],\"transitions\":[[\"e114\",null,\"e214\"],[\"f14\",null,\"e114\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0091","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s15\",\"m15\",\"f15\",\"e115\",\"e215\",\"d15\"],\"alphabet\":[\"a15\",\"b15\"],\"start_state\":\"s15\",\"final_states\":[\"f15\"],\"transitions\":[[\"s15\",null,\"m15\"],[\"s15\",null,\"d15\"],[\"m15\",\"a15\",\"m15\"],[\"m15\",\"b15\",\"f15\"],[\"f15\",null,\"e115\"],[\"e115\",null,\"e215\"]],\"input\":[\"a15\",\"a15\",\"a15\",\"b15\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a15, a15, a15, b15], [[d15, m15, s15], [m15], [m15], [m15], [e115, e215, f15]], [[d15, m15, s15], [m15], [m15], [m15], [e115, e215, f15]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a15, a15, a15, b15], [[d15, m15, s15], [m15], [m15], [m15], [e115, e215, f15]], [[d15, m15, s15], [m15], [m15], [m15], [e115, e215, f15]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127091,"parameters":{"states":["s15","m15","f15","e115","e215","d15"],"alphabet":["a15","b15"],"start_state":"s15","final_states":["f15"],"transitions":[["s15",null,"m15"],["s15",null,"d15"],["m15","a15","m15"],["m15","b15","f15"],["f15",null,"e115"],["e115",null,"e215"]],"input":["a15","a15","a15","b15"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a15\",\"b15\"],\"final_states\":[\"f15\"],\"input\":[\"a15\",\"a15\",\"a15\",\"b15\"],\"start_state\":\"s15\",\"states\":[\"d15\",\"e115\",\"e215\",\"f15\",\"m15\",\"s15\"],\"transitions\":[[\"e115\",null,\"e215\"],[\"f15\",null,\"e115\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0092","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s16\",\"m16\",\"f16\",\"e116\",\"e216\",\"d16\"],\"alphabet\":[\"a16\",\"b16\"],\"start_state\":\"s16\",\"final_states\":[\"f16\"],\"transitions\":[[\"s16\",null,\"m16\"],[\"s16\",null,\"d16\"],[\"m16\",\"a16\",\"m16\"],[\"m16\",\"b16\",\"f16\"],[\"f16\",null,\"e116\"],[\"e116\",null,\"e216\"]],\"input\":[\"b16\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b16], [[d16, m16, s16], [e116, e216, f16]], [[d16, m16, s16], [e116, e216, f16]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([b16], [[d16, m16, s16], [e116, e216, f16]], [[d16, m16, s16], [e116, e216, f16]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127092,"parameters":{"states":["s16","m16","f16","e116","e216","d16"],"alphabet":["a16","b16"],"start_state":"s16","final_states":["f16"],"transitions":[["s16",null,"m16"],["s16",null,"d16"],["m16","a16","m16"],["m16","b16","f16"],["f16",null,"e116"],["e116",null,"e216"]],"input":["b16"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a16\",\"b16\"],\"final_states\":[\"f16\"],\"input\":[\"b16\"],\"start_state\":\"s16\",\"states\":[\"d16\",\"e116\",\"e216\",\"f16\",\"m16\",\"s16\"],\"transitions\":[[\"e116\",null,\"e216\"],[\"f16\",null,\"e116\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0093","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s17\",\"m17\",\"f17\",\"e117\",\"e217\",\"d17\"],\"alphabet\":[\"a17\",\"b17\"],\"start_state\":\"s17\",\"final_states\":[\"f17\"],\"transitions\":[[\"s17\",null,\"m17\"],[\"s17\",null,\"d17\"],[\"m17\",\"a17\",\"m17\"],[\"m17\",\"b17\",\"f17\"],[\"f17\",null,\"e117\"],[\"e117\",null,\"e217\"]],\"input\":[\"a17\",\"b17\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a17, b17], [[d17, m17, s17], [m17], [e117, e217, f17]], [[d17, m17, s17], [m17], [e117, e217, f17]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a17, b17], [[d17, m17, s17], [m17], [e117, e217, f17]], [[d17, m17, s17], [m17], [e117, e217, f17]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127093,"parameters":{"states":["s17","m17","f17","e117","e217","d17"],"alphabet":["a17","b17"],"start_state":"s17","final_states":["f17"],"transitions":[["s17",null,"m17"],["s17",null,"d17"],["m17","a17","m17"],["m17","b17","f17"],["f17",null,"e117"],["e117",null,"e217"]],"input":["a17","b17"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a17\",\"b17\"],\"final_states\":[\"f17\"],\"input\":[\"a17\",\"b17\"],\"start_state\":\"s17\",\"states\":[\"d17\",\"e117\",\"e217\",\"f17\",\"m17\",\"s17\"],\"transitions\":[[\"e117\",null,\"e217\"],[\"f17\",null,\"e117\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0094","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s18\",\"m18\",\"f18\",\"e118\",\"e218\",\"d18\"],\"alphabet\":[\"a18\",\"b18\"],\"start_state\":\"s18\",\"final_states\":[\"f18\"],\"transitions\":[[\"s18\",null,\"m18\"],[\"s18\",null,\"d18\"],[\"m18\",\"a18\",\"m18\"],[\"m18\",\"b18\",\"f18\"],[\"f18\",null,\"e118\"],[\"e118\",null,\"e218\"]],\"input\":[\"a18\",\"a18\",\"b18\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a18, a18, b18], [[d18, m18, s18], [m18], [m18], [e118, e218, f18]], [[d18, m18, s18], [m18], [m18], [e118, e218, f18]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a18, a18, b18], [[d18, m18, s18], [m18], [m18], [e118, e218, f18]], [[d18, m18, s18], [m18], [m18], [e118, e218, f18]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127094,"parameters":{"states":["s18","m18","f18","e118","e218","d18"],"alphabet":["a18","b18"],"start_state":"s18","final_states":["f18"],"transitions":[["s18",null,"m18"],["s18",null,"d18"],["m18","a18","m18"],["m18","b18","f18"],["f18",null,"e118"],["e118",null,"e218"]],"input":["a18","a18","b18"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a18\",\"b18\"],\"final_states\":[\"f18\"],\"input\":[\"a18\",\"a18\",\"b18\"],\"start_state\":\"s18\",\"states\":[\"d18\",\"e118\",\"e218\",\"f18\",\"m18\",\"s18\"],\"transitions\":[[\"e118\",null,\"e218\"],[\"f18\",null,\"e118\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0095","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s19\",\"m19\",\"f19\",\"e119\",\"e219\",\"d19\"],\"alphabet\":[\"a19\",\"b19\"],\"start_state\":\"s19\",\"final_states\":[\"f19\"],\"transitions\":[[\"s19\",null,\"m19\"],[\"s19\",null,\"d19\"],[\"m19\",\"a19\",\"m19\"],[\"m19\",\"b19\",\"f19\"],[\"f19\",null,\"e119\"],[\"e119\",null,\"e219\"]],\"input\":[\"a19\",\"a19\",\"a19\",\"b19\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a19, a19, a19, b19], [[d19, m19, s19], [m19], [m19], [m19], [e119, e219, f19]], [[d19, m19, s19], [m19], [m19], [m19], [e119, e219, f19]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a19, a19, a19, b19], [[d19, m19, s19], [m19], [m19], [m19], [e119, e219, f19]], [[d19, m19, s19], [m19], [m19], [m19], [e119, e219, f19]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127095,"parameters":{"states":["s19","m19","f19","e119","e219","d19"],"alphabet":["a19","b19"],"start_state":"s19","final_states":["f19"],"transitions":[["s19",null,"m19"],["s19",null,"d19"],["m19","a19","m19"],["m19","b19","f19"],["f19",null,"e119"],["e119",null,"e219"]],"input":["a19","a19","a19","b19"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a19\",\"b19\"],\"final_states\":[\"f19\"],\"input\":[\"a19\",\"a19\",\"a19\",\"b19\"],\"start_state\":\"s19\",\"states\":[\"d19\",\"e119\",\"e219\",\"f19\",\"m19\",\"s19\"],\"transitions\":[[\"e119\",null,\"e219\"],[\"f19\",null,\"e119\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0096","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s20\",\"m20\",\"f20\",\"e120\",\"e220\",\"d20\"],\"alphabet\":[\"a20\",\"b20\"],\"start_state\":\"s20\",\"final_states\":[\"f20\"],\"transitions\":[[\"s20\",null,\"m20\"],[\"s20\",null,\"d20\"],[\"m20\",\"a20\",\"m20\"],[\"m20\",\"b20\",\"f20\"],[\"f20\",null,\"e120\"],[\"e120\",null,\"e220\"]],\"input\":[\"b20\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b20], [[d20, m20, s20], [e120, e220, f20]], [[d20, m20, s20], [e120, e220, f20]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([b20], [[d20, m20, s20], [e120, e220, f20]], [[d20, m20, s20], [e120, e220, f20]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127096,"parameters":{"states":["s20","m20","f20","e120","e220","d20"],"alphabet":["a20","b20"],"start_state":"s20","final_states":["f20"],"transitions":[["s20",null,"m20"],["s20",null,"d20"],["m20","a20","m20"],["m20","b20","f20"],["f20",null,"e120"],["e120",null,"e220"]],"input":["b20"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a20\",\"b20\"],\"final_states\":[\"f20\"],\"input\":[\"b20\"],\"start_state\":\"s20\",\"states\":[\"d20\",\"e120\",\"e220\",\"f20\",\"m20\",\"s20\"],\"transitions\":[[\"e120\",null,\"e220\"],[\"f20\",null,\"e120\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0097","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s21\",\"m21\",\"f21\",\"e121\",\"e221\",\"d21\"],\"alphabet\":[\"a21\",\"b21\"],\"start_state\":\"s21\",\"final_states\":[\"f21\"],\"transitions\":[[\"s21\",null,\"m21\"],[\"s21\",null,\"d21\"],[\"m21\",\"a21\",\"m21\"],[\"m21\",\"b21\",\"f21\"],[\"f21\",null,\"e121\"],[\"e121\",null,\"e221\"]],\"input\":[\"a21\",\"b21\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a21, b21], [[d21, m21, s21], [m21], [e121, e221, f21]], [[d21, m21, s21], [m21], [e121, e221, f21]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a21, b21], [[d21, m21, s21], [m21], [e121, e221, f21]], [[d21, m21, s21], [m21], [e121, e221, f21]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127097,"parameters":{"states":["s21","m21","f21","e121","e221","d21"],"alphabet":["a21","b21"],"start_state":"s21","final_states":["f21"],"transitions":[["s21",null,"m21"],["s21",null,"d21"],["m21","a21","m21"],["m21","b21","f21"],["f21",null,"e121"],["e121",null,"e221"]],"input":["a21","b21"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a21\",\"b21\"],\"final_states\":[\"f21\"],\"input\":[\"a21\",\"b21\"],\"start_state\":\"s21\",\"states\":[\"d21\",\"e121\",\"e221\",\"f21\",\"m21\",\"s21\"],\"transitions\":[[\"e121\",null,\"e221\"],[\"f21\",null,\"e121\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0098","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s22\",\"m22\",\"f22\",\"e122\",\"e222\",\"d22\"],\"alphabet\":[\"a22\",\"b22\"],\"start_state\":\"s22\",\"final_states\":[\"f22\"],\"transitions\":[[\"s22\",null,\"m22\"],[\"s22\",null,\"d22\"],[\"m22\",\"a22\",\"m22\"],[\"m22\",\"b22\",\"f22\"],[\"f22\",null,\"e122\"],[\"e122\",null,\"e222\"]],\"input\":[\"a22\",\"a22\",\"b22\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a22, a22, b22], [[d22, m22, s22], [m22], [m22], [e122, e222, f22]], [[d22, m22, s22], [m22], [m22], [e122, e222, f22]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a22, a22, b22], [[d22, m22, s22], [m22], [m22], [e122, e222, f22]], [[d22, m22, s22], [m22], [m22], [e122, e222, f22]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127098,"parameters":{"states":["s22","m22","f22","e122","e222","d22"],"alphabet":["a22","b22"],"start_state":"s22","final_states":["f22"],"transitions":[["s22",null,"m22"],["s22",null,"d22"],["m22","a22","m22"],["m22","b22","f22"],["f22",null,"e122"],["e122",null,"e222"]],"input":["a22","a22","b22"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a22\",\"b22\"],\"final_states\":[\"f22\"],\"input\":[\"a22\",\"a22\",\"b22\"],\"start_state\":\"s22\",\"states\":[\"d22\",\"e122\",\"e222\",\"f22\",\"m22\",\"s22\"],\"transitions\":[[\"e122\",null,\"e222\"],[\"f22\",null,\"e122\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0099","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s23\",\"m23\",\"f23\",\"e123\",\"e223\",\"d23\"],\"alphabet\":[\"a23\",\"b23\"],\"start_state\":\"s23\",\"final_states\":[\"f23\"],\"transitions\":[[\"s23\",null,\"m23\"],[\"s23\",null,\"d23\"],[\"m23\",\"a23\",\"m23\"],[\"m23\",\"b23\",\"f23\"],[\"f23\",null,\"e123\"],[\"e123\",null,\"e223\"]],\"input\":[\"a23\",\"a23\",\"a23\",\"b23\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a23, a23, a23, b23], [[d23, m23, s23], [m23], [m23], [m23], [e123, e223, f23]], [[d23, m23, s23], [m23], [m23], [m23], [e123, e223, f23]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([a23, a23, a23, b23], [[d23, m23, s23], [m23], [m23], [m23], [e123, e223, f23]], [[d23, m23, s23], [m23], [m23], [m23], [e123, e223, f23]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127099,"parameters":{"states":["s23","m23","f23","e123","e223","d23"],"alphabet":["a23","b23"],"start_state":"s23","final_states":["f23"],"transitions":[["s23",null,"m23"],["s23",null,"d23"],["m23","a23","m23"],["m23","b23","f23"],["f23",null,"e123"],["e123",null,"e223"]],"input":["a23","a23","a23","b23"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a23\",\"b23\"],\"final_states\":[\"f23\"],\"input\":[\"a23\",\"a23\",\"a23\",\"b23\"],\"start_state\":\"s23\",\"states\":[\"d23\",\"e123\",\"e223\",\"f23\",\"m23\",\"s23\"],\"transitions\":[[\"e123\",null,\"e223\"],[\"f23\",null,\"e123\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、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-20261112-r07-subset-construction-nfa-to-dfa-0100","batch_id":"batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations","language":"zh-Hant","source_mko_ids":["mko-subset-construction-nfa-to-dfa"],"title_zh":"NFA到DFA的子集合構造","stem_zh":"epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-full-word-trace-invariant；資料={\"states\":[\"s24\",\"m24\",\"f24\",\"e124\",\"e224\",\"d24\"],\"alphabet\":[\"a24\",\"b24\"],\"start_state\":\"s24\",\"final_states\":[\"f24\"],\"transitions\":[[\"s24\",null,\"m24\"],[\"s24\",null,\"d24\"],[\"m24\",\"a24\",\"m24\"],[\"m24\",\"b24\",\"f24\"],[\"f24\",null,\"e124\"],[\"e124\",null,\"e224\"]],\"input\":[\"b24\"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([b24], [[d24, m24, s24], [e124, e224, f24]], [[d24, m24, s24], [e124, e224, f24]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)","explanation_zh":"Wave6第六層核對=([b24], [[d24, m24, s24], [e124, e224, f24]], [[d24, m24, s24], [e124, e224, f24]], 是, 是, each_DFA_prefix_subset_equals_all_epsilon_closed_NFA_states_reachable_after_that_prefix, 否, finite_word_tests_do_not_prove_language_equivalence_without_the_prefix_induction_invariant)；依完整明示資料獨立重算；empty subset是合法dead state，DFA prefix subset須等於全部epsilon-closed NFA reachable states；language equivalence依任意word prefix induction；有限accept/reject tests不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["NFA到DFA的子集合構造"]},"variant":{"family_id":"qf-mod43-subsetdfa-full-word-trace-invariant","seed":202611127100,"parameters":{"states":["s24","m24","f24","e124","e224","d24"],"alphabet":["a24","b24"],"start_state":"s24","final_states":["f24"],"transitions":[["s24",null,"m24"],["s24",null,"d24"],["m24","a24","m24"],["m24","b24","f24"],["f24",null,"e124"],["e124",null,"e224"]],"input":["b24"],"domain":"Epsilon_NFA_subset_construction","operation":"subsetdfa-full-word-trace-invariant","semantic_template":"qf-mod43-subsetdfa-full-word-trace-invariant/{\"alphabet\":[\"a24\",\"b24\"],\"final_states\":[\"f24\"],\"input\":[\"b24\"],\"start_state\":\"s24\",\"states\":[\"d24\",\"e124\",\"e224\",\"f24\",\"m24\",\"s24\"],\"transitions\":[[\"e124\",null,\"e224\"],[\"f24\",null,\"e124\"],[\"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、一般定理的有限枚舉替代、未宣告瑕積分、未明示係數律、Euler criterion循環、有限word等價、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}