{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0001","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":2,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [[0, 1], [1, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1], [[0, 1], [1, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027001,"parameters":{"modulus":2,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":2,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0002","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":3,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2], [[0, 1], [1, 2], [2, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2], [[0, 1], [1, 2], [2, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027002,"parameters":{"modulus":3,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":3,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0003","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":4,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3], [[0, 1], [1, 2], [2, 3], [3, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3], [[0, 1], [1, 2], [2, 3], [3, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027003,"parameters":{"modulus":4,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":4,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0004","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":5,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027004,"parameters":{"modulus":5,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":5,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0005","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":6,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027005,"parameters":{"modulus":6,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":6,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0006","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":7,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027006,"parameters":{"modulus":7,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":7,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0007","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":8,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027007,"parameters":{"modulus":8,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":8,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0008","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":9,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027008,"parameters":{"modulus":9,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":9,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0009","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":10,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027009,"parameters":{"modulus":10,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":10,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0010","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":11,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027010,"parameters":{"modulus":11,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":11,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0011","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":12,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027011,"parameters":{"modulus":12,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":12,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0012","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":13,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027012,"parameters":{"modulus":13,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":13,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0013","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":14,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027013,"parameters":{"modulus":14,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":14,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0014","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":15,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027014,"parameters":{"modulus":15,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":15,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0015","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":16,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027015,"parameters":{"modulus":16,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":16,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0016","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":17,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027016,"parameters":{"modulus":17,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":17,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0017","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":18,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027017,"parameters":{"modulus":18,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":18,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0018","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":19,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027018,"parameters":{"modulus":19,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":19,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0019","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":20,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 0]], 0, [0], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027019,"parameters":{"modulus":20,"residue":0,"target_symbol":1,"alphabet_count":2,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":2,\"modulus\":20,\"residue\":0,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0020","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":2,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [[0, 1, 0], [1, 0, 1]], 0, [1], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1], [[0, 1, 0], [1, 0, 1]], 0, [1], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027020,"parameters":{"modulus":2,"residue":1,"target_symbol":1,"alphabet_count":3,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":3,\"modulus\":2,\"residue\":1,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0021","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":3,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2], [[0, 1, 0], [1, 2, 1], [2, 0, 2]], 0, [1], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2], [[0, 1, 0], [1, 2, 1], [2, 0, 2]], 0, [1], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027021,"parameters":{"modulus":3,"residue":1,"target_symbol":1,"alphabet_count":3,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":3,\"modulus\":3,\"residue\":1,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0022","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":4,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3], [[0, 1, 0], [1, 2, 1], [2, 3, 2], [3, 0, 3]], 0, [1], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3], [[0, 1, 0], [1, 2, 1], [2, 3, 2], [3, 0, 3]], 0, [1], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027022,"parameters":{"modulus":4,"residue":1,"target_symbol":1,"alphabet_count":3,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":3,\"modulus\":4,\"residue\":1,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0023","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":5,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4], [[0, 1, 0], [1, 2, 1], [2, 3, 2], [3, 4, 3], [4, 0, 4]], 0, [1], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4], [[0, 1, 0], [1, 2, 1], [2, 3, 2], [3, 4, 3], [4, 0, 4]], 0, [1], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027023,"parameters":{"modulus":5,"residue":1,"target_symbol":1,"alphabet_count":3,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":3,\"modulus\":5,\"residue\":1,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0024","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":6,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [[0, 1, 0], [1, 2, 1], [2, 3, 2], [3, 4, 3], [4, 5, 4], [5, 0, 5]], 0, [1], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5], [[0, 1, 0], [1, 2, 1], [2, 3, 2], [3, 4, 3], [4, 5, 4], [5, 0, 5]], 0, [1], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027024,"parameters":{"modulus":6,"residue":1,"target_symbol":1,"alphabet_count":3,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":3,\"modulus\":6,\"residue\":1,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0025","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-mod-count-certificate；資料={\"modulus\":7,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3}。請依 [states,transition,start,accepting,regular,universal_invariant] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6], [[0, 1, 0], [1, 2, 1], [2, 3, 2], [3, 4, 3], [4, 5, 4], [5, 6, 5], [6, 0, 6]], 0, [1], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)","explanation_zh":"Wave5第二層核對=([0, 1, 2, 3, 4, 5, 6], [[0, 1, 0], [1, 2, 1], [2, 3, 2], [3, 4, 3], [4, 5, 4], [5, 6, 5], [6, 0, 6]], 0, [1], 是, state_equals_target_symbol_count_mod_modulus_for_all_prefixes)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-mod-count-certificate","seed":202611027025,"parameters":{"modulus":7,"residue":1,"target_symbol":1,"alphabet_count":3,"domain":"Exact_DFA_regular_language_certificate","operation":"regular-mod-count-certificate","semantic_template":"qf-mod33-regular-mod-count-certificate/{\"alphabet_count\":3,\"modulus\":7,\"residue\":1,\"target_symbol\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0026","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-word-membership；資料={\"modulus\":2,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"word\":[0,0,0,0,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], 0, 是)","explanation_zh":"Wave5第二層核對=([0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], 0, 是)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-word-membership","seed":202611027026,"parameters":{"modulus":2,"residue":0,"target_symbol":1,"alphabet_count":2,"word":[0,0,0,0,0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-word-membership","semantic_template":"qf-mod33-regular-word-membership/{\"alphabet_count\":2,\"modulus\":2,\"residue\":0,\"target_symbol\":1,\"word\":[0,0,0,0,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0028","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-word-membership；資料={\"modulus\":4,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"word\":[0,1,0,0,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1], 1, 否)","explanation_zh":"Wave5第二層核對=([0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1], 1, 否)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-word-membership","seed":202611027028,"parameters":{"modulus":4,"residue":0,"target_symbol":1,"alphabet_count":2,"word":[0,1,0,0,0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-word-membership","semantic_template":"qf-mod33-regular-word-membership/{\"alphabet_count\":2,\"modulus\":4,\"residue\":0,\"target_symbol\":1,\"word\":[0,1,0,0,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0049","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-word-membership；資料={\"modulus\":6,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3,\"word\":[1,1,1,0,1]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 1], [0, 1, 2, 3, 3, 4], 4, 否)","explanation_zh":"Wave5第二層核對=([1, 1, 1, 0, 1], [0, 1, 2, 3, 3, 4], 4, 否)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-word-membership","seed":202611027049,"parameters":{"modulus":6,"residue":1,"target_symbol":1,"alphabet_count":3,"word":[1,1,1,0,1],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-word-membership","semantic_template":"qf-mod33-regular-word-membership/{\"alphabet_count\":3,\"modulus\":6,\"residue\":1,\"target_symbol\":1,\"word\":[1,1,1,0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0050","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-word-membership；資料={\"modulus\":7,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3,\"word\":[0,0,0,1,1]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 2], 2, 否)","explanation_zh":"Wave5第二層核對=([0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 2], 2, 否)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-word-membership","seed":202611027050,"parameters":{"modulus":7,"residue":1,"target_symbol":1,"alphabet_count":3,"word":[0,0,0,1,1],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-word-membership","semantic_template":"qf-mod33-regular-word-membership/{\"alphabet_count\":3,\"modulus\":7,\"residue\":1,\"target_symbol\":1,\"word\":[0,0,0,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0051","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,0,0,0,0]],\"probe\":[1,0,0,0,0,0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8], [8, 8]], [1, 0, 0, 0, 0, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8], [8, 8]], [1, 0, 0, 0, 0, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027051,"parameters":{"alphabet_count":2,"words":[[0],[1,0,0,0,0,0]],"probe":[1,0,0,0,0,0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,0,0,0,0],\"words\":[[0],[1,0,0,0,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0052","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,1,0,0,0,0]],\"probe\":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 0], [1, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 0], [1, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027052,"parameters":{"alphabet_count":2,"words":[[0],[1,1,0,0,0,0]],"probe":[0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[0],\"words\":[[0],[1,1,0,0,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0053","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,1,0,0,0]],\"probe\":[1,0,1,0,0,0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 1], [1, 0, 1, 0], [1, 0, 1, 0, 0], [1, 0, 1, 0, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [8, 4], [5, 8], [6, 8], [7, 8], [8, 8], [8, 8]], [1, 0, 1, 0, 0, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 1], [1, 0, 1, 0], [1, 0, 1, 0, 0], [1, 0, 1, 0, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [8, 4], [5, 8], [6, 8], [7, 8], [8, 8], [8, 8]], [1, 0, 1, 0, 0, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027053,"parameters":{"alphabet_count":2,"words":[[0],[1,0,1,0,0,0]],"probe":[1,0,1,0,0,0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,1,0,0,0],\"words\":[[0],[1,0,1,0,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0054","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,1,1,0,0,0]],\"probe\":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 1], [1, 1, 1], [1, 1, 1, 0], [1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [8, 4], [5, 8], [6, 8], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 1], [1, 1, 1], [1, 1, 1, 0], [1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [8, 4], [5, 8], [6, 8], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027054,"parameters":{"alphabet_count":2,"words":[[0],[1,1,1,0,0,0]],"probe":[0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[0],\"words\":[[0],[1,1,1,0,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0055","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,0,1,0,0]],\"probe\":[1,0,0,1,0,0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 1], [1, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [8, 5], [6, 8], [7, 8], [8, 8], [8, 8]], [1, 0, 0, 1, 0, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 1], [1, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [8, 5], [6, 8], [7, 8], [8, 8], [8, 8]], [1, 0, 0, 1, 0, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027055,"parameters":{"alphabet_count":2,"words":[[0],[1,0,0,1,0,0]],"probe":[1,0,0,1,0,0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,0,1,0,0],\"words\":[[0],[1,0,0,1,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0056","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,1,0,1,0,0]],\"probe\":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 1], [1, 1, 0, 1, 0], [1, 1, 0, 1, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [8, 5], [6, 8], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 1], [1, 1, 0, 1, 0], [1, 1, 0, 1, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [8, 5], [6, 8], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027056,"parameters":{"alphabet_count":2,"words":[[0],[1,1,0,1,0,0]],"probe":[0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[0],\"words\":[[0],[1,1,0,1,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0057","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,1,1,0,0]],\"probe\":[1,0,1,1,0,0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 1], [1, 0, 1, 1], [1, 0, 1, 1, 0], [1, 0, 1, 1, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [8, 4], [8, 5], [6, 8], [7, 8], [8, 8], [8, 8]], [1, 0, 1, 1, 0, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 1], [1, 0, 1, 1], [1, 0, 1, 1, 0], [1, 0, 1, 1, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [8, 4], [8, 5], [6, 8], [7, 8], [8, 8], [8, 8]], [1, 0, 1, 1, 0, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027057,"parameters":{"alphabet_count":2,"words":[[0],[1,0,1,1,0,0]],"probe":[1,0,1,1,0,0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,1,1,0,0],\"words\":[[0],[1,0,1,1,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0058","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,1,1,1,0,0]],\"probe\":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [8, 4], [8, 5], [6, 8], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [8, 4], [8, 5], [6, 8], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027058,"parameters":{"alphabet_count":2,"words":[[0],[1,1,1,1,0,0]],"probe":[0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[0],\"words\":[[0],[1,1,1,1,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0059","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,0,0,1,0]],\"probe\":[1,0,0,0,1,0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [5, 8], [8, 6], [7, 8], [8, 8], [8, 8]], [1, 0, 0, 0, 1, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [5, 8], [8, 6], [7, 8], [8, 8], [8, 8]], [1, 0, 0, 0, 1, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027059,"parameters":{"alphabet_count":2,"words":[[0],[1,0,0,0,1,0]],"probe":[1,0,0,0,1,0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,0,0,1,0],\"words\":[[0],[1,0,0,0,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0060","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,1,0,0,1,0]],\"probe\":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 0], [1, 1, 0, 0, 1], [1, 1, 0, 0, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [5, 8], [8, 6], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 0], [1, 1, 0, 0, 1], [1, 1, 0, 0, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [5, 8], [8, 6], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027060,"parameters":{"alphabet_count":2,"words":[[0],[1,1,0,0,1,0]],"probe":[0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[0],\"words\":[[0],[1,1,0,0,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0061","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,1,0,1,0]],\"probe\":[1,0,1,0,1,0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 1], [1, 0, 1, 0], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [8, 4], [5, 8], [8, 6], [7, 8], [8, 8], [8, 8]], [1, 0, 1, 0, 1, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 1], [1, 0, 1, 0], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [8, 4], [5, 8], [8, 6], [7, 8], [8, 8], [8, 8]], [1, 0, 1, 0, 1, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027061,"parameters":{"alphabet_count":2,"words":[[0],[1,0,1,0,1,0]],"probe":[1,0,1,0,1,0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,1,0,1,0],\"words\":[[0],[1,0,1,0,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0062","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,1,1,0,1,0]],\"probe\":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 1], [1, 1, 1], [1, 1, 1, 0], [1, 1, 1, 0, 1], [1, 1, 1, 0, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [8, 4], [5, 8], [8, 6], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 1], [1, 1, 1], [1, 1, 1, 0], [1, 1, 1, 0, 1], [1, 1, 1, 0, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [8, 4], [5, 8], [8, 6], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027062,"parameters":{"alphabet_count":2,"words":[[0],[1,1,1,0,1,0]],"probe":[0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[0],\"words\":[[0],[1,1,1,0,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0063","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,0,1,1,0]],\"probe\":[1,0,0,1,1,0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 1], [1, 0, 0, 1, 1], [1, 0, 0, 1, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [8, 5], [8, 6], [7, 8], [8, 8], [8, 8]], [1, 0, 0, 1, 1, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 1], [1, 0, 0, 1, 1], [1, 0, 0, 1, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [8, 5], [8, 6], [7, 8], [8, 8], [8, 8]], [1, 0, 0, 1, 1, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027063,"parameters":{"alphabet_count":2,"words":[[0],[1,0,0,1,1,0]],"probe":[1,0,0,1,1,0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,0,1,1,0],\"words\":[[0],[1,0,0,1,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0064","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,1,0,1,1,0]],\"probe\":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 1], [1, 1, 0, 1, 1], [1, 1, 0, 1, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [8, 5], [8, 6], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 1], [1, 1, 0, 1, 1], [1, 1, 0, 1, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [8, 5], [8, 6], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027064,"parameters":{"alphabet_count":2,"words":[[0],[1,1,0,1,1,0]],"probe":[0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[0],\"words\":[[0],[1,1,0,1,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0065","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,1,1,1,0]],\"probe\":[1,0,1,1,1,0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 1], [1, 0, 1, 1], [1, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [8, 4], [8, 5], [8, 6], [7, 8], [8, 8], [8, 8]], [1, 0, 1, 1, 1, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 1], [1, 0, 1, 1], [1, 0, 1, 1, 1], [1, 0, 1, 1, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [8, 4], [8, 5], [8, 6], [7, 8], [8, 8], [8, 8]], [1, 0, 1, 1, 1, 0], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027065,"parameters":{"alphabet_count":2,"words":[[0],[1,0,1,1,1,0]],"probe":[1,0,1,1,1,0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,1,1,1,0],\"words\":[[0],[1,0,1,1,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0066","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,1,1,1,1,0]],\"probe\":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [8, 4], [8, 5], [8, 6], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [8, 4], [8, 5], [8, 6], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027066,"parameters":{"alphabet_count":2,"words":[[0],[1,1,1,1,1,0]],"probe":[0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[0],\"words\":[[0],[1,1,1,1,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0067","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,0,0,0,1]],\"probe\":[1,0,0,0,0,1]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [5, 8], [6, 8], [8, 7], [8, 8], [8, 8]], [1, 0, 0, 0, 0, 1], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [5, 8], [6, 8], [8, 7], [8, 8], [8, 8]], [1, 0, 0, 0, 0, 1], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027067,"parameters":{"alphabet_count":2,"words":[[0],[1,0,0,0,0,1]],"probe":[1,0,0,0,0,1],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,0,0,0,1],\"words\":[[0],[1,0,0,0,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0068","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,1,0,0,0,1]],\"probe\":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 0], [1, 1, 0, 0, 0], [1, 1, 0, 0, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [5, 8], [6, 8], [8, 7], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 0], [1, 1, 0, 0, 0], [1, 1, 0, 0, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [5, 8], [6, 8], [8, 7], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027068,"parameters":{"alphabet_count":2,"words":[[0],[1,1,0,0,0,1]],"probe":[0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[0],\"words\":[[0],[1,1,0,0,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0069","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,1,0,0,1]],\"probe\":[1,0,1,0,0,1]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 1], [1, 0, 1, 0], [1, 0, 1, 0, 0], [1, 0, 1, 0, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [8, 4], [5, 8], [6, 8], [8, 7], [8, 8], [8, 8]], [1, 0, 1, 0, 0, 1], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 1], [1, 0, 1, 0], [1, 0, 1, 0, 0], [1, 0, 1, 0, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [8, 4], [5, 8], [6, 8], [8, 7], [8, 8], [8, 8]], [1, 0, 1, 0, 0, 1], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027069,"parameters":{"alphabet_count":2,"words":[[0],[1,0,1,0,0,1]],"probe":[1,0,1,0,0,1],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,1,0,0,1],\"words\":[[0],[1,0,1,0,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0070","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,1,1,0,0,1]],\"probe\":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 1], [1, 1, 1], [1, 1, 1, 0], [1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [8, 4], [5, 8], [6, 8], [8, 7], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 1], [1, 1, 1], [1, 1, 1, 0], [1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [8, 4], [5, 8], [6, 8], [8, 7], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027070,"parameters":{"alphabet_count":2,"words":[[0],[1,1,1,0,0,1]],"probe":[0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[0],\"words\":[[0],[1,1,1,0,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0071","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,0,1,0,1]],\"probe\":[1,0,0,1,0,1]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 1], [1, 0, 0, 1, 0], [1, 0, 0, 1, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [8, 5], [6, 8], [8, 7], [8, 8], [8, 8]], [1, 0, 0, 1, 0, 1], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 1], [1, 0, 0, 1, 0], [1, 0, 0, 1, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [8, 5], [6, 8], [8, 7], [8, 8], [8, 8]], [1, 0, 0, 1, 0, 1], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027071,"parameters":{"alphabet_count":2,"words":[[0],[1,0,0,1,0,1]],"probe":[1,0,0,1,0,1],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,0,1,0,1],\"words\":[[0],[1,0,0,1,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0072","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,1,0,1,0,1]],\"probe\":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 1], [1, 1, 0, 1, 0], [1, 1, 0, 1, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [8, 5], [6, 8], [8, 7], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 1], [1, 1, 0, 1, 0], [1, 1, 0, 1, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [8, 5], [6, 8], [8, 7], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027072,"parameters":{"alphabet_count":2,"words":[[0],[1,1,0,1,0,1]],"probe":[0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[0],\"words\":[[0],[1,1,0,1,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0073","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,1,1,0,1]],\"probe\":[1,0,1,1,0,1]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 1], [1, 0, 1, 1], [1, 0, 1, 1, 0], [1, 0, 1, 1, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [8, 4], [8, 5], [6, 8], [8, 7], [8, 8], [8, 8]], [1, 0, 1, 1, 0, 1], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 1], [1, 0, 1, 1], [1, 0, 1, 1, 0], [1, 0, 1, 1, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [8, 4], [8, 5], [6, 8], [8, 7], [8, 8], [8, 8]], [1, 0, 1, 1, 0, 1], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027073,"parameters":{"alphabet_count":2,"words":[[0],[1,0,1,1,0,1]],"probe":[1,0,1,1,0,1],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,1,1,0,1],\"words\":[[0],[1,0,1,1,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0074","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,1,1,1,0,1]],\"probe\":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [8, 4], [8, 5], [6, 8], [8, 7], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 1]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [8, 4], [8, 5], [6, 8], [8, 7], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027074,"parameters":{"alphabet_count":2,"words":[[0],[1,1,1,1,0,1]],"probe":[0],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[0],\"words\":[[0],[1,1,1,1,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0075","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={\"alphabet_count\":2,\"words\":[[0],[1,0,0,0,1,1]],\"probe\":[1,0,0,0,1,1]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 1]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [5, 8], [8, 6], [8, 7], [8, 8], [8, 8]], [1, 0, 0, 0, 1, 1], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)","explanation_zh":"Wave5第二層核對=([[], [0], [1], [1, 0], [1, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 1]], 8, [1, 7], [[1, 2], [8, 8], [3, 8], [4, 8], [5, 8], [8, 6], [8, 7], [8, 8], [8, 8]], [1, 0, 0, 0, 1, 1], [0, 2, 3, 4, 5, 6, 7], 是, explicit_DFA_recognizes_exact_finite_language)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-language-construction","seed":202611027075,"parameters":{"alphabet_count":2,"words":[[0],[1,0,0,0,1,1]],"probe":[1,0,0,0,1,1],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-language-construction","semantic_template":"qf-mod33-regular-finite-language-construction/{\"alphabet_count\":2,\"probe\":[1,0,0,0,1,1],\"words\":[[0],[1,0,0,0,1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0076","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":2,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[0,0,0,0,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[0, 0, 0, 0, 0], 是]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[0, 0, 0, 0, 0], 是]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027076,"parameters":{"modulus":2,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[0,0,0,0,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":2,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[0,0,0,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0077","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":3,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[1,0,0,0,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[1, 0, 0, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[1, 0, 0, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027077,"parameters":{"modulus":3,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[1,0,0,0,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":3,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[1,0,0,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0078","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":4,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[0,1,0,0,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[0, 1, 0, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[0, 1, 0, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027078,"parameters":{"modulus":4,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[0,1,0,0,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":4,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[0,1,0,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0079","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":5,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[1,1,0,0,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[1, 1, 0, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[1, 1, 0, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027079,"parameters":{"modulus":5,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[1,1,0,0,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":5,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[1,1,0,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0080","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":6,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[0,0,1,0,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[0, 0, 1, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[0, 0, 1, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027080,"parameters":{"modulus":6,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[0,0,1,0,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":6,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[0,0,1,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0081","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":7,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[1,0,1,0,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[1, 0, 1, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[1, 0, 1, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027081,"parameters":{"modulus":7,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[1,0,1,0,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":7,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[1,0,1,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0082","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":8,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[0,1,1,0,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[0, 1, 1, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[0, 1, 1, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027082,"parameters":{"modulus":8,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[0,1,1,0,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":8,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[0,1,1,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0083","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":9,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[1,1,1,0,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[1, 1, 1, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[1, 1, 1, 0, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027083,"parameters":{"modulus":9,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[1,1,1,0,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":9,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[1,1,1,0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0084","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":10,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[0,0,0,1,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[0, 0, 0, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[0, 0, 0, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027084,"parameters":{"modulus":10,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[0,0,0,1,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":10,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[0,0,0,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0085","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":11,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[1,0,0,1,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[1, 0, 0, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[1, 0, 0, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027085,"parameters":{"modulus":11,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[1,0,0,1,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":11,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[1,0,0,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0086","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":12,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[0,1,0,1,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[0, 1, 0, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[0, 1, 0, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027086,"parameters":{"modulus":12,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[0,1,0,1,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":12,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[0,1,0,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0087","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":13,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[1,1,0,1,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[1, 1, 0, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[1, 1, 0, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027087,"parameters":{"modulus":13,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[1,1,0,1,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":13,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[1,1,0,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0088","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":14,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[0,0,1,1,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[0, 0, 1, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[0, 0, 1, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027088,"parameters":{"modulus":14,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[0,0,1,1,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":14,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[0,0,1,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0089","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":15,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[1,0,1,1,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[1, 0, 1, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[1, 0, 1, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027089,"parameters":{"modulus":15,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[1,0,1,1,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":15,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[1,0,1,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0090","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":16,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[0,1,1,1,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[0, 1, 1, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[0, 1, 1, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027090,"parameters":{"modulus":16,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[0,1,1,1,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":16,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[0,1,1,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0091","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":17,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[1,1,1,1,0]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[1, 1, 1, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[1, 1, 1, 1, 0], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027091,"parameters":{"modulus":17,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[1,1,1,1,0]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":17,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[1,1,1,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0092","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":18,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[0,0,0,0,1]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[0, 0, 0, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[0, 0, 0, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027092,"parameters":{"modulus":18,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[0,0,0,0,1]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":18,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[0,0,0,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0093","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":19,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[1,0,0,0,1]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[1, 0, 0, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[1, 0, 0, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027093,"parameters":{"modulus":19,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[1,0,0,0,1]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":19,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[1,0,0,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0094","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":20,\"residue\":0,\"target_symbol\":1,\"alphabet_count\":2,\"test_words\":[[],[0,1,0,0,1]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 是], [[0, 1, 0, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 是], [[0, 1, 0, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027094,"parameters":{"modulus":20,"residue":0,"target_symbol":1,"alphabet_count":2,"test_words":[[],[0,1,0,0,1]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":2,\"modulus\":20,\"residue\":0,\"target_symbol\":1,\"test_words\":[[],[0,1,0,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0095","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":2,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3,\"test_words\":[[],[1,1,0,0,1]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 否], [[1, 1, 0, 0, 1], 是]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 否], [[1, 1, 0, 0, 1], 是]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027095,"parameters":{"modulus":2,"residue":1,"target_symbol":1,"alphabet_count":3,"test_words":[[],[1,1,0,0,1]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":3,\"modulus\":2,\"residue\":1,\"target_symbol\":1,\"test_words\":[[],[1,1,0,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0096","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":3,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3,\"test_words\":[[],[0,0,1,0,1]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 否], [[0, 0, 1, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 否], [[0, 0, 1, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027096,"parameters":{"modulus":3,"residue":1,"target_symbol":1,"alphabet_count":3,"test_words":[[],[0,0,1,0,1]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":3,\"modulus\":3,\"residue\":1,\"target_symbol\":1,\"test_words\":[[],[0,0,1,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0097","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":4,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3,\"test_words\":[[],[1,0,1,0,1]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 否], [[1, 0, 1, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 否], [[1, 0, 1, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027097,"parameters":{"modulus":4,"residue":1,"target_symbol":1,"alphabet_count":3,"test_words":[[],[1,0,1,0,1]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":3,\"modulus\":4,\"residue\":1,\"target_symbol\":1,\"test_words\":[[],[1,0,1,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0098","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":5,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3,\"test_words\":[[],[0,1,1,0,1]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 否], [[0, 1, 1, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 否], [[0, 1, 1, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027098,"parameters":{"modulus":5,"residue":1,"target_symbol":1,"alphabet_count":3,"test_words":[[],[0,1,1,0,1]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":3,\"modulus\":5,\"residue\":1,\"target_symbol\":1,\"test_words\":[[],[0,1,1,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0099","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":6,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3,\"test_words\":[[],[1,1,1,0,1]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 否], [[1, 1, 1, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 否], [[1, 1, 1, 0, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027099,"parameters":{"modulus":6,"residue":1,"target_symbol":1,"alphabet_count":3,"test_words":[[],[1,1,1,0,1]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":3,\"modulus\":6,\"residue\":1,\"target_symbol\":1,\"test_words\":[[],[1,1,1,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r07-regular-language-0100","batch_id":"batch-20261014-advance-20261102-r07-regular-language-foundations","language":"zh-Hant","source_mko_ids":["mko-regular-language"],"title_zh":"正規語言","stem_zh":"完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-test-boundary；資料={\"modulus\":7,\"residue\":1,\"target_symbol\":1,\"alphabet_count\":3,\"test_words\":[[],[0,0,0,1,1]]}。請依 [tested_words,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"([[[], 否], [[0, 0, 0, 1, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)","explanation_zh":"Wave5第二層核對=([[[], 否], [[0, 0, 0, 1, 1], 否]], 否, finite_test_suite_not_regular_language_or_equivalence_certificate)；依完整明示資料重算；mod-count證書須涵蓋任意word length而不只是測試集；不引入regex、NFA、epsilon、minimization或pumping lemma；有限測試不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["正規語言"]},"variant":{"family_id":"qf-mod33-regular-finite-test-boundary","seed":202611027100,"parameters":{"modulus":7,"residue":1,"target_symbol":1,"alphabet_count":3,"test_words":[[],[0,0,0,1,1]],"domain":"Exact_DFA_regular_language_certificate","operation":"regular-finite-test-boundary","semantic_template":"qf-mod33-regular-finite-test-boundary/{\"alphabet_count\":3,\"modulus\":7,\"residue\":1,\"target_symbol\":1,\"test_words\":[[],[0,0,0,1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}