{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r07-finite-automaton-0001","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,0],[0,0],[0,0]],\"start\":0,\"accepting\":[0]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017001,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,0],[0,0],[0,0]],"start":0,"accepting":[0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,0],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0002","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,0],[0,0],[0,0]],\"start\":1,\"accepting\":[1]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017002,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,0],[0,0],[0,0]],"start":1,"accepting":[1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0003","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,0],[0,0],[0,0]],\"start\":2,\"accepting\":[2]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017003,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,0],[0,0],[0,0]],"start":2,"accepting":[2],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,0],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0004","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,1],[0,0],[0,0]],\"start\":0,\"accepting\":[0]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017004,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,1],[0,0],[0,0]],"start":0,"accepting":[0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,1],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0005","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,1],[0,0],[0,0]],\"start\":1,\"accepting\":[1]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017005,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,1],[0,0],[0,0]],"start":1,"accepting":[1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0006","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,1],[0,0],[0,0]],\"start\":2,\"accepting\":[2]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017006,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,1],[0,0],[0,0]],"start":2,"accepting":[2],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,1],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0007","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,2],[0,0],[0,0]],\"start\":0,\"accepting\":[0]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017007,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,2],[0,0],[0,0]],"start":0,"accepting":[0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,2],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0008","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,2],[0,0],[0,0]],\"start\":1,\"accepting\":[1]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017008,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,2],[0,0],[0,0]],"start":1,"accepting":[1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,2],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0009","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,2],[0,0],[0,0]],\"start\":2,\"accepting\":[2]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017009,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,2],[0,0],[0,0]],"start":2,"accepting":[2],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,2],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0010","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,0],[1,0],[0,0]],\"start\":0,\"accepting\":[0]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017010,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,0],[1,0],[0,0]],"start":0,"accepting":[0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,0],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0011","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,0],[1,0],[0,0]],\"start\":1,\"accepting\":[1]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017011,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,0],[1,0],[0,0]],"start":1,"accepting":[1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0012","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,0],[1,0],[0,0]],\"start\":2,\"accepting\":[2]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017012,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,0],[1,0],[0,0]],"start":2,"accepting":[2],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,0],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0013","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,1],[1,0],[0,0]],\"start\":0,\"accepting\":[0]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017013,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,1],[1,0],[0,0]],"start":0,"accepting":[0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,1],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0014","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,1],[1,0],[0,0]],\"start\":1,\"accepting\":[1]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017014,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,1],[1,0],[0,0]],"start":1,"accepting":[1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0015","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,1],[1,0],[0,0]],\"start\":2,\"accepting\":[2]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017015,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,1],[1,0],[0,0]],"start":2,"accepting":[2],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,1],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0016","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,2],[1,0],[0,0]],\"start\":0,\"accepting\":[0]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017016,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,2],[1,0],[0,0]],"start":0,"accepting":[0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,2],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0017","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,2],[1,0],[0,0]],\"start\":1,\"accepting\":[1]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017017,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,2],[1,0],[0,0]],"start":1,"accepting":[1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,2],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0018","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,2],[1,0],[0,0]],\"start\":2,\"accepting\":[2]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017018,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,2],[1,0],[0,0]],"start":2,"accepting":[2],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,2],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0019","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,0],[2,0],[0,0]],\"start\":0,\"accepting\":[0]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017019,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,0],[2,0],[0,0]],"start":0,"accepting":[0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,0],[2,0],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0020","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,0],[2,0],[0,0]],\"start\":1,\"accepting\":[1]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017020,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,0],[2,0],[0,0]],"start":1,"accepting":[1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,0],[2,0],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0021","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,0],[2,0],[0,0]],\"start\":2,\"accepting\":[2]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017021,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,0],[2,0],[0,0]],"start":2,"accepting":[2],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,0],[2,0],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0022","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,1],[2,0],[0,0]],\"start\":0,\"accepting\":[0]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017022,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,1],[2,0],[0,0]],"start":0,"accepting":[0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,1],[2,0],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0023","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,1],[2,0],[0,0]],\"start\":1,\"accepting\":[1]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 1, [1], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017023,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,1],[2,0],[0,0]],"start":1,"accepting":[1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,1],[2,0],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0024","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,1],[2,0],[0,0]],\"start\":2,\"accepting\":[2]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 2, [2], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017024,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,1],[2,0],[0,0]],"start":2,"accepting":[2],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,1],[2,0],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0025","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-qualification；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,2],[2,0],[0,0]],\"start\":0,\"accepting\":[0]}。請依 [state_count,alphabet_count,start,accepting,transition_cell_count,qualified,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)","explanation_zh":"Wave5根節點核對=(3, 2, 0, [0], 6, 是, complete_total_deterministic_table)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-qualification","seed":202611017025,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,2],[2,0],[0,0]],"start":0,"accepting":[0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-qualification","semantic_template":"qf-mod32-dfa-qualification/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,2],[2,0],[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0026","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,0],[0,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,0,0,0,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], 0)","explanation_zh":"Wave5根節點核對=([0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017026,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,0],[0,0],[0,0]],"start":0,"accepting":[0],"word":[0,0,0,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,0],[0,0],[0,0]],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0027","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,0],[0,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[1,0,0,0,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0], 0)","explanation_zh":"Wave5根節點核對=([1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017027,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,0],[0,0],[0,0]],"start":1,"accepting":[1],"word":[1,0,0,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,0],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0028","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,0],[0,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[0,1,0,0,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 0], [2, 0, 0, 2, 0, 2], 2)","explanation_zh":"Wave5根節點核對=([0, 1, 0, 0, 0], [2, 0, 0, 2, 0, 2], 2)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017028,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,0],[0,0],[0,0]],"start":2,"accepting":[2],"word":[0,1,0,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,0],[0,0],[0,0]],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0029","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,1],[0,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[1,1,0,0,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], 0)","explanation_zh":"Wave5根節點核對=([1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017029,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,1],[0,0],[0,0]],"start":0,"accepting":[0],"word":[1,1,0,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,1],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0030","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,1],[0,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[0,0,1,0,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 0], [1, 0, 1, 0, 1, 0], 0)","explanation_zh":"Wave5根節點核對=([0, 0, 1, 0, 0], [1, 0, 1, 0, 1, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017030,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,1],[0,0],[0,0]],"start":1,"accepting":[1],"word":[0,0,1,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,1],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0031","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,1],[0,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[1,0,1,0,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 0], [2, 0, 2, 0, 2, 0], 0)","explanation_zh":"Wave5根節點核對=([1, 0, 1, 0, 0], [2, 0, 2, 0, 2, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017031,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,1],[0,0],[0,0]],"start":2,"accepting":[2],"word":[1,0,1,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,1],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0032","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,2],[0,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,1,1,0,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 0], [0, 0, 2, 0, 0, 0], 0)","explanation_zh":"Wave5根節點核對=([0, 1, 1, 0, 0], [0, 0, 2, 0, 0, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017032,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,2],[0,0],[0,0]],"start":0,"accepting":[0],"word":[0,1,1,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,2],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0033","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,2],[0,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[1,1,1,0,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 0], [1, 0, 2, 0, 1, 0], 0)","explanation_zh":"Wave5根節點核對=([1, 1, 1, 0, 0], [1, 0, 2, 0, 1, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017033,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,2],[0,0],[0,0]],"start":1,"accepting":[1],"word":[1,1,1,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,2],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0034","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,2],[0,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[0,0,0,1,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0, 1, 0], [2, 0, 2, 0, 2, 0], 0)","explanation_zh":"Wave5根節點核對=([0, 0, 0, 1, 0], [2, 0, 2, 0, 2, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017034,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,2],[0,0],[0,0]],"start":2,"accepting":[2],"word":[0,0,0,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,2],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0035","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,0],[1,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[1,0,0,1,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], 0)","explanation_zh":"Wave5根節點核對=([1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017035,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,0],[1,0],[0,0]],"start":0,"accepting":[0],"word":[1,0,0,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,0],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0036","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,0],[1,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[0,1,0,1,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0, 1, 0], [1, 1, 0, 1, 0, 1], 1)","explanation_zh":"Wave5根節點核對=([0, 1, 0, 1, 0], [1, 1, 0, 1, 0, 1], 1)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017036,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,0],[1,0],[0,0]],"start":1,"accepting":[1],"word":[0,1,0,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,0],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0037","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,0],[1,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[1,1,0,1,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 0, 1, 0], [2, 0, 0, 2, 0, 2], 2)","explanation_zh":"Wave5根節點核對=([1, 1, 0, 1, 0], [2, 0, 0, 2, 0, 2], 2)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017037,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,0],[1,0],[0,0]],"start":2,"accepting":[2],"word":[1,1,0,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,0],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0038","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,1],[1,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,0,1,1,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 1, 1, 0], [0, 0, 0, 1, 0, 0], 0)","explanation_zh":"Wave5根節點核對=([0, 0, 1, 1, 0], [0, 0, 0, 1, 0, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017038,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,1],[1,0],[0,0]],"start":0,"accepting":[0],"word":[0,0,1,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,1],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0039","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,1],[1,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[1,0,1,1,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 1, 1, 0], [1, 0, 1, 0, 1, 1], 1)","explanation_zh":"Wave5根節點核對=([1, 0, 1, 1, 0], [1, 0, 1, 0, 1, 1], 1)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017039,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,1],[1,0],[0,0]],"start":1,"accepting":[1],"word":[1,0,1,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,1],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0040","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,1],[1,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[0,1,1,1,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 1, 1, 0], [2, 0, 1, 0, 1, 1], 1)","explanation_zh":"Wave5根節點核對=([0, 1, 1, 1, 0], [2, 0, 1, 0, 1, 1], 1)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017040,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,1],[1,0],[0,0]],"start":2,"accepting":[2],"word":[0,1,1,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,1],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0041","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,2],[1,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[1,1,1,1,0]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 0], 0)","explanation_zh":"Wave5根節點核對=([1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017041,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,2],[1,0],[0,0]],"start":0,"accepting":[0],"word":[1,1,1,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,2],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0042","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,2],[1,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[0,0,0,0,1]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 0], 0)","explanation_zh":"Wave5根節點核對=([0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017042,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,2],[1,0],[0,0]],"start":1,"accepting":[1],"word":[0,0,0,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,2],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0043","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,2],[1,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[1,0,0,0,1]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 1], [2, 0, 2, 0, 2, 0], 0)","explanation_zh":"Wave5根節點核對=([1, 0, 0, 0, 1], [2, 0, 2, 0, 2, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017043,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,2],[1,0],[0,0]],"start":2,"accepting":[2],"word":[1,0,0,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,2],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0044","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,0],[2,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,1,0,0,1]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0], 0)","explanation_zh":"Wave5根節點核對=([0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017044,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,0],[2,0],[0,0]],"start":0,"accepting":[0],"word":[0,1,0,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,0],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0045","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,0],[2,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[1,1,0,0,1]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 1], [1, 0, 0, 1, 2, 0], 0)","explanation_zh":"Wave5根節點核對=([1, 1, 0, 0, 1], [1, 0, 0, 1, 2, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017045,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,0],[2,0],[0,0]],"start":1,"accepting":[1],"word":[1,1,0,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,0],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0046","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,0],[2,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[0,0,1,0,1]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 1], [2, 0, 2, 0, 2, 0], 0)","explanation_zh":"Wave5根節點核對=([0, 0, 1, 0, 1], [2, 0, 2, 0, 2, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017046,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,0],[2,0],[0,0]],"start":2,"accepting":[2],"word":[0,0,1,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,0],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0047","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,1],[2,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[1,0,1,0,1]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 1], [0, 1, 2, 0, 0, 1], 1)","explanation_zh":"Wave5根節點核對=([1, 0, 1, 0, 1], [0, 1, 2, 0, 0, 1], 1)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017047,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,1],[2,0],[0,0]],"start":0,"accepting":[0],"word":[1,0,1,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,1],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0048","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,1],[2,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[0,1,1,0,1]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 1], [1, 2, 0, 1, 2, 0], 0)","explanation_zh":"Wave5根節點核對=([0, 1, 1, 0, 1], [1, 2, 0, 1, 2, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017048,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,1],[2,0],[0,0]],"start":1,"accepting":[1],"word":[0,1,1,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,1],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0049","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,1],[2,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[1,1,1,0,1]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 1], [2, 0, 1, 0, 2, 0], 0)","explanation_zh":"Wave5根節點核對=([1, 1, 1, 0, 1], [2, 0, 1, 0, 2, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017049,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,1],[2,0],[0,0]],"start":2,"accepting":[2],"word":[1,1,1,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,1],[2,0],[0,0]],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0050","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-word-trace；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,2],[2,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,0,0,1,1]}。請依 [word,state_trace,final_state] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], 0)","explanation_zh":"Wave5根節點核對=([0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], 0)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-word-trace","seed":202611017050,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,2],[2,0],[0,0]],"start":0,"accepting":[0],"word":[0,0,0,1,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-word-trace","semantic_template":"qf-mod32-dfa-word-trace/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,2],[2,0],[0,0]],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0051","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,0],[0,0],[0,0]],\"start\":0,\"accepting\":[0],\"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根節點核對=([0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], 0, 是)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017051,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,0],[0,0],[0,0]],"start":0,"accepting":[0],"word":[0,0,0,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,0],[0,0],[0,0]],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0052","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,0],[0,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[1,0,0,0,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0], 0, 否)","explanation_zh":"Wave5根節點核對=([1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0], 0, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017052,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,0],[0,0],[0,0]],"start":1,"accepting":[1],"word":[1,0,0,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,0],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0053","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,0],[0,0],[0,0]],\"start\":2,\"accepting\":[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], [2, 0, 0, 2, 0, 2], 2, 是)","explanation_zh":"Wave5根節點核對=([0, 1, 0, 0, 0], [2, 0, 0, 2, 0, 2], 2, 是)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017053,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,0],[0,0],[0,0]],"start":2,"accepting":[2],"word":[0,1,0,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,0],[0,0],[0,0]],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0054","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,1],[0,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[1,1,0,0,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], 0, 是)","explanation_zh":"Wave5根節點核對=([1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], 0, 是)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017054,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,1],[0,0],[0,0]],"start":0,"accepting":[0],"word":[1,1,0,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,1],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0055","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,1],[0,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[0,0,1,0,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 0], [1, 0, 1, 0, 1, 0], 0, 否)","explanation_zh":"Wave5根節點核對=([0, 0, 1, 0, 0], [1, 0, 1, 0, 1, 0], 0, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017055,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,1],[0,0],[0,0]],"start":1,"accepting":[1],"word":[0,0,1,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,1],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0056","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,1],[0,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[1,0,1,0,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 0], [2, 0, 2, 0, 2, 0], 0, 否)","explanation_zh":"Wave5根節點核對=([1, 0, 1, 0, 0], [2, 0, 2, 0, 2, 0], 0, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017056,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,1],[0,0],[0,0]],"start":2,"accepting":[2],"word":[1,0,1,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,1],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0057","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,2],[0,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,1,1,0,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 0], [0, 0, 2, 0, 0, 0], 0, 是)","explanation_zh":"Wave5根節點核對=([0, 1, 1, 0, 0], [0, 0, 2, 0, 0, 0], 0, 是)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017057,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,2],[0,0],[0,0]],"start":0,"accepting":[0],"word":[0,1,1,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,2],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0058","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,2],[0,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[1,1,1,0,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 0], [1, 0, 2, 0, 1, 0], 0, 否)","explanation_zh":"Wave5根節點核對=([1, 1, 1, 0, 0], [1, 0, 2, 0, 1, 0], 0, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017058,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,2],[0,0],[0,0]],"start":1,"accepting":[1],"word":[1,1,1,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,2],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0059","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,2],[0,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[0,0,0,1,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0, 1, 0], [2, 0, 2, 0, 2, 0], 0, 否)","explanation_zh":"Wave5根節點核對=([0, 0, 0, 1, 0], [2, 0, 2, 0, 2, 0], 0, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017059,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,2],[0,0],[0,0]],"start":2,"accepting":[2],"word":[0,0,0,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,2],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0060","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,0],[1,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[1,0,0,1,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], 0, 是)","explanation_zh":"Wave5根節點核對=([1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], 0, 是)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017060,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,0],[1,0],[0,0]],"start":0,"accepting":[0],"word":[1,0,0,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,0],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0061","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,0],[1,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[0,1,0,1,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0, 1, 0], [1, 1, 0, 1, 0, 1], 1, 是)","explanation_zh":"Wave5根節點核對=([0, 1, 0, 1, 0], [1, 1, 0, 1, 0, 1], 1, 是)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017061,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,0],[1,0],[0,0]],"start":1,"accepting":[1],"word":[0,1,0,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,0],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0062","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,0],[1,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[1,1,0,1,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 0, 1, 0], [2, 0, 0, 2, 0, 2], 2, 是)","explanation_zh":"Wave5根節點核對=([1, 1, 0, 1, 0], [2, 0, 0, 2, 0, 2], 2, 是)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017062,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,0],[1,0],[0,0]],"start":2,"accepting":[2],"word":[1,1,0,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,0],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0063","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,1],[1,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,0,1,1,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 1, 1, 0], [0, 0, 0, 1, 0, 0], 0, 是)","explanation_zh":"Wave5根節點核對=([0, 0, 1, 1, 0], [0, 0, 0, 1, 0, 0], 0, 是)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017063,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,1],[1,0],[0,0]],"start":0,"accepting":[0],"word":[0,0,1,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,1],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0064","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,1],[1,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[1,0,1,1,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 1, 1, 0], [1, 0, 1, 0, 1, 1], 1, 是)","explanation_zh":"Wave5根節點核對=([1, 0, 1, 1, 0], [1, 0, 1, 0, 1, 1], 1, 是)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017064,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,1],[1,0],[0,0]],"start":1,"accepting":[1],"word":[1,0,1,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,1],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0065","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,1],[1,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[0,1,1,1,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 1, 1, 0], [2, 0, 1, 0, 1, 1], 1, 否)","explanation_zh":"Wave5根節點核對=([0, 1, 1, 1, 0], [2, 0, 1, 0, 1, 1], 1, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017065,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,1],[1,0],[0,0]],"start":2,"accepting":[2],"word":[0,1,1,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,1],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0066","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,2],[1,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[1,1,1,1,0]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 0], 0, 是)","explanation_zh":"Wave5根節點核對=([1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 0], 0, 是)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017066,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,2],[1,0],[0,0]],"start":0,"accepting":[0],"word":[1,1,1,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,2],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0067","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,2],[1,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[0,0,0,0,1]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 0], 0, 否)","explanation_zh":"Wave5根節點核對=([0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 0], 0, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017067,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,2],[1,0],[0,0]],"start":1,"accepting":[1],"word":[0,0,0,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,2],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0068","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,2],[1,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[1,0,0,0,1]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 1], [2, 0, 2, 0, 2, 0], 0, 否)","explanation_zh":"Wave5根節點核對=([1, 0, 0, 0, 1], [2, 0, 2, 0, 2, 0], 0, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017068,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,2],[1,0],[0,0]],"start":2,"accepting":[2],"word":[1,0,0,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,2],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0069","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,0],[2,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,1,0,0,1]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0], 0, 是)","explanation_zh":"Wave5根節點核對=([0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0], 0, 是)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017069,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,0],[2,0],[0,0]],"start":0,"accepting":[0],"word":[0,1,0,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,0],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0070","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,0],[2,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[1,1,0,0,1]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 1], [1, 0, 0, 1, 2, 0], 0, 否)","explanation_zh":"Wave5根節點核對=([1, 1, 0, 0, 1], [1, 0, 0, 1, 2, 0], 0, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017070,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,0],[2,0],[0,0]],"start":1,"accepting":[1],"word":[1,1,0,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,0],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0071","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,0],[2,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[0,0,1,0,1]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 1], [2, 0, 2, 0, 2, 0], 0, 否)","explanation_zh":"Wave5根節點核對=([0, 0, 1, 0, 1], [2, 0, 2, 0, 2, 0], 0, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017071,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,0],[2,0],[0,0]],"start":2,"accepting":[2],"word":[0,0,1,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,0],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0072","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,1],[2,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[1,0,1,0,1]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 1], [0, 1, 2, 0, 0, 1], 1, 否)","explanation_zh":"Wave5根節點核對=([1, 0, 1, 0, 1], [0, 1, 2, 0, 0, 1], 1, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017072,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,1],[2,0],[0,0]],"start":0,"accepting":[0],"word":[1,0,1,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,1],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0073","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,1],[2,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[0,1,1,0,1]}。請依 [word,state_trace,final_state,accepted] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 1], [1, 2, 0, 1, 2, 0], 0, 否)","explanation_zh":"Wave5根節點核對=([0, 1, 1, 0, 1], [1, 2, 0, 1, 2, 0], 0, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017073,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,1],[2,0],[0,0]],"start":1,"accepting":[1],"word":[0,1,1,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,1],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0074","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,1],[2,0],[0,0]],\"start\":2,\"accepting\":[2],\"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], [2, 0, 1, 0, 2, 0], 0, 否)","explanation_zh":"Wave5根節點核對=([1, 1, 1, 0, 1], [2, 0, 1, 0, 2, 0], 0, 否)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017074,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,1],[2,0],[0,0]],"start":2,"accepting":[2],"word":[1,1,1,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,1],[2,0],[0,0]],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0075","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-acceptance；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,2],[2,0],[0,0]],\"start\":0,\"accepting\":[0],\"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, 2, 0], 0, 是)","explanation_zh":"Wave5根節點核對=([0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], 0, 是)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-acceptance","seed":202611017075,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,2],[2,0],[0,0]],"start":0,"accepting":[0],"word":[0,0,0,1,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-acceptance","semantic_template":"qf-mod32-dfa-acceptance/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,2],[2,0],[0,0]],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0076","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,0],[0,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,0,0,0,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017076,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,0],[0,0],[0,0]],"start":0,"accepting":[0],"word":[0,0,0,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,0],[0,0],[0,0]],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0077","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,0],[0,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[1,0,0,0,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017077,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,0],[0,0],[0,0]],"start":1,"accepting":[1],"word":[1,0,0,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,0],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0078","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,0],[0,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[0,1,0,0,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 0], [2, 0, 0, 2, 0, 2], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 1, 0, 0, 0], [2, 0, 0, 2, 0, 2], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017078,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,0],[0,0],[0,0]],"start":2,"accepting":[2],"word":[0,1,0,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,0],[0,0],[0,0]],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0079","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,1],[0,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[1,1,0,0,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017079,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,1],[0,0],[0,0]],"start":0,"accepting":[0],"word":[1,1,0,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,1],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0080","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,1],[0,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[0,0,1,0,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 0], [1, 0, 1, 0, 1, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 0, 1, 0, 0], [1, 0, 1, 0, 1, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017080,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,1],[0,0],[0,0]],"start":1,"accepting":[1],"word":[0,0,1,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,1],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0081","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,1],[0,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[1,0,1,0,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 0], [2, 0, 2, 0, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([1, 0, 1, 0, 0], [2, 0, 2, 0, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017081,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,1],[0,0],[0,0]],"start":2,"accepting":[2],"word":[1,0,1,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,1],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0082","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,2],[0,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,1,1,0,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 0], [0, 0, 2, 0, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 1, 1, 0, 0], [0, 0, 2, 0, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017082,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,2],[0,0],[0,0]],"start":0,"accepting":[0],"word":[0,1,1,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,2],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0083","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,2],[0,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[1,1,1,0,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 0], [1, 0, 2, 0, 1, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([1, 1, 1, 0, 0], [1, 0, 2, 0, 1, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017083,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,2],[0,0],[0,0]],"start":1,"accepting":[1],"word":[1,1,1,0,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,2],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0084","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,2],[0,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[0,0,0,1,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0, 1, 0], [2, 0, 2, 0, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 0, 0, 1, 0], [2, 0, 2, 0, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017084,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,2],[0,0],[0,0]],"start":2,"accepting":[2],"word":[0,0,0,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,2],[0,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0085","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,0],[1,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[1,0,0,1,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017085,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,0],[1,0],[0,0]],"start":0,"accepting":[0],"word":[1,0,0,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,0],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0086","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,0],[1,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[0,1,0,1,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0, 1, 0], [1, 1, 0, 1, 0, 1], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 1, 0, 1, 0], [1, 1, 0, 1, 0, 1], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017086,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,0],[1,0],[0,0]],"start":1,"accepting":[1],"word":[0,1,0,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,0],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0087","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,0],[1,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[1,1,0,1,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 0, 1, 0], [2, 0, 0, 2, 0, 2], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([1, 1, 0, 1, 0], [2, 0, 0, 2, 0, 2], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017087,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,0],[1,0],[0,0]],"start":2,"accepting":[2],"word":[1,1,0,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,0],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0088","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,1],[1,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,0,1,1,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 1, 1, 0], [0, 0, 0, 1, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 0, 1, 1, 0], [0, 0, 0, 1, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017088,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,1],[1,0],[0,0]],"start":0,"accepting":[0],"word":[0,0,1,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,1],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0089","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,1],[1,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[1,0,1,1,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 1, 1, 0], [1, 0, 1, 0, 1, 1], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([1, 0, 1, 1, 0], [1, 0, 1, 0, 1, 1], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017089,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,1],[1,0],[0,0]],"start":1,"accepting":[1],"word":[1,0,1,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,1],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0090","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,1],[1,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[0,1,1,1,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 1, 1, 0], [2, 0, 1, 0, 1, 1], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 1, 1, 1, 0], [2, 0, 1, 0, 1, 1], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017090,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,1],[1,0],[0,0]],"start":2,"accepting":[2],"word":[0,1,1,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,1],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0091","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,2],[1,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[1,1,1,1,0]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([1, 1, 1, 1, 0], [0, 2, 0, 2, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017091,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,2],[1,0],[0,0]],"start":0,"accepting":[0],"word":[1,1,1,1,0],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,2],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0092","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,2],[1,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[0,0,0,0,1]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017092,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,2],[1,0],[0,0]],"start":1,"accepting":[1],"word":[0,0,0,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,2],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0093","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,2],[1,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[1,0,0,0,1]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 1], [2, 0, 2, 0, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([1, 0, 0, 0, 1], [2, 0, 2, 0, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017093,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,2],[1,0],[0,0]],"start":2,"accepting":[2],"word":[1,0,0,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,2],[1,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0094","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,0],[2,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,1,0,0,1]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017094,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,0],[2,0],[0,0]],"start":0,"accepting":[0],"word":[0,1,0,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,0],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0095","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,0],[2,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[1,1,0,0,1]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 1], [1, 0, 0, 1, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([1, 1, 0, 0, 1], [1, 0, 0, 1, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017095,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,0],[2,0],[0,0]],"start":1,"accepting":[1],"word":[1,1,0,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,0],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0096","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,0],[2,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[0,0,1,0,1]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 1], [2, 0, 2, 0, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 0, 1, 0, 1], [2, 0, 2, 0, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017096,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,0],[2,0],[0,0]],"start":2,"accepting":[2],"word":[0,0,1,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,0],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0097","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,1],[2,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[1,0,1,0,1]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 1], [0, 1, 2, 0, 0, 1], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([1, 0, 1, 0, 1], [0, 1, 2, 0, 0, 1], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017097,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,1],[2,0],[0,0]],"start":0,"accepting":[0],"word":[1,0,1,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,1],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0098","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[1,1],[2,0],[0,0]],\"start\":1,\"accepting\":[1],\"word\":[0,1,1,0,1]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 1], [1, 2, 0, 1, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 1, 1, 0, 1], [1, 2, 0, 1, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017098,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[1,1],[2,0],[0,0]],"start":1,"accepting":[1],"word":[0,1,1,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[1],\"alphabet_count\":2,\"start\":1,\"state_count\":3,\"transition\":[[1,1],[2,0],[0,0]],\"word\":[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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0099","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[2,1],[2,0],[0,0]],\"start\":2,\"accepting\":[2],\"word\":[1,1,1,0,1]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 1], [2, 0, 1, 0, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([1, 1, 1, 0, 1], [2, 0, 1, 0, 2, 0], 否, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017099,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[2,1],[2,0],[0,0]],"start":2,"accepting":[2],"word":[1,1,1,0,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[2],\"alphabet_count\":2,\"start\":2,\"state_count\":3,\"transition\":[[2,1],[2,0],[0,0]],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r07-finite-automaton-0100","batch_id":"batch-20261014-advance-20261101-r07-finite-automaton-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-automaton"],"title_zh":"確定有限自動機","stem_zh":"完整有限DFA總轉移表與有序有限word。操作=dfa-single-trace-boundary；資料={\"state_count\":3,\"alphabet_count\":2,\"transition\":[[0,2],[2,0],[0,0]],\"start\":0,\"accepting\":[0],\"word\":[0,0,0,1,1]}。請依 [word,state_trace,accepted,proves_language_equivalence,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)","explanation_zh":"Wave5根節點核對=([0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], 是, 否, one_trace_does_not_prove_language_equivalence_or_regularity)；依完整明示資料重算；唯一初始狀態、接受子集且逐符號追蹤；空字留在初始狀態；不引入NFA或epsilon transition；有限trace不證語言等價或regularity。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["確定有限自動機"]},"variant":{"family_id":"qf-mod32-dfa-single-trace-boundary","seed":202611017100,"parameters":{"state_count":3,"alphabet_count":2,"transition":[[0,2],[2,0],[0,0]],"start":0,"accepting":[0],"word":[0,0,0,1,1],"domain":"Complete_deterministic_finite_automaton","operation":"dfa-single-trace-boundary","semantic_template":"qf-mod32-dfa-single-trace-boundary/{\"accepting\":[0],\"alphabet_count\":2,\"start\":0,\"state_count\":3,\"transition\":[[0,2],[2,0],[0,0]],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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"}}