# 第 23932 題：NFA到DFA的子集合構造 [返回所在分頁 120](https://ocme.evemisslab.com/zh-Hant/questions/page/120/) [← 逐題詳解目錄](https://ocme.evemisslab.com/zh-Hant/questions/) · [原題批次](https://ocme.evemisslab.com/zh-Hant/practice/batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations/#q-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-0007) 本頁是已完成第二對話 AI 數理與中英語義覆核的教學詳解，只支持本題明示的模型與前提。沒有人工審查或新 Lean 證明，也不提升原題或 MKO 的 Canonical 真值狀態。 R0046-23932 · q-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-0007 ## 原題與已知條件 epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={"states":["s6","m6","f6","e16","e26","d6"],"alphabet":["a6","b6"],"start_state":"s6","final_states":["f6"],"transitions":[["s6",null,"m6"],["s6",null,"d6"],["m6","a6","m6"],["m6","b6","f6"],["f6",null,"e16"],["e16",null,"e26"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 - G001 — epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={"states":["s6","m6","f6","e16","e26","d6"],"alphabet":["a6","b6"],"start_state":"s6","final_states":["f6"],"transitions":[["s6",null,"m6"],["s6",null,"d6"],["m6","a6","m6"],["m6","b6","f6"],["f6",null,"e16"],["e16",null,"e26"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 ## 定義與適用範圍 沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。 - [mko-subset-construction-nfa-to-dfa](https://ocme.evemisslab.com/zh-Hant/mko/mko-subset-construction-nfa-to-dfa/) ## 逐步推導 S001 · implies操作前 source operation=subsetdfa-epsilon-start;original snapshot and mathematics retained 操作後 explicit ordered source output fields=[NFA_start, DFA_start_subset, epsilon_closed_certificate, certificate] 條件：無 保留原題介面快照，本頁直接列來源欄序，不需JavaScript。radius由原mode選6／11欄，不補欄；No與實際否定依來源責任分清。 步驟識別與依賴規則：source_ordered_interface_explicit_without_javascript · 依賴：G001 S002 · implies操作前 ORIGINAL states=[s6, m6, f6, e16, e26, d6],alphabet=[a6, b6],start=s6;ORIGINAL transition order=[[s6, null, m6], [s6, null, d6], [m6, a6, m6], [m6, b6, f6], [f6, null, e16], [e16, null, e26]] 操作後 final set normalized UTF16=[f6];states nonempty,alphabet/finals/relation MAYEMPTY;DUPLICATE triples rejected in THIS model 條件：無 此題與前一NFA節點不同：transition triple須唯一，finals須排序。所有subset都是真carrier子集合；不偷用舊wrapper的duplicate／final-order慣例。 步驟識別與依賴規則：subsetdfa_qualified_NFA_signature_DUPLICATE_edges_REJECTED_here · 依賴：G001, S001 S003 · implies操作前 Subset DFA ORIGINAL start:stage=0;seed set=[s6];previous set=[s6] 操作後 ALL [ORIGINAL edge index,from,to,enabled] EPS rows=[[0, s6, m6, 是], [1, s6, d6, 是], [4, f6, e16, 否], [5, e16, e26, 否]];next set=[d6, m6, s6];stable=否 條件：無 新增state都有前一層有限EPS路徑，任何含seed的EPS封閉集合都必含每層；有限states使飽和終止，得到完整且最小closure，不消耗input。 步驟識別與依賴規則：subsetdfa_ALL_EPS_fixedpoint_reachability_not_input_consumption · 依賴：G001, S002 S004 · implies操作前 Subset DFA ORIGINAL start:stage=1;seed set=[s6];previous set=[d6, m6, s6] 操作後 ALL [ORIGINAL edge index,from,to,enabled] EPS rows=[[0, s6, m6, 是], [1, s6, d6, 是], [4, f6, e16, 否], [5, e16, e26, 否]];next set=[d6, m6, s6];stable=是 條件：無 新增state都有前一層有限EPS路徑，任何含seed的EPS封閉集合都必含每層；有限states使飽和終止，得到完整且最小closure，不消耗input。 步驟識別與依賴規則：subsetdfa_ALL_EPS_fixedpoint_reachability_not_input_consumption · 依賴：G001, S003 ## 逐步反向核對 - S004 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 ## 結論 (s6, [d6, m6, s6], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton) 依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。 ## 本題覆核與來源綁定 覆核日期：2026-10-26 原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。 來源雜湊與覆核憑證 - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: 3ae714185b1e4a6d4fcf0411867441b55a94de42a75da47450d4fb572cca0404 - candidate record SHA-256: b50da2712560896de508601431f7a552e257524be10c94ee2db3156b36010a57 - semantic review receipt SHA-256: a7c0d888ade6d307703c4222c4137c78c0d2448babdcba2fa3446fe6fdd343c1 - question-first witness SHA-256: c9571f97a37d503ad6a61034cc00108543a05c37ef246d1c4962f55136a3de02 - Lean: NOT_RUN · human review: NOT_PERFORMED [同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-0007.json)