# 第 23941 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-0016) 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。 R0046-23941 · q-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-0016 ## 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":["s15","m15","f15","e115","e215","d15"],"alphabet":["a15","b15"],"start_state":"s15","final_states":["f15"],"transitions":[["s15",null,"m15"],["s15",null,"d15"],["m15","a15","m15"],["m15","b15","f15"],["f15",null,"e115"],["e115",null,"e215"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 - G001 — epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={"states":["s15","m15","f15","e115","e215","d15"],"alphabet":["a15","b15"],"start_state":"s15","final_states":["f15"],"transitions":[["s15",null,"m15"],["s15",null,"d15"],["m15","a15","m15"],["m15","b15","f15"],["f15",null,"e115"],["e115",null,"e215"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 ## 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=[s15, m15, f15, e115, e215, d15],alphabet=[a15, b15],start=s15;ORIGINAL transition order=[[s15, null, m15], [s15, null, d15], [m15, a15, m15], [m15, b15, f15], [f15, null, e115], [e115, null, e215]] 操作後 final set normalized UTF16=[f15];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=[s15];previous set=[s15] 操作後 ALL [ORIGINAL edge index,from,to,enabled] EPS rows=[[0, s15, m15, 是], [1, s15, d15, 是], [4, f15, e115, 否], [5, e115, e215, 否]];next set=[d15, m15, s15];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=[s15];previous set=[d15, m15, s15] 操作後 ALL [ORIGINAL edge index,from,to,enabled] EPS rows=[[0, s15, m15, 是], [1, s15, d15, 是], [4, f15, e115, 否], [5, e115, e215, 否]];next set=[d15, m15, s15];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 (s15, [d15, m15, s15], 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: 3af046dc8db837db38ac5c3e1944bce9131aaedc35759e74bab02aa45d220019 - candidate record SHA-256: 6abe7eabee3892db77000fb3ac179332fb029f478224dd5d563499c554cb9d35 - 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-0016.json)