# 第 23981 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-0031) 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。 R0046-23981 · q-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-0031 ## 原題與已知條件 epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={"states":["s5","m5","f5","e15","e25","d5"],"alphabet":["a5","b5"],"start_state":"s5","final_states":["f5"],"transitions":[["s5",null,"m5"],["s5",null,"d5"],["m5","a5","m5"],["m5","b5","f5"],["f5",null,"e15"],["e15",null,"e25"]],"subset":["s5","m5","d5"],"symbol":"b5"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 - G001 — epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={"states":["s5","m5","f5","e15","e25","d5"],"alphabet":["a5","b5"],"start_state":"s5","final_states":["f5"],"transitions":[["s5",null,"m5"],["s5",null,"d5"],["m5","a5","m5"],["m5","b5","f5"],["f5",null,"e15"],["e15",null,"e25"]],"subset":["s5","m5","d5"],"symbol":"b5"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 ## 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-symbol-transition;original snapshot and mathematics retained 操作後 explicit ordered source output fields=[subset, symbol, symbol_targets, epsilon_closed_targets, empty_dead_state, 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=[s5, m5, f5, e15, e25, d5],alphabet=[a5, b5],start=s5;ORIGINAL transition order=[[s5, null, m5], [s5, null, d5], [m5, a5, m5], [m5, b5, f5], [f5, null, e15], [e15, null, e25]] 操作後 final set normalized UTF16=[f5];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 one-symbol transition:EXACT ORIGINAL supplied S=[d5, m5, s5];symbol=b5;ALL matching ORIGINAL edge rows=[[3, m5, f5]] 操作後 direct symbol targets=[f5];NO EPS preclosure inserted into S;now close ONLY these targets 條件：無 任意給定S未必已EPS-closed，先preclose會改本題運算；定義明示先move(S,a)再closure。empty move得到合法empty dead state。 步驟識別與依賴規則：subsetdfa_GIVEN_S_symbol_move_BEFORE_closure_NO_preclose · 依賴：G001, S002 S004 · implies操作前 Subset DFA ORIGINAL one-symbol transition post-symbol EPS closure:stage=0;seed set=[f5];previous set=[f5] 操作後 ALL [ORIGINAL edge index,from,to,enabled] EPS rows=[[0, s5, m5, 否], [1, s5, d5, 否], [4, f5, e15, 是], [5, e15, e25, 否]];next set=[e15, f5];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, S003 S005 · implies操作前 Subset DFA ORIGINAL one-symbol transition post-symbol EPS closure:stage=1;seed set=[f5];previous set=[e15, f5] 操作後 ALL [ORIGINAL edge index,from,to,enabled] EPS rows=[[0, s5, m5, 否], [1, s5, d5, 否], [4, f5, e15, 是], [5, e15, e25, 是]];next set=[e15, e25, f5];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, S004 S006 · implies操作前 Subset DFA ORIGINAL one-symbol transition post-symbol EPS closure:stage=2;seed set=[f5];previous set=[e15, e25, f5] 操作後 ALL [ORIGINAL edge index,from,to,enabled] EPS rows=[[0, s5, m5, 否], [1, s5, d5, 否], [4, f5, e15, 是], [5, e15, e25, 是]];next set=[e15, e25, f5];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, S005 ## 逐步反向核對 - S006 · 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。 - S005 · 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。 - 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 ([d5, m5, s5], b5, [f5], [e15, e25, f5], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state) 依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: 23ef8a53fa8c2b40ba84430ec7828c1a1ad467eae651095ef790fc0bd9c063b4 - candidate record SHA-256: 4b81bf63de0ad3907058a03a553006b6e2195663f87d20f3e8e61deb961fd07f - 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-0031.json)