# 第 23911 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-0061) 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。 R0046-23911 · q-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-0061 ## 原題與已知條件 epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-accepting-subset；資料={"states":["s10","m10","f10","e110","e210","d10"],"alphabet":["a10","b10"],"start_state":"s10","final_states":["f10"],"transitions":[["s10",null,"m10"],["s10",null,"d10"],["m10","a10","m10"],["m10","b10","f10"],["f10",null,"e110"],["e110",null,"e210"]],"subset":["f10","m10"]}。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-accepting-subset；資料={"states":["s10","m10","f10","e110","e210","d10"],"alphabet":["a10","b10"],"start_state":"s10","final_states":["f10"],"transitions":[["s10",null,"m10"],["s10",null,"d10"],["m10","a10","m10"],["m10","b10","f10"],["f10",null,"e110"],["e110",null,"e210"]],"subset":["f10","m10"]}。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-accepting-subset;original snapshot and mathematics retained 操作後 explicit ordered source output fields=[subset, NFA_final_states, intersection, accepting_subset, 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=[s10, m10, f10, e110, e210, d10],alphabet=[a10, b10],start=s10;ORIGINAL transition order=[[s10, null, m10], [s10, null, d10], [m10, a10, m10], [m10, b10, f10], [f10, null, e110], [e110, null, e210]] 操作後 final set normalized UTF16=[f10];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 EXACT ORIGINAL supplied S=[f10, m10];normalized SAME-machine final set=[f10] 操作後 actual intersection=[f10];accepting_subset=是;NO EPS closure inserted 條件：無 這是DFA接受subset的定義，不改為從任意未closed S出發的NFA空字接受判定；empty subset是合法rejecting dead state。 步驟識別與依賴規則：subsetdfa_EXACT_given_subset_final_intersection_NO_hidden_closure · 依賴：G001, S002 ## 逐步反向核對 - 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 ([f10, m10], [f10], [f10], 是, DFA_subset_accepts_exactly_when_it_intersects_the_NFA_final_set) 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: 23f566cf28a3f4af4ce490926987eaef8259c204bf768db7a5b7d876fb5800fd - candidate record SHA-256: 8e431d7ec70bf40de24469e7d10b62574cbc67927e42df1db5a02f9c8ef7429f - 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-0061.json)