第 23903 題：NFA到DFA的子集合構造

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":["s2","m2","f2","e12","e22","d2"],"alphabet":["a2","b2"],"start_state":"s2","final_states":["f2"],"transitions":[["s2",null,"m2"],["s2",null,"d2"],["m2","a2","m2"],["m2","b2","f2"],["f2",null,"e12"],["e12",null,"e22"]],"subset":["f2","m2"]}。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":["s2","m2","f2","e12","e22","d2"],"alphabet":["a2","b2"],"start_state":"s2","final_states":["f2"],"transitions":[["s2",null,"m2"],["s2",null,"d2"],["m2","a2","m2"],["m2","b2","f2"],["f2",null,"e12"],["e12",null,"e22"]],"subset":["f2","m2"]}。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

逐步推導

source operation=subsetdfa-accepting-subset;original snapshot and mathematics retained

explicit ordered source output fields=[subset, NFA_final_states, intersection, accepting_subset, certificate]

ORIGINAL states=[s2, m2, f2, e12, e22, d2],alphabet=[a2, b2],start=s2;ORIGINAL transition order=[[s2, null, m2], [s2, null, d2], [m2, a2, m2], [m2, b2, f2], [f2, null, e12], [e12, null, e22]]

final set normalized UTF16=[f2];states nonempty,alphabet/finals/relation MAYEMPTY;DUPLICATE triples rejected in THIS model

EXACT ORIGINAL supplied S=[f2, m2];normalized SAME-machine final set=[f2]

actual intersection=[f2];accepting_subset=是;NO EPS closure inserted

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

([f2, m2], [f2], [f2], 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。