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第 23901 題：NFA到DFA的子集合構造

本頁導覽
  1. 原題與已知條件
  2. 定義與適用範圍
  3. 逐步推導
  4. 逐步反向核對
  5. 結論
  6. 本題覆核與來源綁定

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← 逐題詳解目錄 · 原題批次

R0046-23901 · q-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-0051

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":["s0","m0","f0","e10","e20","d0"],"alphabet":["a0","b0"],"start_state":"s0","final_states":["f0"],"transitions":[["s0",null,"m0"],["s0",null,"d0"],["m0","a0","m0"],["m0","b0","f0"],["f0",null,"e10"],["e10",null,"e20"]],"subset":["f0","m0"]}。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":["s0","m0","f0","e10","e20","d0"],"alphabet":["a0","b0"],"start_state":"s0","final_states":["f0"],"transitions":[["s0",null,"m0"],["s0",null,"d0"],["m0","a0","m0"],["m0","b0","f0"],["f0",null,"e10"],["e10",null,"e20"]],"subset":["f0","m0"]}。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。

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=[s0, m0, f0, e10, e20, d0],alphabet=[a0, b0],start=s0;ORIGINAL transition order=[[s0, null, m0], [s0, null, d0], [m0, a0, m0], [m0, b0, f0], [f0, null, e10], [e10, null, e20]]

操作後

final set normalized UTF16=[f0];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=[f0, m0];normalized SAME-machine final set=[f0]

操作後

actual intersection=[f0];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

([f0, m0], [f0], [f0], 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: a6f495c2f1a272a3676e97fab805aef3bba91c822ef7ce2c661e79da10c3c736
  • candidate record SHA-256: e0486631fc6a0869e6295efd39e5160e43337d2766a35cde41da8d862b4edefc
  • semantic review receipt SHA-256: a7c0d888ade6d307703c4222c4137c78c0d2448babdcba2fa3446fe6fdd343c1
  • question-first witness SHA-256: c9571f97a37d503ad6a61034cc00108543a05c37ef246d1c4962f55136a3de02
  • Lean: NOT_RUN · human review: NOT_PERFORMED
同源完整 JSON