第 17202 題：正規語言

原題與已知條件

完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={"alphabet_count":2,"words":[[0],[1,1,0,0,0,0]],"probe":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 欄序回答。

• G001 — 完整DFA總轉移與任意word invariant或明示有限語言構造。操作=regular-finite-language-construction；資料={"alphabet_count":2,"words":[[0],[1,1,0,0,0,0]],"probe":[0]}。請依 [prefix_states,dead_state,accepting,transition,probe,trace,accepted,certificate] 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-regular-language

逐步推導

DECLARED complete nonempty duplicate-free word FAMILY=[[0], [1, 1, 0, 0, 0, 0]];alphabet Fin(2)

all prefixes including empty sorted by length then source JSON order=[[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 0], [1, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0]];dead state appended index=8

prefix state=0;represented prefix=[];next symbol=0;extended word=[0]

extension is declared prefix=是;next state=1

prefix state=0;represented prefix=[];next symbol=1;extended word=[1]

extension is declared prefix=是;next state=2

prefix state=1;represented prefix=[0];next symbol=0;extended word=[0, 0]

extension is declared prefix=否;next state=8

prefix state=1;represented prefix=[0];next symbol=1;extended word=[0, 1]

extension is declared prefix=否;next state=8

prefix state=2;represented prefix=[1];next symbol=0;extended word=[1, 0]

extension is declared prefix=否;next state=8

prefix state=2;represented prefix=[1];next symbol=1;extended word=[1, 1]

extension is declared prefix=是;next state=3

prefix state=3;represented prefix=[1, 1];next symbol=0;extended word=[1, 1, 0]

extension is declared prefix=是;next state=4

prefix state=3;represented prefix=[1, 1];next symbol=1;extended word=[1, 1, 1]

extension is declared prefix=否;next state=8

prefix state=4;represented prefix=[1, 1, 0];next symbol=0;extended word=[1, 1, 0, 0]

extension is declared prefix=是;next state=5

prefix state=4;represented prefix=[1, 1, 0];next symbol=1;extended word=[1, 1, 0, 1]

extension is declared prefix=否;next state=8

prefix state=5;represented prefix=[1, 1, 0, 0];next symbol=0;extended word=[1, 1, 0, 0, 0]

extension is declared prefix=是;next state=6

prefix state=5;represented prefix=[1, 1, 0, 0];next symbol=1;extended word=[1, 1, 0, 0, 1]

extension is declared prefix=否;next state=8

prefix state=6;represented prefix=[1, 1, 0, 0, 0];next symbol=0;extended word=[1, 1, 0, 0, 0, 0]

extension is declared prefix=是;next state=7

prefix state=6;represented prefix=[1, 1, 0, 0, 0];next symbol=1;extended word=[1, 1, 0, 0, 0, 1]

extension is declared prefix=否;next state=8

prefix state=7;represented prefix=[1, 1, 0, 0, 0, 0];next symbol=0;extended word=[1, 1, 0, 0, 0, 0, 0]

extension is declared prefix=否;next state=8

prefix state=7;represented prefix=[1, 1, 0, 0, 0, 0];next symbol=1;extended word=[1, 1, 0, 0, 0, 0, 1]

extension is declared prefix=否;next state=8

dead state=8;all alphabet symbols Fin(2);full supplied words=[[0], [1, 1, 0, 0, 0, 0]]

dead loops row=[8, 8];accepting prefix-state indices=[1, 7];complete table=[[1, 2], [8, 8], [8, 3], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8], [8, 8]]

same complete prefix-state table and full word family=[[0], [1, 1, 0, 0, 0, 0]];start state0 represents empty prefix

for EVERY finite input prefix,its state is that exact prefix index if present,otherwise dead;prefix extension closure and dead absorption preserve this by induction;accepted iff input is one FULL supplied word

finite-language probe:original ordered word=[0];start=0

trace before consuming symbols=[0]

finite-language probe:word position=0;symbol=0;current state=0;complete original row=[1, 2]

next state=1;ordered prefix trace=[0, 1]

original probe=[0];final state=1;accepting indices=[1, 7]

probe accepted=是;separate all-word construction certificate retained

逐步反向核對

• S022 · 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。
• S021 · 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。
• S020 · 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。
• S019 · 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。
• S018 · 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。
• S017 · 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。
• S016 · 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。
• S015 · 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。
• S014 · 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。
• S013 · 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。
• S012 · 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。
• S011 · 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。
• S010 · 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。
• S009 · 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。
• S008 · 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。
• S007 · 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。
• 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

([[], [0], [1], [1, 1], [1, 1, 0], [1, 1, 0, 0], [1, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0]], 8, [1, 7], [[1, 2], [8, 8], [8, 3], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8], [8, 8]], [0], [0, 1], 是, explicit_DFA_recognizes_exact_finite_language)

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。