# 第 27345 題：正規語言Pumping引理

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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。

R0053-27345 · q-20261015-advance-20261118-r07-pumping-lemma-regular-languages-0095



## 原題與已知條件

exists p forall w exists split forall i量詞與split constraints責任。操作=pump-boundary；資料={"mode":"decomposition_order","model":{"p":20,"word":["a","a","a","a","a","a","a","a","a","a","a","a","a","a","a","a","a","a","a","a","b"]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。


- G001 — exists p forall w exists split forall i量詞與split constraints責任。操作=pump-boundary；資料={"mode":"decomposition_order","model":{"p":20,"word":["a","a","a","a","a","a","a","a","a","a","a","a","a","a","a","a","a","a","a","a","b"]}}。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-pumping-lemma-regular-languages](https://ocme.evemisslab.com/zh-Hant/mko/mko-pumping-lemma-regular-languages/)





## 逐步推導

S001 · implies操作前

source roles = [pump-boundary]

操作後

derived = [[mode, p, word, legal_split_count, all_splits_obligation, preselected_split_suffices_claim]]

條件：無

此頁直接列完整來源欄序與mode特定角色，不靠JavaScript或由答案外形猜介面；No、undefined、infinity各保原意。

步驟識別與依賴規則：source_ordered_fields_without_JS · 依賴：G001





S002 · implies操作前

source roles = [decomposition_order, 20, [a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, b]]

操作後

derived = [210, all_legal_splits_must_be_addressed_not_a_preselected_decomposition, 否]

條件：無

nonregularity反證須先對任意p選member word，再對prover可選的每個合法split找到pump i；不能把split與word或i的量詞對調，也不能只攻一個預選split。

步驟識別與依賴規則：Pumping_adversarial_choice_order_AND_ALL_splits_obligation · 依賴：G001, S001









## 逐步反向核對


- S002 · premise_and_result_audit — 回查原始完整資料、步驟操作數與本步前提；有限核對、條件式定理引用與一般形式證明分開。
- S001 · premise_and_result_audit — 回查原始完整資料、步驟操作數與本步前提；有限核對、條件式定理引用與一般形式證明分開。





## 結論

(decomposition_order, 20, [a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, b], 210, all_legal_splits_must_be_addressed_not_a_preselected_decomposition, 否)

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: 3e0fd95c80d69cc37ee3c0f9c4df159fd7a63b04fef36587a72bb11f65c18f0f
- candidate record SHA-256: 636cef052c546b6bfc30e16dc1c59c72de9aa2e9ed0f5a2ba5115a151914aa31
- semantic review receipt SHA-256: 1b7a62514347b82518305d5feb4369a52d7d44c442a0f2b131e9eb3cd7b45f62
- question-first witness SHA-256: 79dc2a1077081f3ea2a03f75e32778163bf05e814cdf4c29ed86e567295f9ee1
- Lean: NOT_RUN · human review: NOT_PERFORMED

[同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261118-r07-pumping-lemma-regular-languages-0095.json)