第 27388 題：正規語言Pumping引理

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-quantifier-audit；資料={"p":13,"word":["a","a","a","a","a","a","a","a","a","a","a","a","a","b"],"x_length":12,"y_length":1}。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-quantifier-audit；資料={"p":13,"word":["a","a","a","a","a","a","a","a","a","a","a","a","a","b"],"x_length":12,"y_length":1}。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

逐步推導

source roles = [pump-quantifier-audit]

derived = [[p, word, word_length, x_length, y_length, z_length, word_long_enough, xy_within_p, y_nonempty, quantifier_order]]

source roles = [13, [a, a, a, a, a, a, a, a, a, a, a, a, a, b], 12, 1]

derived = [14, 1, 是, 是, 是, exists p forall MEMBER w exists split forall i>=0]

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

(13, [a, a, a, a, a, a, a, a, a, a, a, a, a, b], 14, 12, 1, 1, 是, 是, 是, exists_p_forall_w_exists_split_forall_i)

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。