# 第 21588 題：上下文無關文法 [返回所在分頁 108](https://ocme.evemisslab.com/zh-Hant/questions/page/108/) [← 逐題詳解目錄](https://ocme.evemisslab.com/zh-Hant/questions/) · [原題批次](https://ocme.evemisslab.com/zh-Hant/practice/batch-20261014-advance-20261109-r07-context-free-grammar-foundations/#q-20261014-advance-20261109-r07-context-free-grammar-0013) 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。 R0042-21588 · q-20261014-advance-20261109-r07-context-free-grammar-0013 ## 原題與已知條件 finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S12","A12"],"terminals":["a12","b12"],"start":"S12","productions":[["S12",["a12","A12"]],["A12",["b12","A12"]],["A12",[]]],"allow_epsilon":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 - G001 — finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S12","A12"],"terminals":["a12","b12"],"start":"S12","productions":[["S12",["a12","A12"]],["A12",["b12","A12"]],["A12",[]]],"allow_epsilon":true}。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-context-free-grammar](https://ocme.evemisslab.com/zh-Hant/mko/mko-context-free-grammar/) ## 逐步推導 S001 · implies操作前 source operation=cfg-qualification;original snapshot and mathematics retained 操作後 explicit ordered source output fields=[nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 條件：無 原題歷史介面標記保留，本頁直接列來源有序欄位，不需JavaScript。tag不是額外證據，固定No保留其原聲稱範圍。 步驟識別與依賴規則：source_ordered_interface_explicit_without_javascript · 依賴：G001 S002 · implies操作前 ORIGINAL production index=0;lhs=S12,rhs=[a12, A12];N=[S12, A12],T=[a12, b12],allow_epsilon=是 操作後 lhs is ONE declared nonterminal;every rhs symbol legal;empty rhs accepted ONLY under the explicit epsilon convention;original production position retained 條件：無 每條production左邊只有一個非終結符；右邊逐symbol核合法，空右邊依明示epsilon慣例。重複production位置可存在，不能排序改變首witness索引。 步驟識別與依賴規則：cfg_each_original_production_single_nonterminal_legal_rhs · 依賴：G001, S001 S003 · implies操作前 ORIGINAL production index=1;lhs=A12,rhs=[b12, A12];N=[S12, A12],T=[a12, b12],allow_epsilon=是 操作後 lhs is ONE declared nonterminal;every rhs symbol legal;empty rhs accepted ONLY under the explicit epsilon convention;original production position retained 條件：無 每條production左邊只有一個非終結符；右邊逐symbol核合法，空右邊依明示epsilon慣例。重複production位置可存在，不能排序改變首witness索引。 步驟識別與依賴規則：cfg_each_original_production_single_nonterminal_legal_rhs · 依賴：G001, S002 S004 · implies操作前 ORIGINAL production index=2;lhs=A12,rhs=[];N=[S12, A12],T=[a12, b12],allow_epsilon=是 操作後 lhs is ONE declared nonterminal;every rhs symbol legal;empty rhs accepted ONLY under the explicit epsilon convention;original production position retained 條件：無 每條production左邊只有一個非終結符；右邊逐symbol核合法，空右邊依明示epsilon慣例。重複production位置可存在，不能排序改變首witness索引。 步驟識別與依賴規則：cfg_each_original_production_single_nonterminal_legal_rhs · 依賴：G001, S003 S005 · implies操作前 ORIGINAL unique disjoint N=[S12, A12],T=[a12, b12];start=S12;complete productions=[[S12, [a12, A12]], [A12, [b12, A12]], [A12, []]];allow_epsilon=是 操作後 start belongs to nonterminals;finite grammar qualified;NO derivation,membership,regularity,unambiguity or PDA equivalence inferred 條件：無 定義合格只是文法的資格，不自動有某個word的推導，也不推regular、unambiguous等額外性質。非終結符／終結符順序保原輸入。 步驟識別與依賴規則：cfg_qualified_alphabets_start_not_language_property · 依賴：G001, S004 ## 逐步反向核對 - 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 ([S12, A12], [a12, b12], S12, [[S12, [a12, A12]], [A12, [b12, A12]], [A12, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs) 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: 31638300525162f19636c0947d0c292fbc09adaf8ffedb5bf2d1f09a00abab85 - candidate record SHA-256: 5277871102c440c45444c6d95de83f04335e18913c6e53e36f1acdf301fb975c - semantic review receipt SHA-256: dd44555041dfbb6fe9936aa00b9a5f8c5982c2784ef61dd0cbd5d1a303a49c1a - question-first witness SHA-256: 9a6011263f6ac53b9a1fd57addf2f3e2f6088b54802c539f332d689480dc2d17 - Lean: NOT_RUN · human review: NOT_PERFORMED [同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261014-advance-20261109-r07-context-free-grammar-0013.json)