R0042-21592 · q-20261014-advance-20261109-r07-context-free-grammar-0017
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S16","A16"],"terminals":["a16","b16"],"start":"S16","productions":[["S16",["a16","A16"]],["A16",["b16","A16"]],["A16",[]]],"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":["S16","A16"],"terminals":["a16","b16"],"start":"S16","productions":[["S16",["a16","A16"]],["A16",["b16","A16"]],["A16",[]]],"allow_epsilon":true}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。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。
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。
規則：source_ordered_interface_explicit_without_javascript · 依賴：G001
操作前
ORIGINAL production index=0;lhs=S16,rhs=[a16, A16];N=[S16, A16],T=[a16, b16],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。
規則：cfg_each_original_production_single_nonterminal_legal_rhs · 依賴：G001, S001
操作前
ORIGINAL production index=1;lhs=A16,rhs=[b16, A16];N=[S16, A16],T=[a16, b16],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。
規則：cfg_each_original_production_single_nonterminal_legal_rhs · 依賴：G001, S002
操作前
ORIGINAL production index=2;lhs=A16,rhs=[];N=[S16, A16],T=[a16, b16],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。
規則：cfg_each_original_production_single_nonterminal_legal_rhs · 依賴：G001, S003
操作前
ORIGINAL unique disjoint N=[S16, A16],T=[a16, b16];start=S16;complete productions=[[S16, [a16, A16]], [A16, [b16, A16]], [A16, []]];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。
規則：cfg_qualified_alphabets_start_not_language_property · 依賴：G001, S004
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。([S16, A16], [a16, b16], S16, [[S16, [a16, A16]], [A16, [b16, A16]], [A16, []]], 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。
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。
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 04eb811b62ce7ae6f2b1577998f5c33896da7f2200a59bf2ad4d711d6cf9b8cdcandidate record SHA-256: 8b8924ddaae79f80a2c090a56ad5611c373fae20ea06db786000b9e0a7dea3fcsemantic review receipt SHA-256: dd44555041dfbb6fe9936aa00b9a5f8c5982c2784ef61dd0cbd5d1a303a49c1aquestion-first witness SHA-256: 9a6011263f6ac53b9a1fd57addf2f3e2f6088b54802c539f332d689480dc2d17Lean: NOT_RUN · human review: NOT_PERFORMED