R0042-21507 · q-20261014-advance-20261109-r07-context-free-grammar-0082
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S6","A6"],"terminals":["a6","b6"],"start":"S6","productions":[["S6",["a6","A6"]],["A6",["b6","A6"]],["A6",[]]],"allow_epsilon":true,"word":["a6","b6","b6"],"max_steps":1}。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-bounded-search-boundary；資料={"nonterminals":["S6","A6"],"terminals":["a6","b6"],"start":"S6","productions":[["S6",["a6","A6"]],["A6",["b6","A6"]],["A6",[]]],"allow_epsilon":true,"word":["a6","b6","b6"],"max_steps":1}。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-bounded-search-boundary;original snapshot and mathematics retained
操作後
explicit ordered source output fields=[word, max_steps, found_in_bounded_search, nonmembership_claim, boundary]
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=S6,rhs=[a6, A6];N=[S6, A6],T=[a6, b6],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=A6,rhs=[b6, A6];N=[S6, A6],T=[a6, b6],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=A6,rhs=[];N=[S6, A6],T=[a6, b6],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=[S6, A6],T=[a6, b6];start=S6;complete productions=[[S6, [a6, A6]], [A6, [b6, A6]], [A6, []]];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
操作前
ORIGINAL target form=[a6, b6, b6];start=S6;max_steps=1;length cap=5
操作後
initial depth0 frontier=[[S6]];target already found=否;form equality itself does NOT require terminal-only target
條件：無
這是來源指定的深度／長度有限搜尋，不是一般文法判定器；depth0也要核精確形式相等。若target含非終結符，找到形式仍不等於word成員證書。
規則：cfg_bounded_search_initial_exact_form_not_terminal_membership · 依賴：G001, S005
操作前
ORIGINAL depth=0;ALL frontier forms=[[S6]];length cap=5
操作後
ALL [from,position,production_index,next,target_equal,within_cap] transitions=[[[S6], 0, 0, [a6, A6], 否, 是]];next distinct frontier=[[a6, A6]];any hit=否
條件：無
每層列出全部可用production替換，只在同層去重；先核是否等target，再按來源length cap保留後續形式。展示排序只讓集合可讀，不更動原production索引或found的存在性。
規則：cfg_every_bounded_frontier_expansion_and_length_filter · 依賴：G001, S006
操作前
ORIGINAL target=[a6, b6, b6],depth bound=1;bounded found=否
操作後
nonmembership_claim fixed No whether found or not;longer or excluded derivations have NOT been ruled out
條件：無
no-hit只排除本次明示深度與長度限制內的路徑；除非另有完整性界，不能說word不在language。found若是terminal字串才另有成員意義，也不推unambiguous。
規則：cfg_bounded_nohit_never_nonmembership_claim · 依賴：G001, S007
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。([a6, b6, b6], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
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: bbbfb18eebcc780c4c96b551690c59c1aae0526f20625abbc649107781a13418candidate record SHA-256: 7518fdaa27f7bb86856ce8d3a329789c7b0dba19a0abe84a315b98159b93ded5semantic review receipt SHA-256: dd44555041dfbb6fe9936aa00b9a5f8c5982c2784ef61dd0cbd5d1a303a49c1aquestion-first witness SHA-256: 9a6011263f6ac53b9a1fd57addf2f3e2f6088b54802c539f332d689480dc2d17Lean: NOT_RUN · human review: NOT_PERFORMED