# 第 22463 題：下推自動機 [返回所在分頁 113](https://ocme.evemisslab.com/zh-Hant/questions/page/113/) [← 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-20261110-r07-pushdown-automaton-foundations/#q-20261014-advance-20261110-r07-pushdown-automaton-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。 R0043-22463 · q-20261014-advance-20261110-r07-pushdown-automaton-0013 ## 原題與已知條件 transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push12","pop12","accept12"],"input_alphabet":["a12","b12"],"stack_alphabet":["Z12","A12"],"start_state":"push12","bottom_symbol":"Z12","final_states":["accept12"],"transitions":[["push12","a12","Z12","push12",["Z12","A12"]],["push12","a12","A12","push12",["A12","A12"]],["push12","b12","A12","pop12",[]],["pop12","b12","A12","pop12",[]],["push12",null,"Z12","accept12",["Z12"]],["pop12",null,"Z12","accept12",["Z12"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 - G001 — transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push12","pop12","accept12"],"input_alphabet":["a12","b12"],"stack_alphabet":["Z12","A12"],"start_state":"push12","bottom_symbol":"Z12","final_states":["accept12"],"transitions":[["push12","a12","Z12","push12",["Z12","A12"]],["push12","a12","A12","push12",["A12","A12"]],["push12","b12","A12","pop12",[]],["pop12","b12","A12","pop12",[]],["push12",null,"Z12","accept12",["Z12"]],["pop12",null,"Z12","accept12",["Z12"]]]}。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-pushdown-automaton](https://ocme.evemisslab.com/zh-Hant/mko/mko-pushdown-automaton/) ## 逐步推導 S001 · implies操作前 source operation=pda-qualification;original snapshot and mathematics retained 操作後 explicit ordered source output fields=[states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 條件：無 原題歷史介面標記保留，直接列來源有序欄位，不需JavaScript；MVT由原mode選欄序，不補空欄或看答案形狀猜。tag與固定No保原聲稱範圍。 步驟識別與依賴規則：source_ordered_interface_explicit_without_javascript · 依賴：G001 S002 · implies操作前 ORIGINAL transition index=0;[from,input_or_null,required_top,to,replacement_bottom_to_top]=[push12, a12, Z12, push12, [Z12, A12]];bottom=Z12 操作後 states/input/stack symbols legal;null input consumes0;top=bottom requires replacement first bottom,otherwise replacement contains NO bottom;ORIGINAL transition position retained 條件：無 逐原transition核state、input與stack角色，不把字母表混用；null是epsilon而不是一個字母。stack bottom-first/top-last，pop一個top再按原replacement順序append；只施來源明示bottom guard，不另加更強慣例。 步驟識別與依賴規則：pda_EVERY_original_transition_roles_epsilon_bottom_guard · 依賴：G001, S001 S003 · implies操作前 ORIGINAL transition index=1;[from,input_or_null,required_top,to,replacement_bottom_to_top]=[push12, a12, A12, push12, [A12, A12]];bottom=Z12 操作後 states/input/stack symbols legal;null input consumes0;top=bottom requires replacement first bottom,otherwise replacement contains NO bottom;ORIGINAL transition position retained 條件：無 逐原transition核state、input與stack角色，不把字母表混用；null是epsilon而不是一個字母。stack bottom-first/top-last，pop一個top再按原replacement順序append；只施來源明示bottom guard，不另加更強慣例。 步驟識別與依賴規則：pda_EVERY_original_transition_roles_epsilon_bottom_guard · 依賴：G001, S002 S004 · implies操作前 ORIGINAL transition index=2;[from,input_or_null,required_top,to,replacement_bottom_to_top]=[push12, b12, A12, pop12, []];bottom=Z12 操作後 states/input/stack symbols legal;null input consumes0;top=bottom requires replacement first bottom,otherwise replacement contains NO bottom;ORIGINAL transition position retained 條件：無 逐原transition核state、input與stack角色，不把字母表混用；null是epsilon而不是一個字母。stack bottom-first/top-last，pop一個top再按原replacement順序append；只施來源明示bottom guard，不另加更強慣例。 步驟識別與依賴規則：pda_EVERY_original_transition_roles_epsilon_bottom_guard · 依賴：G001, S003 S005 · implies操作前 ORIGINAL transition index=3;[from,input_or_null,required_top,to,replacement_bottom_to_top]=[pop12, b12, A12, pop12, []];bottom=Z12 操作後 states/input/stack symbols legal;null input consumes0;top=bottom requires replacement first bottom,otherwise replacement contains NO bottom;ORIGINAL transition position retained 條件：無 逐原transition核state、input與stack角色，不把字母表混用；null是epsilon而不是一個字母。stack bottom-first/top-last，pop一個top再按原replacement順序append；只施來源明示bottom guard，不另加更強慣例。 步驟識別與依賴規則：pda_EVERY_original_transition_roles_epsilon_bottom_guard · 依賴：G001, S004 S006 · implies操作前 ORIGINAL transition index=4;[from,input_or_null,required_top,to,replacement_bottom_to_top]=[push12, null, Z12, accept12, [Z12]];bottom=Z12 操作後 states/input/stack symbols legal;null input consumes0;top=bottom requires replacement first bottom,otherwise replacement contains NO bottom;ORIGINAL transition position retained 條件：無 逐原transition核state、input與stack角色，不把字母表混用；null是epsilon而不是一個字母。stack bottom-first/top-last，pop一個top再按原replacement順序append；只施來源明示bottom guard，不另加更強慣例。 步驟識別與依賴規則：pda_EVERY_original_transition_roles_epsilon_bottom_guard · 依賴：G001, S005 S007 · implies操作前 ORIGINAL transition index=5;[from,input_or_null,required_top,to,replacement_bottom_to_top]=[pop12, null, Z12, accept12, [Z12]];bottom=Z12 操作後 states/input/stack symbols legal;null input consumes0;top=bottom requires replacement first bottom,otherwise replacement contains NO bottom;ORIGINAL transition position retained 條件：無 逐原transition核state、input與stack角色，不把字母表混用；null是epsilon而不是一個字母。stack bottom-first/top-last，pop一個top再按原replacement順序append；只施來源明示bottom guard，不另加更強慣例。 步驟識別與依賴規則：pda_EVERY_original_transition_roles_epsilon_bottom_guard · 依賴：G001, S006 S008 · calculation操作前 PDA complete ORIGINAL transition count := sum(1, 1, 1, 1, 1, 1) 操作後 PDA complete ORIGINAL transition count = 6 條件：無 依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。 步驟識別與依賴規則：exact_rational_arithmetic · 依賴：G001, S007 S009 · implies操作前 ORIGINAL states=[push12, pop12, accept12],input alphabet=[a12, b12],stack alphabet=[Z12, A12];start=push12,bottom=Z12,final states=[accept12] 操作後 finite unique pairwise-disjoint alphabets qualified;transition count=6;acceptance convention FULL input in final state,NOT empty stack;qualification alone proves NO run,determinism or CFG equivalence 條件：無 有限完整定義的資格不等於存在接受run，也不推deterministic或CFG等價。接受時可保非空stack（至少bottom），但必須讀完整input到final。 步驟識別與依賴規則：pda_complete_definition_not_determinism_or_accepting_run · 依賴：G001, S008 ## 逐步反向核對 - S009 · 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。 - S008 · premise_and_result_audit — 以精確有理數重算 PDA complete ORIGINAL transition count，不以小數近似替代。 - 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。 ## 結論 ([push12, pop12, accept12], [a12, b12], [Z12, A12], push12, Z12, [accept12], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved) 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: 7de5cd716f8ea05e991899cfa9e2f8590355993e37de257d65f6bd9f6697a4a0 - candidate record SHA-256: 3989b69fc022adc364818047fedd7d17ed2bb757ae65a8af48e058101d571251 - semantic review receipt SHA-256: 49cf6ec60211c92d1c0c302663af4d44479635dc8181fb61a20c3374288e21c5 - question-first witness SHA-256: 10fd25b4643e5ff12753daceaa61f9f2499bf381f65ef96e9d21185c7c0d0c5e - Lean: NOT_RUN · human review: NOT_PERFORMED [同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261014-advance-20261110-r07-pushdown-automaton-0013.json)