# 第 22472 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-0022) 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。 R0043-22472 · q-20261014-advance-20261110-r07-pushdown-automaton-0022 ## 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":["push21","pop21","accept21"],"input_alphabet":["a21","b21"],"stack_alphabet":["Z21","A21"],"start_state":"push21","bottom_symbol":"Z21","final_states":["accept21"],"transitions":[["push21","a21","Z21","push21",["Z21","A21"]],["push21","a21","A21","push21",["A21","A21"]],["push21","b21","A21","pop21",[]],["pop21","b21","A21","pop21",[]],["push21",null,"Z21","accept21",["Z21"]],["pop21",null,"Z21","accept21",["Z21"]]]}。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":["push21","pop21","accept21"],"input_alphabet":["a21","b21"],"stack_alphabet":["Z21","A21"],"start_state":"push21","bottom_symbol":"Z21","final_states":["accept21"],"transitions":[["push21","a21","Z21","push21",["Z21","A21"]],["push21","a21","A21","push21",["A21","A21"]],["push21","b21","A21","pop21",[]],["pop21","b21","A21","pop21",[]],["push21",null,"Z21","accept21",["Z21"]],["pop21",null,"Z21","accept21",["Z21"]]]}。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]=[push21, a21, Z21, push21, [Z21, A21]];bottom=Z21 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]=[push21, a21, A21, push21, [A21, A21]];bottom=Z21 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]=[push21, b21, A21, pop21, []];bottom=Z21 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]=[pop21, b21, A21, pop21, []];bottom=Z21 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]=[push21, null, Z21, accept21, [Z21]];bottom=Z21 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]=[pop21, null, Z21, accept21, [Z21]];bottom=Z21 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=[push21, pop21, accept21],input alphabet=[a21, b21],stack alphabet=[Z21, A21];start=push21,bottom=Z21,final states=[accept21] 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 ([push21, pop21, accept21], [a21, b21], [Z21, A21], push21, Z21, [accept21], 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: 8039d2d1803bc7f3cf295237c41ca3f2929afbae250fbbed7dd78c23d2ec7e20 - candidate record SHA-256: 9cf9964433753a641b56c6d1d795631865b0eaca7b1e45aaeb87e09dffc72677 - 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-0022.json)