# 第 24761 題：Turing機判定模型

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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。

R0048-24761 · q-20261015-advance-20261113-r05-turing-machine-decision-model-0086



## 原題與已知條件

deterministic single-tape signature、exact configuration semantics與decider total-correctness boundary。操作=tm-recognizer-loop-boundary；資料={"states":["scan","accept","reject"],"input_alphabet":["a10","b10"],"tape_alphabet":["a10","b10","_"],"blank":"_","start_state":"scan","accept_state":"accept","reject_state":"reject","transitions":[["scan","a10","scan","a10","R"],["scan","b10","accept","b10","S"],["scan","_","scan","_","S"]],"target_symbol":"b10","input":["a10","a10"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。


- G001 — deterministic single-tape signature、exact configuration semantics與decider total-correctness boundary。操作=tm-recognizer-loop-boundary；資料={"states":["scan","accept","reject"],"input_alphabet":["a10","b10"],"tape_alphabet":["a10","b10","_"],"blank":"_","start_state":"scan","accept_state":"accept","reject_state":"reject","transitions":[["scan","a10","scan","a10","R"],["scan","b10","accept","b10","S"],["scan","_","scan","_","S"]],"target_symbol":"b10","input":["a10","a10"]}。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-turing-machine-decision-model](https://ocme.evemisslab.com/zh-Hant/mko/mko-turing-machine-decision-model/)





## 逐步推導

S001 · implies操作前

source roles = [tm-recognizer-loop-boundary]

操作後

derived = [[states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary]]

條件：無

直接列來源完整欄序，不需JavaScript；原題、布林旗標、數學物件與非聲稱保持分層。

步驟識別與依賴規則：source_ordered_fields_without_JS · 依賴：G001





S002 · implies操作前

source roles = [[scan, accept, reject], [a10, b10], [a10, b10, _], _, scan, accept, reject, [[scan, a10, scan, a10, R], [scan, b10, accept, b10, S], [scan, _, scan, _, S]]]

操作後

derived = [[accept, reject, scan], [a10, b10], [_, a10, b10], [[scan, _, scan, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]], 是]

條件：無

三個清單皆非空且唯一；input是blank-free tape子集，但state與字母標籤不要求不相交。每個(from,read)的來源NUL-joined key唯一、halt無出邊。partial table合法，不補reject規則；canonical transition序與UTF16集合序分開。

步驟識別與依賴規則：TM_complete_signature_partial_transition_table_allowed · 依賴：G001, S001





S003 · implies操作前

source roles = [b10, 是, [[accept, reject, scan], [a10, b10], [_, a10, b10], _, scan, accept, reject, [[scan, _, scan, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]]]]

操作後

derived = [[[accept, reject, scan], [a10, b10], [_, a10, b10], _, scan, accept, reject, [[scan, _, scan, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]]], 是]

條件：無

要整個signature與所有transition符合指定schema，不能由幾個成功trace給任意TM全域證書。

步驟識別與依賴規則：TM_EXACT_canonical_scan_schema_not_sampled_machine · 依賴：G001, S002





S004 · implies操作前

source roles = [[a10, a10], b10, [[scan, _, scan, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]]]

操作後

derived = [[scan, 2, [[0, a10], [1, a10]]], [scan, 2, [[0, a10], [1, a10]]], 是, 否]

條件：無

逐input的非目標字元copy/R可達head=|w|的blank；scan/blank規則寫blank、S、仍scan，整個configuration精確重複。決定性使此input永遠loop，這才反證此recognizer是decider，不靠有限budget未停。

步驟識別與依賴規則：TM_actual_target_free_input_reaches_EXACT_blank_SELFLOOP · 依賴：G001, S003









## 逐步反向核對


- 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

([accept, reject, scan], [a10, b10], [_, a10, b10], [[scan, _, scan, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]], b10, [a10, a10], [scan, 2, [[0, a10], [1, a10]]], [scan, 2, [[0, a10], [1, a10]]], 是, 否, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)

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: 95de256b3255234c753ac24b3402400ea50df2c4748afc48a022ebdb7a03bd7a
- candidate record SHA-256: 29db2477745f41c157cc717cd63a7564f1b837dc6db984373082a024897bc4b3
- semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0
- question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9
- Lean: NOT_RUN · human review: NOT_PERFORMED

[同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261113-r05-turing-machine-decision-model-0086.json)