OCME中英數學知識與推導English

查找相關知識與題目 →

第 24763 題：Turing機判定模型

本頁導覽
  1. 原題與已知條件
  2. 定義與適用範圍
  3. 逐步推導
  4. 逐步反向核對
  5. 結論
  6. 本題覆核與來源綁定

返回所在分頁 124

← 逐題詳解目錄 · 原題批次

R0048-24763 · q-20261015-advance-20261113-r05-turing-machine-decision-model-0088

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":["a12","b12"],"tape_alphabet":["a12","b12","_"],"blank":"_","start_state":"scan","accept_state":"accept","reject_state":"reject","transitions":[["scan","a12","scan","a12","R"],["scan","b12","accept","b12","S"],["scan","_","scan","_","S"]],"target_symbol":"b12","input":["a12","a12"]}。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":["a12","b12"],"tape_alphabet":["a12","b12","_"],"blank":"_","start_state":"scan","accept_state":"accept","reject_state":"reject","transitions":[["scan","a12","scan","a12","R"],["scan","b12","accept","b12","S"],["scan","_","scan","_","S"]],"target_symbol":"b12","input":["a12","a12"]}。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。

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], [a12, b12], [a12, b12, _], _, scan, accept, reject, [[scan, a12, scan, a12, R], [scan, b12, accept, b12, S], [scan, _, scan, _, S]]]

操作後

derived = [[accept, reject, scan], [a12, b12], [_, a12, b12], [[scan, _, scan, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, 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 = [b12, 是, [[accept, reject, scan], [a12, b12], [_, a12, b12], _, scan, accept, reject, [[scan, _, scan, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, S]]]]

操作後

derived = [[[accept, reject, scan], [a12, b12], [_, a12, b12], _, scan, accept, reject, [[scan, _, scan, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, 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 = [[a12, a12], b12, [[scan, _, scan, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, S]]]

操作後

derived = [[scan, 2, [[0, a12], [1, a12]]], [scan, 2, [[0, a12], [1, a12]]], 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], [a12, b12], [_, a12, b12], [[scan, _, scan, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, S]], b12, [a12, a12], [scan, 2, [[0, a12], [1, a12]]], [scan, 2, [[0, a12], [1, a12]]], 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: 923fe9ab6e5759d2680580dfa80c8032d1064dd80a714e4c33a767c5a3b21808
  • candidate record SHA-256: 54d544015bd24a9f633efbef883e970e807d96c9b94f0803b7e1453ede99cb57
  • semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0
  • question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9
  • Lean: NOT_RUN · human review: NOT_PERFORMED
同源完整 JSON