OCME中英數學知識與推導English

查找相關知識與題目 →

第 24736 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

R0048-24736 · q-20261015-advance-20261113-r05-turing-machine-decision-model-0061

原題與已知條件

deterministic single-tape signature、exact configuration semantics與decider total-correctness boundary。操作=tm-global-decider-ranking；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","_","reject","_","S"]],"target_symbol":"b10"}。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-global-decider-ranking；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","_","reject","_","S"]],"target_symbol":"b10"}。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-global-decider-ranking]

操作後

derived = [[states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate]]

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, _, reject, _, S]]]

操作後

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

操作後

derived = [ANY legal w:scan head k<=|w|,first k symbols target-free,tape unchanged, scan rank=|w|-k+1;halting rank=0, nontarget R step lowers rank by1;target accept or blank reject lowers to0, EVERY word halts within |w|+1;accept iff target occurs]

條件：無

歸納任意字的scan prefix；每個非目標字元copy並R，遇target接受，抵blank拒絕。halt後rank定0才涵蓋最後一步的嚴格下降。合法input無blank，故界|w|+1；同一invariant同時證答案正確，不只是終止。

步驟識別與依賴

規則：TM_ANY_word_prefix_invariant_rank0_after_halt_bound · 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, accept, reject, [[scan, _, reject, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]], b10, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, 是, global_termination_and_answer_correctness_certificate_for_all_words)

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: 220a0549d899e3cd02c84e6a3a2bcc9ec88d7c355bd7195d9ed222459bbdcad1
  • candidate record SHA-256: 6714da336e95183469b983ddb2dce27380000e664aa3dfdf02c6c4ee08d2c58c
  • semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0
  • question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9
  • Lean: NOT_RUN · human review: NOT_PERFORMED
同源完整 JSON