# 第 24721 題：Turing機判定模型 [返回所在分頁 124](https://ocme.evemisslab.com/zh-Hant/questions/page/124/) [← 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-20261015-advance-20261113-r05-turing-machine-decision-model-foundations/#q-20261015-advance-20261113-r05-turing-machine-decision-model-0046) 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。 R0048-24721 · q-20261015-advance-20261113-r05-turing-machine-decision-model-0046 ## 原題與已知條件 deterministic single-tape signature、exact configuration semantics與decider total-correctness boundary。操作=tm-exact-step-trace；資料={"states":["q020","q120","qa20","qr20"],"input_alphabet":["020"],"tape_alphabet":["020","X20","_20"],"blank":"_20","start_state":"q020","accept_state":"qa20","reject_state":"qr20","transitions":[["q020","020","q120","X20","R"],["q020","_20","qr20","_20","S"],["q120","_20","qa20","_20","L"]],"input":["020"],"steps":2}。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-exact-step-trace；資料={"states":["q020","q120","qa20","qr20"],"input_alphabet":["020"],"tape_alphabet":["020","X20","_20"],"blank":"_20","start_state":"q020","accept_state":"qa20","reject_state":"qr20","transitions":[["q020","020","q120","X20","R"],["q020","_20","qr20","_20","S"],["q120","_20","qa20","_20","L"]],"input":["020"],"steps":2}。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-exact-step-trace] 操作後 derived = [[input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, 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 = [[q020, q120, qa20, qr20], [020], [020, X20, _20], _20, q020, qa20, qr20, [[q020, 020, q120, X20, R], [q020, _20, qr20, _20, S], [q120, _20, qa20, _20, L]]] 操作後 derived = [[q020, q120, qa20, qr20], [020], [020, X20, _20], [[q020, _20, qr20, _20, S], [q020, 020, q120, X20, R], [q120, _20, qa20, _20, L]], 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 = [[020], q020, _20] 操作後 derived = [[q020, 0, [[0, 020]]]] 條件：無 初始head0、input放0起的整數格，其餘全blank；稀疏記錄僅保非blank。tape可往負index伸展。 步驟識別與依賴規則：TM_exact_initial_configuration_blank_elsewhere · 依賴：G001, S002 S004 · calculation操作前 TM exact integer head move0 := sum(0, 1) 操作後 TM exact integer head move0 = 1 條件：無 依原始角色與已證中間量精確代值，分母先核非零，不用浮點近似。 步驟識別與依賴規則：exact_rational_arithmetic · 依賴：G001, S003 S005 · implies操作前 source roles = [0, [q020, 0, [[0, 020]]], 020, [q020, 020, q120, X20, R]] 操作後 derived = [step, [q120, 1, [[0, X20]]]] 條件：無 先在舊head寫字（blank刪格），再換state及移head；全部L/R/S按原rule，不混成停機語意。 步驟識別與依賴規則：TM_source_rule_exact_read_write_state_move · 依賴：G001, S004 S006 · calculation操作前 TM exact integer head move1 := sum(1, -1) 操作後 TM exact integer head move1 = 0 條件：無 依原始角色與已證中間量精確代值，分母先核非零，不用浮點近似。 步驟識別與依賴規則：exact_rational_arithmetic · 依賴：G001, S005 S007 · implies操作前 source roles = [1, [q120, 1, [[0, X20]]], _20, [q120, _20, qa20, _20, L]] 操作後 derived = [step, [qa20, 0, [[0, X20]]]] 條件：無 先在舊head寫字（blank刪格），再換state及移head；全部L/R/S按原rule，不混成停機語意。 步驟識別與依賴規則：TM_source_rule_exact_read_write_state_move · 依賴：G001, S006 S008 · implies操作前 source roles = [[020], 2, [[q020, 0, [[0, 020]]], [q120, 1, [[0, X20]]], [qa20, 0, [[0, X20]]]], [step, step]] 操作後 derived = [qa20, accept, 否] 條件：無 已halt才接受／拒絕；budget用盡或stuck不是普通reject，也不證永久不停止。一個input的有限trace不提供all-input decider證書。 步驟識別與依賴規則：TM_finite_trace_input_budget_scope_NOT_global_decider · 依賴：G001, S007 ## 逐步反向核對 - S008 · 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。 - 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 — 以精確有理數重算 TM exact integer head move1，不以小數近似替代。 - 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 — 以精確有理數重算 TM exact integer head move0，不以小數近似替代。 - 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 ([020], 2, [[q020, 0, [[0, 020]]], [q120, 1, [[0, X20]]], [qa20, 0, [[0, X20]]]], [step, step], qa20, accept, 否, finite_trace_is_input_local_and_does_not_certify_a_global_decider) 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: e584ba8ef5fa90ade0e329ef4716175720373c39eca34e862bdadcb8fe6e7ea0 - candidate record SHA-256: 29a15363e7fd4609870e44e5e70fade68c686ed47fb5852c46312cea46565b49 - 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-0046.json)