第 24737 題：Turing機判定模型

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":["a11","b11"],"tape_alphabet":["a11","b11","_"],"blank":"_","start_state":"scan","accept_state":"accept","reject_state":"reject","transitions":[["scan","a11","scan","a11","R"],["scan","b11","accept","b11","S"],["scan","_","reject","_","S"]],"target_symbol":"b11"}。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":["a11","b11"],"tape_alphabet":["a11","b11","_"],"blank":"_","start_state":"scan","accept_state":"accept","reject_state":"reject","transitions":[["scan","a11","scan","a11","R"],["scan","b11","accept","b11","S"],["scan","_","reject","_","S"]],"target_symbol":"b11"}。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

逐步推導

source roles = [tm-global-decider-ranking]

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

source roles = [[scan, accept, reject], [a11, b11], [a11, b11, _], _, scan, accept, reject, [[scan, a11, scan, a11, R], [scan, b11, accept, b11, S], [scan, _, reject, _, S]]]

derived = [[accept, reject, scan], [a11, b11], [_, a11, b11], [[scan, _, reject, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]], 是]

source roles = [b11, 否, [[accept, reject, scan], [a11, b11], [_, a11, b11], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]]]]

derived = [[[accept, reject, scan], [a11, b11], [_, a11, b11], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]]], 是]

source roles = [b11, [a11, b11], [[scan, _, reject, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]]]

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]

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], [a11, b11], [_, a11, b11], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]], b11, 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。