第 24767 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-recognizer-loop-boundary；資料={"states":["scan","accept","reject"],"input_alphabet":["a16","b16"],"tape_alphabet":["a16","b16","_"],"blank":"_","start_state":"scan","accept_state":"accept","reject_state":"reject","transitions":[["scan","a16","scan","a16","R"],["scan","b16","accept","b16","S"],["scan","_","scan","_","S"]],"target_symbol":"b16","input":["a16","a16"]}。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":["a16","b16"],"tape_alphabet":["a16","b16","_"],"blank":"_","start_state":"scan","accept_state":"accept","reject_state":"reject","transitions":[["scan","a16","scan","a16","R"],["scan","b16","accept","b16","S"],["scan","_","scan","_","S"]],"target_symbol":"b16","input":["a16","a16"]}。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-recognizer-loop-boundary]

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

source roles = [[scan, accept, reject], [a16, b16], [a16, b16, _], _, scan, accept, reject, [[scan, a16, scan, a16, R], [scan, b16, accept, b16, S], [scan, _, scan, _, S]]]

derived = [[accept, reject, scan], [a16, b16], [_, a16, b16], [[scan, _, scan, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]], 是]

source roles = [b16, 是, [[accept, reject, scan], [a16, b16], [_, a16, b16], _, scan, accept, reject, [[scan, _, scan, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]]]]

derived = [[[accept, reject, scan], [a16, b16], [_, a16, b16], _, scan, accept, reject, [[scan, _, scan, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]]], 是]

source roles = [[a16, a16], b16, [[scan, _, scan, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]]]

derived = [[scan, 2, [[0, a16], [1, a16]]], [scan, 2, [[0, a16], [1, a16]]], 是, 否]

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], [a16, b16], [_, a16, b16], [[scan, _, scan, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]], b16, [a16, a16], [scan, 2, [[0, a16], [1, a16]]], [scan, 2, [[0, a16], [1, a16]]], 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。