# 多對一歸約基礎 · 脈衝 R07

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261015-advance-20261115-r07-many-one-reduction-foundations · 2026-10-15 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2],"target_carrier":[0,1,2],"mapping":[0,1,null]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, null, 否]], 否, [2, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, null, 否]], 否, [2, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0001/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 2. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3],"target_carrier":[0,1,2],"mapping":[1,2,0,1]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0002/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 3. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0003/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 4. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0004/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 5. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0005/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 6. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,null]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, null, 否]], 否, [7, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, null, 否]], 否, [7, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0006/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 7. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0007/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 8. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1,2,0,1]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0008/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 9. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,0,1,2,0]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0009/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 10. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2,0,1,2]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0010/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 11. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1,2,0,1,2,0,null]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, null, 否]], 否, [12, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, null, 否]], 否, [12, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0011/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 12. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,0,1,2,0,1,2,0]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0012/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 13. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0013/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 14. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0014/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 15. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0015/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 16. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,null]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, null, 否]], 否, [17, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, null, 否]], 否, [17, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0016/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 17. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是], [16, 2, 是], [17, 0, 是], [18, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是], [16, 2, 是], [17, 0, 是], [18, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0017/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 18. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是], [17, 1, 是], [18, 2, 是], [19, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是], [17, 1, 是], [18, 2, 是], [19, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0018/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 19. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, 2, 是], [18, 0, 是], [19, 1, 是], [20, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, 2, 是], [18, 0, 是], [19, 1, 是], [20, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0019/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 20. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是], [16, 2, 是], [17, 0, 是], [18, 1, 是], [19, 2, 是], [20, 0, 是], [21, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是], [16, 2, 是], [17, 0, 是], [18, 1, 是], [19, 2, 是], [20, 0, 是], [21, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0020/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 21. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,null]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是], [17, 1, 是], [18, 2, 是], [19, 0, 是], [20, 1, 是], [21, 2, 是], [22, null, 否]], 否, [22, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是], [17, 1, 是], [18, 2, 是], [19, 0, 是], [20, 1, 是], [21, 2, 是], [22, null, 否]], 否, [22, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0021/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 22. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, 2, 是], [18, 0, 是], [19, 1, 是], [20, 2, 是], [21, 0, 是], [22, 1, 是], [23, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, 2, 是], [18, 0, 是], [19, 1, 是], [20, 2, 是], [21, 0, 是], [22, 1, 是], [23, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0022/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 23. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是], [16, 2, 是], [17, 0, 是], [18, 1, 是], [19, 2, 是], [20, 0, 是], [21, 1, 是], [22, 2, 是], [23, 0, 是], [24, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是], [16, 2, 是], [17, 0, 是], [18, 1, 是], [19, 2, 是], [20, 0, 是], [21, 1, 是], [22, 2, 是], [23, 0, 是], [24, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0023/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 24. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是], [17, 1, 是], [18, 2, 是], [19, 0, 是], [20, 1, 是], [21, 2, 是], [22, 0, 是], [23, 1, 是], [24, 2, 是], [25, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是], [17, 1, 是], [18, 2, 是], [19, 0, 是], [20, 1, 是], [21, 2, 是], [22, 0, 是], [23, 1, 是], [24, 2, 是], [25, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0024/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 25. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2]}。請依 [source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, 2, 是], [18, 0, 是], [19, 1, 是], [20, 2, 是], [21, 0, 是], [22, 1, 是], [23, 2, 是], [24, 0, 是], [25, 1, 是], [26, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)

Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, 2, 是], [18, 0, 是], [19, 1, 是], [20, 2, 是], [21, 0, 是], [22, 1, 是], [23, 2, 是], [24, 0, 是], [25, 1, 是], [26, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0025/)

多對一歸約 · qf-mod46-mreduction-total-map-qualification · candidate





## 26. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2],"target_carrier":[0,1],"source_yes":[1],"target_yes":[1],"mapping":[0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0026/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 27. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3],"target_carrier":[0,1],"source_yes":[1,3],"target_yes":[1],"mapping":[0,1,0,1]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0027/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 28. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4],"target_carrier":[0,1],"source_yes":[1,3],"target_yes":[1],"mapping":[0,1,0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0028/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 29. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5],"target_carrier":[0,1],"source_yes":[1,3,5],"target_yes":[1],"mapping":[0,1,0,1,0,1]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0029/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 30. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6],"target_carrier":[0,1],"source_yes":[1,3,5],"target_yes":[1],"mapping":[0,1,0,1,0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0030/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 31. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7],"target_carrier":[0,1],"source_yes":[1,3,5,7],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0031/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 32. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8],"target_carrier":[0,1],"source_yes":[1,3,5,7],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0032/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 33. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9],"target_carrier":[0,1],"source_yes":[1,3,5,7,9],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0033/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 34. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10],"target_carrier":[0,1],"source_yes":[1,3,5,7,9],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0034/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 35. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0035/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 36. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0036/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 37. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0037/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 38. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0038/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 39. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13, 15], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0039/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 40. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13, 15], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0040/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 41. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13, 15, 17], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0041/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 42. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13, 15, 17], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0042/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 43. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0043/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 44. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0044/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 45. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0045/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 46. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0046/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 47. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0047/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 48. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0048/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 49. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23,25],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0049/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 50. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23,25],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 [source_yes, target_yes, membership_rows, reduction, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)

Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0050/)

多對一歸約 · qf-mod46-mreduction-iff-audit · candidate





## 51. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0051/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 52. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0052/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 53. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0053/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 54. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0054/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 55. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0055/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 56. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0056/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 57. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0057/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 58. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0058/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 59. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0059/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 60. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0060/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 61. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0061/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 62. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0062/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 63. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0063/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 64. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0064/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 65. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0065/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 66. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0066/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 67. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0067/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 68. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0068/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 69. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0069/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 70. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0070/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 71. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0071/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 72. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0072/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 73. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0073/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 74. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23,25],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是], [25, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是], [25, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0074/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 75. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23,25],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 [first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate] 欄序回答。

查看答案與解釋([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是], [25, 是, 11, 是, 是], [26, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是], [25, 是, 11, 是, 是], [26, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0075/)

多對一歸約 · qf-mod46-mreduction-composition-direction · candidate





## 76. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"valid_transfer","source_carrier":[0,1,2],"target_carrier":[0,1],"source_yes":[1],"target_yes":[1],"mapping":[0,1,0],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0076/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 77. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"reverse_misuse","source_carrier":[0,1,2,3],"target_carrier":[0,1],"source_yes":[1,3],"target_yes":[1],"mapping":[0,1,0,1],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0077/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 78. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"partial_map","source_carrier":[0,1,2,3,4],"target_carrier":[0,1],"source_yes":[1,3],"target_yes":[1],"mapping":[0,1,0,1,null],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0078/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 79. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0],"target_decider":[true,false]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0079/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 80. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"valid_transfer","source_carrier":[0,1,2,3,4,5,6],"target_carrier":[0,1],"source_yes":[1,3,5],"target_yes":[1],"mapping":[0,1,0,1,0,1,0],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0080/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 81. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"reverse_misuse","source_carrier":[0,1,2,3,4,5,6,7],"target_carrier":[0,1],"source_yes":[1,3,5,7],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0081/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 82. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"partial_map","source_carrier":[0,1,2,3,4,5,6,7,8],"target_carrier":[0,1],"source_yes":[1,3,5,7],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,null],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0082/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 83. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5,6,7,8,9],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0,0,0,0,0],"target_decider":[true,false]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0083/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 84. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"valid_transfer","source_carrier":[0,1,2,3,4,5,6,7,8,9,10],"target_carrier":[0,1],"source_yes":[1,3,5,7,9],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0084/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 85. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"reverse_misuse","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0085/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 86. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"partial_map","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,null],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0086/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 87. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0,0,0,0,0,0,0,0,0],"target_decider":[true,false]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0087/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 88. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"valid_transfer","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0088/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 89. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"reverse_misuse","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0089/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 90. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"partial_map","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,null],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0090/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 91. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"target_decider":[true,false]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否], [14, 否, 0, 是, 否], [15, 否, 0, 是, 否], [16, 否, 0, 是, 否], [17, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否], [14, 否, 0, 是, 否], [15, 否, 0, 是, 否], [16, 否, 0, 是, 否], [17, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0091/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 92. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"valid_transfer","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0092/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 93. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"reverse_misuse","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0093/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 94. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"partial_map","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,null],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0094/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 95. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"target_decider":[true,false]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否], [14, 否, 0, 是, 否], [15, 否, 0, 是, 否], [16, 否, 0, 是, 否], [17, 否, 0, 是, 否], [18, 否, 0, 是, 否], [19, 否, 0, 是, 否], [20, 否, 0, 是, 否], [21, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否], [14, 否, 0, 是, 否], [15, 否, 0, 是, 否], [16, 否, 0, 是, 否], [17, 否, 0, 是, 否], [18, 否, 0, 是, 否], [19, 否, 0, 是, 否], [20, 否, 0, 是, 否], [21, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0095/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 96. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"valid_transfer","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0096/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 97. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"reverse_misuse","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0097/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 98. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"partial_map","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,null],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0098/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 99. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"target_decider":[true,false]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否], [14, 否, 0, 是, 否], [15, 否, 0, 是, 否], [16, 否, 0, 是, 否], [17, 否, 0, 是, 否], [18, 否, 0, 是, 否], [19, 否, 0, 是, 否], [20, 否, 0, 是, 否], [21, 否, 0, 是, 否], [22, 否, 0, 是, 否], [23, 否, 0, 是, 否], [24, 否, 0, 是, 否], [25, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否], [14, 否, 0, 是, 否], [15, 否, 0, 是, 否], [16, 否, 0, 是, 否], [17, 否, 0, 是, 否], [18, 否, 0, 是, 否], [19, 否, 0, 是, 否], [20, 否, 0, 是, 否], [21, 否, 0, 是, 否], [22, 否, 0, 是, 否], [23, 否, 0, 是, 否], [24, 否, 0, 是, 否], [25, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0099/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate





## 100. 多對一歸約

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"valid_transfer","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23,25],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"target_decider":[false,true]}。請依 [mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary] 欄序回答。

四種mode同為11欄；reverse_misuse可有正確constructed A decider，但requested_forward_transfer_certificate仍否，因正在拒絕反向用途。partial map的constructed為null，非空表。有限表不證無限可計算性。

查看答案與解釋(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)

Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r07-many-one-reduction-0100/)

多對一歸約 · qf-mod46-mreduction-decider-transfer-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261115-r07-many-one-reduction-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261115-r07-many-one-reduction-foundations/validation-report.json)