# 第 23279 題：非確定有限自動機 [返回所在分頁 117](https://ocme.evemisslab.com/zh-Hant/questions/page/117/) [← 逐題詳解目錄](https://ocme.evemisslab.com/zh-Hant/questions/) · [原題批次](https://ocme.evemisslab.com/zh-Hant/practice/batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations/#q-20261014-advance-20261111-r07-nondeterministic-finite-automaton-0004) 本頁是已完成第二對話 AI 數理與中英語義覆核的教學詳解，只支持本題明示的模型與前提。沒有人工審查或新 Lean 證明，也不提升原題或 MKO 的 Canonical 真值狀態。 R0045-23279 · q-20261014-advance-20261111-r07-nondeterministic-finite-automaton-0004 ## 原題與已知條件 transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={"states":["s3","m3","f3","d3"],"alphabet":["a3","b3"],"start_state":"s3","final_states":["f3"],"transitions":[["s3",null,"m3"],["s3",null,"d3"],["m3","a3","m3"],["m3","b3","f3"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 - G001 — transition=[from,input-or-null,to]且允許empty alphabet/final set的finite epsilon-NFA。操作=nfa-qualification；資料={"states":["s3","m3","f3","d3"],"alphabet":["a3","b3"],"start_state":"s3","final_states":["f3"],"transitions":[["s3",null,"m3"],["s3",null,"d3"],["m3","a3","m3"],["m3","b3","f3"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 ## 定義與適用範圍 沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。 - [mko-nondeterministic-finite-automaton](https://ocme.evemisslab.com/zh-Hant/mko/mko-nondeterministic-finite-automaton/) ## 逐步推導 S001 · implies操作前 source operation=nfa-qualification;original snapshot and mathematics retained 操作後 explicit ordered source output fields=[states, alphabet, start, final_states, transitions, empty_target_rows, qualified, convention] 條件：無 原題快照保留歷史介面；此處直接列來源欄序，不依賴JavaScript。tag與No保聲稱範圍，固定來源排序不冒充數學證明。 步驟識別與依賴規則：source_ordered_interface_explicit_without_javascript · 依賴：G001 S002 · implies操作前 ORIGINAL transition index=0;[from,input_or_null,to]=[s3, null, m3];state carrier=[s3, m3, f3, d3];alphabet=[a3, b3] 操作後 state endpoints legal;symbol either declared input or null EPS consuming0;ORIGINAL row position retained,including duplicate rows 條件：無 這是relation不是單值total函數，duplicate／多值／缺邊皆保原資料；null消耗0但不是一個alphabet字串。 步驟識別與依賴規則：nfa_EVERY_original_relation_row_roles_empty_multi_EPS_legal · 依賴：G001, S001 S003 · implies操作前 ORIGINAL transition index=1;[from,input_or_null,to]=[s3, null, d3];state carrier=[s3, m3, f3, d3];alphabet=[a3, b3] 操作後 state endpoints legal;symbol either declared input or null EPS consuming0;ORIGINAL row position retained,including duplicate rows 條件：無 這是relation不是單值total函數，duplicate／多值／缺邊皆保原資料；null消耗0但不是一個alphabet字串。 步驟識別與依賴規則：nfa_EVERY_original_relation_row_roles_empty_multi_EPS_legal · 依賴：G001, S002 S004 · implies操作前 ORIGINAL transition index=2;[from,input_or_null,to]=[m3, a3, m3];state carrier=[s3, m3, f3, d3];alphabet=[a3, b3] 操作後 state endpoints legal;symbol either declared input or null EPS consuming0;ORIGINAL row position retained,including duplicate rows 條件：無 這是relation不是單值total函數，duplicate／多值／缺邊皆保原資料；null消耗0但不是一個alphabet字串。 步驟識別與依賴規則：nfa_EVERY_original_relation_row_roles_empty_multi_EPS_legal · 依賴：G001, S003 S005 · implies操作前 ORIGINAL transition index=3;[from,input_or_null,to]=[m3, b3, f3];state carrier=[s3, m3, f3, d3];alphabet=[a3, b3] 操作後 state endpoints legal;symbol either declared input or null EPS consuming0;ORIGINAL row position retained,including duplicate rows 條件：無 這是relation不是單值total函數，duplicate／多值／缺邊皆保原資料；null消耗0但不是一個alphabet字串。 步驟識別與依賴規則：nfa_EVERY_original_relation_row_roles_empty_multi_EPS_legal · 依賴：G001, S004 S006 · implies操作前 ORIGINAL states=[s3, m3, f3, d3],alphabet=[a3, b3],start=s3,final_states=[f3];complete relation=[[s3, null, m3], [s3, null, d3], [m3, a3, m3], [m3, b3, f3]] 操作後 states nonempty with actual start;alphabet/final set/relation MAY be EMPTY;definition qualification does NOT prove determinism,totality,DFA equivalence or a successful run 條件：無 空final set合法且辨識空語言；空alphabet也合法。定義合格不保存在accepting path，亦不推deterministic或DFA等價。 步驟識別與依賴規則：nfa_qualified_definition_EMPTY_alphabet_finals_edges_allowed · 依賴：G001, S005 S007 · implies操作前 ORIGINAL state order=[s3, m3, f3, d3];ORIGINAL alphabet order=[a3, b3];complete relation=[[s3, null, m3], [s3, null, d3], [m3, a3, m3], [m3, b3, f3]] 操作後 ALL [state,symbol,ORIGINAL-order targets] rows=[[s3, a3, []], [s3, b3, []], [m3, a3, [m3]], [m3, b3, [f3]], [f3, a3, []], [f3, b3, []], [d3, a3, []], [d3, b3, []]];EMPTY target rows=[[s3, a3, []], [s3, b3, []], [f3, a3, []], [f3, b3, []], [d3, a3, []], [d3, b3, []]];no missing edge repaired 條件：無 逐原state再原symbol列全部target，保原transition次序與重複；空target不是不合格。空alphabet時沒有這類pair，空final set亦不變成任意accept。 步驟識別與依賴規則：nfa_ORIGINAL_state_symbol_relation_targets_not_totality_assumption · 依賴：G001, S006 ## 逐步反向核對 - S007 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S006 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S005 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S004 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 ## 結論 ([s3, m3, f3, d3], [a3, b3], s3, [f3], [[s3, null, m3], [s3, null, d3], [m3, a3, m3], [m3, b3, f3]], [[s3, a3, []], [s3, b3, []], [f3, a3, []], [f3, b3, []], [d3, a3, []], [d3, b3, []]], 是, transition_relation_may_be_empty_multi_valued_and_epsilon_enabled) 依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。 ## 本題覆核與來源綁定 覆核日期：2026-10-26 原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。 來源雜湊與覆核憑證 - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: 45b0f34c341053cf9262c9436cdd210fc1f2cfe0d9b647f4f9c2ffb66c90cf16 - candidate record SHA-256: fe5ba2d7f4961ffc1436613fe46755c86bda7c970245456eb1fd397dc5e2d633 - semantic review receipt SHA-256: 357d7ad7a6726b2a757558d3b9586a408ade06526cc023da093719c292704438 - question-first witness SHA-256: 99cefe17e98c7a74321801cf72df6d02fc95b6a6b78aa335accb7e11ed467b2a - Lean: NOT_RUN · human review: NOT_PERFORMED [同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261014-advance-20261111-r07-nondeterministic-finite-automaton-0004.json)