# 第 23285 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-0010) 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。 R0045-23285 · q-20261014-advance-20261111-r07-nondeterministic-finite-automaton-0010 ## 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":["s9","m9","f9","d9"],"alphabet":["a9","b9"],"start_state":"s9","final_states":["f9"],"transitions":[["s9",null,"m9"],["s9",null,"d9"],["m9","a9","m9"],["m9","b9","f9"]]}。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":["s9","m9","f9","d9"],"alphabet":["a9","b9"],"start_state":"s9","final_states":["f9"],"transitions":[["s9",null,"m9"],["s9",null,"d9"],["m9","a9","m9"],["m9","b9","f9"]]}。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]=[s9, null, m9];state carrier=[s9, m9, f9, d9];alphabet=[a9, b9] 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]=[s9, null, d9];state carrier=[s9, m9, f9, d9];alphabet=[a9, b9] 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]=[m9, a9, m9];state carrier=[s9, m9, f9, d9];alphabet=[a9, b9] 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]=[m9, b9, f9];state carrier=[s9, m9, f9, d9];alphabet=[a9, b9] 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=[s9, m9, f9, d9],alphabet=[a9, b9],start=s9,final_states=[f9];complete relation=[[s9, null, m9], [s9, null, d9], [m9, a9, m9], [m9, b9, f9]] 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=[s9, m9, f9, d9];ORIGINAL alphabet order=[a9, b9];complete relation=[[s9, null, m9], [s9, null, d9], [m9, a9, m9], [m9, b9, f9]] 操作後 ALL [state,symbol,ORIGINAL-order targets] rows=[[s9, a9, []], [s9, b9, []], [m9, a9, [m9]], [m9, b9, [f9]], [f9, a9, []], [f9, b9, []], [d9, a9, []], [d9, b9, []]];EMPTY target rows=[[s9, a9, []], [s9, b9, []], [f9, a9, []], [f9, b9, []], [d9, a9, []], [d9, b9, []]];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 ([s9, m9, f9, d9], [a9, b9], s9, [f9], [[s9, null, m9], [s9, null, d9], [m9, a9, m9], [m9, b9, f9]], [[s9, a9, []], [s9, b9, []], [f9, a9, []], [f9, b9, []], [d9, a9, []], [d9, b9, []]], 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: 1152cdfc72c2345ffc334b4f9c39ea23d4171b3a1776ad51850bb027b01d72ae - candidate record SHA-256: 6a32290299618b2250ee3fbe93f176437b5811b3fab771c01aa9e0a5d5ccc68e - 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-0010.json)