R0046-23929 · q-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-0004
epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={"states":["s3","m3","f3","e13","e23","d3"],"alphabet":["a3","b3"],"start_state":"s3","final_states":["f3"],"transitions":[["s3",null,"m3"],["s3",null,"d3"],["m3","a3","m3"],["m3","b3","f3"],["f3",null,"e13"],["e13",null,"e23"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。
G001 — epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-epsilon-start；資料={"states":["s3","m3","f3","e13","e23","d3"],"alphabet":["a3","b3"],"start_state":"s3","final_states":["f3"],"transitions":[["s3",null,"m3"],["s3",null,"d3"],["m3","a3","m3"],["m3","b3","f3"],["f3",null,"e13"],["e13",null,"e23"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。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。
操作前
source operation=subsetdfa-epsilon-start;original snapshot and mathematics retained
操作後
explicit ordered source output fields=[NFA_start, DFA_start_subset, epsilon_closed_certificate, certificate]
條件：無
保留原題介面快照，本頁直接列來源欄序，不需JavaScript。radius由原mode選6／11欄，不補欄；No與實際否定依來源責任分清。
規則：source_ordered_interface_explicit_without_javascript · 依賴：G001
操作前
ORIGINAL states=[s3, m3, f3, e13, e23, d3],alphabet=[a3, b3],start=s3;ORIGINAL transition order=[[s3, null, m3], [s3, null, d3], [m3, a3, m3], [m3, b3, f3], [f3, null, e13], [e13, null, e23]]
操作後
final set normalized UTF16=[f3];states nonempty,alphabet/finals/relation MAYEMPTY;DUPLICATE triples rejected in THIS model
條件：無
此題與前一NFA節點不同：transition triple須唯一，finals須排序。所有subset都是真carrier子集合；不偷用舊wrapper的duplicate／final-order慣例。
規則：subsetdfa_qualified_NFA_signature_DUPLICATE_edges_REJECTED_here · 依賴：G001, S001
操作前
Subset DFA ORIGINAL start:stage=0;seed set=[s3];previous set=[s3]
操作後
ALL [ORIGINAL edge index,from,to,enabled] EPS rows=[[0, s3, m3, 是], [1, s3, d3, 是], [4, f3, e13, 否], [5, e13, e23, 否]];next set=[d3, m3, s3];stable=否
條件：無
新增state都有前一層有限EPS路徑，任何含seed的EPS封閉集合都必含每層；有限states使飽和終止，得到完整且最小closure，不消耗input。
規則：subsetdfa_ALL_EPS_fixedpoint_reachability_not_input_consumption · 依賴：G001, S002
操作前
Subset DFA ORIGINAL start:stage=1;seed set=[s3];previous set=[d3, m3, s3]
操作後
ALL [ORIGINAL edge index,from,to,enabled] EPS rows=[[0, s3, m3, 是], [1, s3, d3, 是], [4, f3, e13, 否], [5, e13, e23, 否]];next set=[d3, m3, s3];stable=是
條件：無
新增state都有前一層有限EPS路徑，任何含seed的EPS封閉集合都必含每層；有限states使飽和終止，得到完整且最小closure，不消耗input。
規則：subsetdfa_ALL_EPS_fixedpoint_reachability_not_input_consumption · 依賴：G001, S003
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。(s3, [d3, m3, s3], 是, DFA_start_is_epsilon_closure_of_the_NFA_start_singleton)
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。
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。
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 59118a0d1df77a0ea8cb58e8fe55aaf8da3916815e161f781c91d5b6603ea4f8candidate record SHA-256: a885b4754575dd5d6a3088e9b232a311bbabade61a70509212e103ada60acd05semantic review receipt SHA-256: a7c0d888ade6d307703c4222c4137c78c0d2448babdcba2fa3446fe6fdd343c1question-first witness SHA-256: c9571f97a37d503ad6a61034cc00108543a05c37ef246d1c4962f55136a3de02Lean: NOT_RUN · human review: NOT_PERFORMED