R0046-23996 · q-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-0046
epsilon-closed start、move後closure與accepting-subset交集規則。操作=subsetdfa-symbol-transition；資料={"states":["s20","m20","f20","e120","e220","d20"],"alphabet":["a20","b20"],"start_state":"s20","final_states":["f20"],"transitions":[["s20",null,"m20"],["s20",null,"d20"],["m20","a20","m20"],["m20","b20","f20"],["f20",null,"e120"],["e120",null,"e220"]],"subset":["s20","m20","d20"],"symbol":"a20"}。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-symbol-transition；資料={"states":["s20","m20","f20","e120","e220","d20"],"alphabet":["a20","b20"],"start_state":"s20","final_states":["f20"],"transitions":[["s20",null,"m20"],["s20",null,"d20"],["m20","a20","m20"],["m20","b20","f20"],["f20",null,"e120"],["e120",null,"e220"]],"subset":["s20","m20","d20"],"symbol":"a20"}。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-symbol-transition;original snapshot and mathematics retained
操作後
explicit ordered source output fields=[subset, symbol, symbol_targets, epsilon_closed_targets, empty_dead_state, 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=[s20, m20, f20, e120, e220, d20],alphabet=[a20, b20],start=s20;ORIGINAL transition order=[[s20, null, m20], [s20, null, d20], [m20, a20, m20], [m20, b20, f20], [f20, null, e120], [e120, null, e220]]
操作後
final set normalized UTF16=[f20];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 one-symbol transition:EXACT ORIGINAL supplied S=[d20, m20, s20];symbol=a20;ALL matching ORIGINAL edge rows=[[2, m20, m20]]
操作後
direct symbol targets=[m20];NO EPS preclosure inserted into S;now close ONLY these targets
條件：無
任意給定S未必已EPS-closed，先preclose會改本題運算；定義明示先move(S,a)再closure。empty move得到合法empty dead state。
規則：subsetdfa_GIVEN_S_symbol_move_BEFORE_closure_NO_preclose · 依賴：G001, S002
操作前
Subset DFA ORIGINAL one-symbol transition post-symbol EPS closure:stage=0;seed set=[m20];previous set=[m20]
操作後
ALL [ORIGINAL edge index,from,to,enabled] EPS rows=[[0, s20, m20, 否], [1, s20, d20, 否], [4, f20, e120, 否], [5, e120, e220, 否]];next set=[m20];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。([d20, m20, s20], a20, [m20], [m20], 否, delta_D_equals_epsilon_closure_after_symbol_move_and_empty_subset_is_a_legal_dead_state)
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: c425cea308be6a715ee5d038a4b44fa5d08197048dd26513ff8723d86ad3c8e9candidate record SHA-256: 142d59ca9e3224e6e18bb6d922f1a1e049f41e817e882980f871c6867819ca2fsemantic review receipt SHA-256: a7c0d888ade6d307703c4222c4137c78c0d2448babdcba2fa3446fe6fdd343c1question-first witness SHA-256: c9571f97a37d503ad6a61034cc00108543a05c37ef246d1c4962f55136a3de02Lean: NOT_RUN · human review: NOT_PERFORMED