下推自動機基礎 · 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-20261014-advance-20261110-r07-pushdown-automaton-foundations · 2026-10-14 · 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
1. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push0","pop0","accept0"],"input_alphabet":["a0","b0"],"stack_alphabet":["Z0","A0"],"start_state":"push0","bottom_symbol":"Z0","final_states":["accept0"],"transitions":[["push0","a0","Z0","push0",["Z0","A0"]],["push0","a0","A0","push0",["A0","A0"]],["push0","b0","A0","pop0",[]],["pop0","b0","A0","pop0",[]],["push0",null,"Z0","accept0",["Z0"]],["pop0",null,"Z0","accept0",["Z0"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push0, pop0, accept0], [a0, b0], [Z0, A0], push0, Z0, [accept0], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push0, pop0, accept0], [a0, b0], [Z0, A0], push0, Z0, [accept0], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
2. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push1","pop1","accept1"],"input_alphabet":["a1","b1"],"stack_alphabet":["Z1","A1"],"start_state":"push1","bottom_symbol":"Z1","final_states":["accept1"],"transitions":[["push1","a1","Z1","push1",["Z1","A1"]],["push1","a1","A1","push1",["A1","A1"]],["push1","b1","A1","pop1",[]],["pop1","b1","A1","pop1",[]],["push1",null,"Z1","accept1",["Z1"]],["pop1",null,"Z1","accept1",["Z1"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push1, pop1, accept1], [a1, b1], [Z1, A1], push1, Z1, [accept1], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push1, pop1, accept1], [a1, b1], [Z1, A1], push1, Z1, [accept1], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
3. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push2","pop2","accept2"],"input_alphabet":["a2","b2"],"stack_alphabet":["Z2","A2"],"start_state":"push2","bottom_symbol":"Z2","final_states":["accept2"],"transitions":[["push2","a2","Z2","push2",["Z2","A2"]],["push2","a2","A2","push2",["A2","A2"]],["push2","b2","A2","pop2",[]],["pop2","b2","A2","pop2",[]],["push2",null,"Z2","accept2",["Z2"]],["pop2",null,"Z2","accept2",["Z2"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push2, pop2, accept2], [a2, b2], [Z2, A2], push2, Z2, [accept2], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push2, pop2, accept2], [a2, b2], [Z2, A2], push2, Z2, [accept2], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
4. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push3","pop3","accept3"],"input_alphabet":["a3","b3"],"stack_alphabet":["Z3","A3"],"start_state":"push3","bottom_symbol":"Z3","final_states":["accept3"],"transitions":[["push3","a3","Z3","push3",["Z3","A3"]],["push3","a3","A3","push3",["A3","A3"]],["push3","b3","A3","pop3",[]],["pop3","b3","A3","pop3",[]],["push3",null,"Z3","accept3",["Z3"]],["pop3",null,"Z3","accept3",["Z3"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push3, pop3, accept3], [a3, b3], [Z3, A3], push3, Z3, [accept3], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push3, pop3, accept3], [a3, b3], [Z3, A3], push3, Z3, [accept3], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
5. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push4","pop4","accept4"],"input_alphabet":["a4","b4"],"stack_alphabet":["Z4","A4"],"start_state":"push4","bottom_symbol":"Z4","final_states":["accept4"],"transitions":[["push4","a4","Z4","push4",["Z4","A4"]],["push4","a4","A4","push4",["A4","A4"]],["push4","b4","A4","pop4",[]],["pop4","b4","A4","pop4",[]],["push4",null,"Z4","accept4",["Z4"]],["pop4",null,"Z4","accept4",["Z4"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push4, pop4, accept4], [a4, b4], [Z4, A4], push4, Z4, [accept4], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push4, pop4, accept4], [a4, b4], [Z4, A4], push4, Z4, [accept4], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
6. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push5","pop5","accept5"],"input_alphabet":["a5","b5"],"stack_alphabet":["Z5","A5"],"start_state":"push5","bottom_symbol":"Z5","final_states":["accept5"],"transitions":[["push5","a5","Z5","push5",["Z5","A5"]],["push5","a5","A5","push5",["A5","A5"]],["push5","b5","A5","pop5",[]],["pop5","b5","A5","pop5",[]],["push5",null,"Z5","accept5",["Z5"]],["pop5",null,"Z5","accept5",["Z5"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push5, pop5, accept5], [a5, b5], [Z5, A5], push5, Z5, [accept5], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push5, pop5, accept5], [a5, b5], [Z5, A5], push5, Z5, [accept5], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
7. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push6","pop6","accept6"],"input_alphabet":["a6","b6"],"stack_alphabet":["Z6","A6"],"start_state":"push6","bottom_symbol":"Z6","final_states":["accept6"],"transitions":[["push6","a6","Z6","push6",["Z6","A6"]],["push6","a6","A6","push6",["A6","A6"]],["push6","b6","A6","pop6",[]],["pop6","b6","A6","pop6",[]],["push6",null,"Z6","accept6",["Z6"]],["pop6",null,"Z6","accept6",["Z6"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push6, pop6, accept6], [a6, b6], [Z6, A6], push6, Z6, [accept6], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push6, pop6, accept6], [a6, b6], [Z6, A6], push6, Z6, [accept6], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
8. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push7","pop7","accept7"],"input_alphabet":["a7","b7"],"stack_alphabet":["Z7","A7"],"start_state":"push7","bottom_symbol":"Z7","final_states":["accept7"],"transitions":[["push7","a7","Z7","push7",["Z7","A7"]],["push7","a7","A7","push7",["A7","A7"]],["push7","b7","A7","pop7",[]],["pop7","b7","A7","pop7",[]],["push7",null,"Z7","accept7",["Z7"]],["pop7",null,"Z7","accept7",["Z7"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push7, pop7, accept7], [a7, b7], [Z7, A7], push7, Z7, [accept7], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push7, pop7, accept7], [a7, b7], [Z7, A7], push7, Z7, [accept7], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
9. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push8","pop8","accept8"],"input_alphabet":["a8","b8"],"stack_alphabet":["Z8","A8"],"start_state":"push8","bottom_symbol":"Z8","final_states":["accept8"],"transitions":[["push8","a8","Z8","push8",["Z8","A8"]],["push8","a8","A8","push8",["A8","A8"]],["push8","b8","A8","pop8",[]],["pop8","b8","A8","pop8",[]],["push8",null,"Z8","accept8",["Z8"]],["pop8",null,"Z8","accept8",["Z8"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push8, pop8, accept8], [a8, b8], [Z8, A8], push8, Z8, [accept8], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push8, pop8, accept8], [a8, b8], [Z8, A8], push8, Z8, [accept8], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
10. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push9","pop9","accept9"],"input_alphabet":["a9","b9"],"stack_alphabet":["Z9","A9"],"start_state":"push9","bottom_symbol":"Z9","final_states":["accept9"],"transitions":[["push9","a9","Z9","push9",["Z9","A9"]],["push9","a9","A9","push9",["A9","A9"]],["push9","b9","A9","pop9",[]],["pop9","b9","A9","pop9",[]],["push9",null,"Z9","accept9",["Z9"]],["pop9",null,"Z9","accept9",["Z9"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push9, pop9, accept9], [a9, b9], [Z9, A9], push9, Z9, [accept9], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push9, pop9, accept9], [a9, b9], [Z9, A9], push9, Z9, [accept9], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
11. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push10","pop10","accept10"],"input_alphabet":["a10","b10"],"stack_alphabet":["Z10","A10"],"start_state":"push10","bottom_symbol":"Z10","final_states":["accept10"],"transitions":[["push10","a10","Z10","push10",["Z10","A10"]],["push10","a10","A10","push10",["A10","A10"]],["push10","b10","A10","pop10",[]],["pop10","b10","A10","pop10",[]],["push10",null,"Z10","accept10",["Z10"]],["pop10",null,"Z10","accept10",["Z10"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push10, pop10, accept10], [a10, b10], [Z10, A10], push10, Z10, [accept10], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push10, pop10, accept10], [a10, b10], [Z10, A10], push10, Z10, [accept10], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
12. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push11","pop11","accept11"],"input_alphabet":["a11","b11"],"stack_alphabet":["Z11","A11"],"start_state":"push11","bottom_symbol":"Z11","final_states":["accept11"],"transitions":[["push11","a11","Z11","push11",["Z11","A11"]],["push11","a11","A11","push11",["A11","A11"]],["push11","b11","A11","pop11",[]],["pop11","b11","A11","pop11",[]],["push11",null,"Z11","accept11",["Z11"]],["pop11",null,"Z11","accept11",["Z11"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push11, pop11, accept11], [a11, b11], [Z11, A11], push11, Z11, [accept11], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push11, pop11, accept11], [a11, b11], [Z11, A11], push11, Z11, [accept11], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
13. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push12","pop12","accept12"],"input_alphabet":["a12","b12"],"stack_alphabet":["Z12","A12"],"start_state":"push12","bottom_symbol":"Z12","final_states":["accept12"],"transitions":[["push12","a12","Z12","push12",["Z12","A12"]],["push12","a12","A12","push12",["A12","A12"]],["push12","b12","A12","pop12",[]],["pop12","b12","A12","pop12",[]],["push12",null,"Z12","accept12",["Z12"]],["pop12",null,"Z12","accept12",["Z12"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push12, pop12, accept12], [a12, b12], [Z12, A12], push12, Z12, [accept12], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push12, pop12, accept12], [a12, b12], [Z12, A12], push12, Z12, [accept12], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
14. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push13","pop13","accept13"],"input_alphabet":["a13","b13"],"stack_alphabet":["Z13","A13"],"start_state":"push13","bottom_symbol":"Z13","final_states":["accept13"],"transitions":[["push13","a13","Z13","push13",["Z13","A13"]],["push13","a13","A13","push13",["A13","A13"]],["push13","b13","A13","pop13",[]],["pop13","b13","A13","pop13",[]],["push13",null,"Z13","accept13",["Z13"]],["pop13",null,"Z13","accept13",["Z13"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push13, pop13, accept13], [a13, b13], [Z13, A13], push13, Z13, [accept13], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push13, pop13, accept13], [a13, b13], [Z13, A13], push13, Z13, [accept13], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
15. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push14","pop14","accept14"],"input_alphabet":["a14","b14"],"stack_alphabet":["Z14","A14"],"start_state":"push14","bottom_symbol":"Z14","final_states":["accept14"],"transitions":[["push14","a14","Z14","push14",["Z14","A14"]],["push14","a14","A14","push14",["A14","A14"]],["push14","b14","A14","pop14",[]],["pop14","b14","A14","pop14",[]],["push14",null,"Z14","accept14",["Z14"]],["pop14",null,"Z14","accept14",["Z14"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push14, pop14, accept14], [a14, b14], [Z14, A14], push14, Z14, [accept14], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push14, pop14, accept14], [a14, b14], [Z14, A14], push14, Z14, [accept14], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
16. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push15","pop15","accept15"],"input_alphabet":["a15","b15"],"stack_alphabet":["Z15","A15"],"start_state":"push15","bottom_symbol":"Z15","final_states":["accept15"],"transitions":[["push15","a15","Z15","push15",["Z15","A15"]],["push15","a15","A15","push15",["A15","A15"]],["push15","b15","A15","pop15",[]],["pop15","b15","A15","pop15",[]],["push15",null,"Z15","accept15",["Z15"]],["pop15",null,"Z15","accept15",["Z15"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push15, pop15, accept15], [a15, b15], [Z15, A15], push15, Z15, [accept15], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push15, pop15, accept15], [a15, b15], [Z15, A15], push15, Z15, [accept15], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
17. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push16","pop16","accept16"],"input_alphabet":["a16","b16"],"stack_alphabet":["Z16","A16"],"start_state":"push16","bottom_symbol":"Z16","final_states":["accept16"],"transitions":[["push16","a16","Z16","push16",["Z16","A16"]],["push16","a16","A16","push16",["A16","A16"]],["push16","b16","A16","pop16",[]],["pop16","b16","A16","pop16",[]],["push16",null,"Z16","accept16",["Z16"]],["pop16",null,"Z16","accept16",["Z16"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push16, pop16, accept16], [a16, b16], [Z16, A16], push16, Z16, [accept16], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push16, pop16, accept16], [a16, b16], [Z16, A16], push16, Z16, [accept16], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
18. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push17","pop17","accept17"],"input_alphabet":["a17","b17"],"stack_alphabet":["Z17","A17"],"start_state":"push17","bottom_symbol":"Z17","final_states":["accept17"],"transitions":[["push17","a17","Z17","push17",["Z17","A17"]],["push17","a17","A17","push17",["A17","A17"]],["push17","b17","A17","pop17",[]],["pop17","b17","A17","pop17",[]],["push17",null,"Z17","accept17",["Z17"]],["pop17",null,"Z17","accept17",["Z17"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push17, pop17, accept17], [a17, b17], [Z17, A17], push17, Z17, [accept17], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push17, pop17, accept17], [a17, b17], [Z17, A17], push17, Z17, [accept17], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
19. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push18","pop18","accept18"],"input_alphabet":["a18","b18"],"stack_alphabet":["Z18","A18"],"start_state":"push18","bottom_symbol":"Z18","final_states":["accept18"],"transitions":[["push18","a18","Z18","push18",["Z18","A18"]],["push18","a18","A18","push18",["A18","A18"]],["push18","b18","A18","pop18",[]],["pop18","b18","A18","pop18",[]],["push18",null,"Z18","accept18",["Z18"]],["pop18",null,"Z18","accept18",["Z18"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push18, pop18, accept18], [a18, b18], [Z18, A18], push18, Z18, [accept18], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push18, pop18, accept18], [a18, b18], [Z18, A18], push18, Z18, [accept18], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
20. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push19","pop19","accept19"],"input_alphabet":["a19","b19"],"stack_alphabet":["Z19","A19"],"start_state":"push19","bottom_symbol":"Z19","final_states":["accept19"],"transitions":[["push19","a19","Z19","push19",["Z19","A19"]],["push19","a19","A19","push19",["A19","A19"]],["push19","b19","A19","pop19",[]],["pop19","b19","A19","pop19",[]],["push19",null,"Z19","accept19",["Z19"]],["pop19",null,"Z19","accept19",["Z19"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push19, pop19, accept19], [a19, b19], [Z19, A19], push19, Z19, [accept19], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push19, pop19, accept19], [a19, b19], [Z19, A19], push19, Z19, [accept19], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
21. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push20","pop20","accept20"],"input_alphabet":["a20","b20"],"stack_alphabet":["Z20","A20"],"start_state":"push20","bottom_symbol":"Z20","final_states":["accept20"],"transitions":[["push20","a20","Z20","push20",["Z20","A20"]],["push20","a20","A20","push20",["A20","A20"]],["push20","b20","A20","pop20",[]],["pop20","b20","A20","pop20",[]],["push20",null,"Z20","accept20",["Z20"]],["pop20",null,"Z20","accept20",["Z20"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push20, pop20, accept20], [a20, b20], [Z20, A20], push20, Z20, [accept20], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push20, pop20, accept20], [a20, b20], [Z20, A20], push20, Z20, [accept20], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
22. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push21","pop21","accept21"],"input_alphabet":["a21","b21"],"stack_alphabet":["Z21","A21"],"start_state":"push21","bottom_symbol":"Z21","final_states":["accept21"],"transitions":[["push21","a21","Z21","push21",["Z21","A21"]],["push21","a21","A21","push21",["A21","A21"]],["push21","b21","A21","pop21",[]],["pop21","b21","A21","pop21",[]],["push21",null,"Z21","accept21",["Z21"]],["pop21",null,"Z21","accept21",["Z21"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push21, pop21, accept21], [a21, b21], [Z21, A21], push21, Z21, [accept21], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push21, pop21, accept21], [a21, b21], [Z21, A21], push21, Z21, [accept21], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
23. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push22","pop22","accept22"],"input_alphabet":["a22","b22"],"stack_alphabet":["Z22","A22"],"start_state":"push22","bottom_symbol":"Z22","final_states":["accept22"],"transitions":[["push22","a22","Z22","push22",["Z22","A22"]],["push22","a22","A22","push22",["A22","A22"]],["push22","b22","A22","pop22",[]],["pop22","b22","A22","pop22",[]],["push22",null,"Z22","accept22",["Z22"]],["pop22",null,"Z22","accept22",["Z22"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push22, pop22, accept22], [a22, b22], [Z22, A22], push22, Z22, [accept22], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push22, pop22, accept22], [a22, b22], [Z22, A22], push22, Z22, [accept22], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
24. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push23","pop23","accept23"],"input_alphabet":["a23","b23"],"stack_alphabet":["Z23","A23"],"start_state":"push23","bottom_symbol":"Z23","final_states":["accept23"],"transitions":[["push23","a23","Z23","push23",["Z23","A23"]],["push23","a23","A23","push23",["A23","A23"]],["push23","b23","A23","pop23",[]],["pop23","b23","A23","pop23",[]],["push23",null,"Z23","accept23",["Z23"]],["pop23",null,"Z23","accept23",["Z23"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push23, pop23, accept23], [a23, b23], [Z23, A23], push23, Z23, [accept23], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push23, pop23, accept23], [a23, b23], [Z23, A23], push23, Z23, [accept23], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
25. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={"states":["push24","pop24","accept24"],"input_alphabet":["a24","b24"],"stack_alphabet":["Z24","A24"],"start_state":"push24","bottom_symbol":"Z24","final_states":["accept24"],"transitions":[["push24","a24","Z24","push24",["Z24","A24"]],["push24","a24","A24","push24",["A24","A24"]],["push24","b24","A24","pop24",[]],["pop24","b24","A24","pop24",[]],["push24",null,"Z24","accept24",["Z24"]],["pop24",null,"Z24","accept24",["Z24"]]]}。請依 [states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention] 欄序回答。
查看答案與解釋
([push24, pop24, accept24], [a24, b24], [Z24, A24], push24, Z24, [accept24], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)
Wave6第四層核對=([push24, pop24, accept24], [a24, b24], [Z24, A24], push24, Z24, [accept24], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-qualification · candidate
26. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push0","pop0","accept0"],"input_alphabet":["a0","b0"],"stack_alphabet":["Z0","A0"],"start_state":"push0","bottom_symbol":"Z0","final_states":["accept0"],"transitions":[["push0","a0","Z0","push0",["Z0","A0"]],["push0","a0","A0","push0",["A0","A0"]],["push0","b0","A0","pop0",[]],["pop0","b0","A0","pop0",[]],["push0",null,"Z0","accept0",["Z0"]],["pop0",null,"Z0","accept0",["Z0"]]],"input":[],"trace":[["push0",0,["Z0"]],["accept0",0,["Z0"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([], [[push0, 0, [Z0]], [accept0, 0, [Z0]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([], [[push0, 0, [Z0]], [accept0, 0, [Z0]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
27. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push1","pop1","accept1"],"input_alphabet":["a1","b1"],"stack_alphabet":["Z1","A1"],"start_state":"push1","bottom_symbol":"Z1","final_states":["accept1"],"transitions":[["push1","a1","Z1","push1",["Z1","A1"]],["push1","a1","A1","push1",["A1","A1"]],["push1","b1","A1","pop1",[]],["pop1","b1","A1","pop1",[]],["push1",null,"Z1","accept1",["Z1"]],["pop1",null,"Z1","accept1",["Z1"]]],"input":["a1","b1"],"trace":[["push1",0,["Z1"]],["push1",1,["Z1","A1"]],["pop1",2,["Z1"]],["accept1",2,["Z1"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a1, b1], [[push1, 0, [Z1]], [push1, 1, [Z1, A1]], [pop1, 2, [Z1]], [accept1, 2, [Z1]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a1, b1], [[push1, 0, [Z1]], [push1, 1, [Z1, A1]], [pop1, 2, [Z1]], [accept1, 2, [Z1]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
28. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push2","pop2","accept2"],"input_alphabet":["a2","b2"],"stack_alphabet":["Z2","A2"],"start_state":"push2","bottom_symbol":"Z2","final_states":["accept2"],"transitions":[["push2","a2","Z2","push2",["Z2","A2"]],["push2","a2","A2","push2",["A2","A2"]],["push2","b2","A2","pop2",[]],["pop2","b2","A2","pop2",[]],["push2",null,"Z2","accept2",["Z2"]],["pop2",null,"Z2","accept2",["Z2"]]],"input":["a2","a2","b2","b2"],"trace":[["push2",0,["Z2"]],["push2",1,["Z2","A2"]],["push2",2,["Z2","A2","A2"]],["pop2",3,["Z2","A2"]],["pop2",4,["Z2"]],["accept2",4,["Z2"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a2, a2, b2, b2], [[push2, 0, [Z2]], [push2, 1, [Z2, A2]], [push2, 2, [Z2, A2, A2]], [pop2, 3, [Z2, A2]], [pop2, 4, [Z2]], [accept2, 4, [Z2]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a2, a2, b2, b2], [[push2, 0, [Z2]], [push2, 1, [Z2, A2]], [push2, 2, [Z2, A2, A2]], [pop2, 3, [Z2, A2]], [pop2, 4, [Z2]], [accept2, 4, [Z2]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
29. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push3","pop3","accept3"],"input_alphabet":["a3","b3"],"stack_alphabet":["Z3","A3"],"start_state":"push3","bottom_symbol":"Z3","final_states":["accept3"],"transitions":[["push3","a3","Z3","push3",["Z3","A3"]],["push3","a3","A3","push3",["A3","A3"]],["push3","b3","A3","pop3",[]],["pop3","b3","A3","pop3",[]],["push3",null,"Z3","accept3",["Z3"]],["pop3",null,"Z3","accept3",["Z3"]]],"input":["a3","a3","a3","b3","b3","b3"],"trace":[["push3",0,["Z3"]],["push3",1,["Z3","A3"]],["push3",2,["Z3","A3","A3"]],["push3",3,["Z3","A3","A3","A3"]],["pop3",4,["Z3","A3","A3"]],["pop3",5,["Z3","A3"]],["pop3",6,["Z3"]],["accept3",6,["Z3"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a3, a3, a3, b3, b3, b3], [[push3, 0, [Z3]], [push3, 1, [Z3, A3]], [push3, 2, [Z3, A3, A3]], [push3, 3, [Z3, A3, A3, A3]], [pop3, 4, [Z3, A3, A3]], [pop3, 5, [Z3, A3]], [pop3, 6, [Z3]], [accept3, 6, [Z3]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a3, a3, a3, b3, b3, b3], [[push3, 0, [Z3]], [push3, 1, [Z3, A3]], [push3, 2, [Z3, A3, A3]], [push3, 3, [Z3, A3, A3, A3]], [pop3, 4, [Z3, A3, A3]], [pop3, 5, [Z3, A3]], [pop3, 6, [Z3]], [accept3, 6, [Z3]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
30. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push4","pop4","accept4"],"input_alphabet":["a4","b4"],"stack_alphabet":["Z4","A4"],"start_state":"push4","bottom_symbol":"Z4","final_states":["accept4"],"transitions":[["push4","a4","Z4","push4",["Z4","A4"]],["push4","a4","A4","push4",["A4","A4"]],["push4","b4","A4","pop4",[]],["pop4","b4","A4","pop4",[]],["push4",null,"Z4","accept4",["Z4"]],["pop4",null,"Z4","accept4",["Z4"]]],"input":[],"trace":[["push4",0,["Z4"]],["accept4",0,["Z4"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([], [[push4, 0, [Z4]], [accept4, 0, [Z4]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([], [[push4, 0, [Z4]], [accept4, 0, [Z4]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
31. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push5","pop5","accept5"],"input_alphabet":["a5","b5"],"stack_alphabet":["Z5","A5"],"start_state":"push5","bottom_symbol":"Z5","final_states":["accept5"],"transitions":[["push5","a5","Z5","push5",["Z5","A5"]],["push5","a5","A5","push5",["A5","A5"]],["push5","b5","A5","pop5",[]],["pop5","b5","A5","pop5",[]],["push5",null,"Z5","accept5",["Z5"]],["pop5",null,"Z5","accept5",["Z5"]]],"input":["a5","b5"],"trace":[["push5",0,["Z5"]],["push5",1,["Z5","A5"]],["pop5",2,["Z5"]],["accept5",2,["Z5"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a5, b5], [[push5, 0, [Z5]], [push5, 1, [Z5, A5]], [pop5, 2, [Z5]], [accept5, 2, [Z5]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a5, b5], [[push5, 0, [Z5]], [push5, 1, [Z5, A5]], [pop5, 2, [Z5]], [accept5, 2, [Z5]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
32. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push6","pop6","accept6"],"input_alphabet":["a6","b6"],"stack_alphabet":["Z6","A6"],"start_state":"push6","bottom_symbol":"Z6","final_states":["accept6"],"transitions":[["push6","a6","Z6","push6",["Z6","A6"]],["push6","a6","A6","push6",["A6","A6"]],["push6","b6","A6","pop6",[]],["pop6","b6","A6","pop6",[]],["push6",null,"Z6","accept6",["Z6"]],["pop6",null,"Z6","accept6",["Z6"]]],"input":["a6","a6","b6","b6"],"trace":[["push6",0,["Z6"]],["push6",1,["Z6","A6"]],["push6",2,["Z6","A6","A6"]],["pop6",3,["Z6","A6"]],["pop6",4,["Z6"]],["accept6",4,["Z6"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a6, a6, b6, b6], [[push6, 0, [Z6]], [push6, 1, [Z6, A6]], [push6, 2, [Z6, A6, A6]], [pop6, 3, [Z6, A6]], [pop6, 4, [Z6]], [accept6, 4, [Z6]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a6, a6, b6, b6], [[push6, 0, [Z6]], [push6, 1, [Z6, A6]], [push6, 2, [Z6, A6, A6]], [pop6, 3, [Z6, A6]], [pop6, 4, [Z6]], [accept6, 4, [Z6]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
33. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push7","pop7","accept7"],"input_alphabet":["a7","b7"],"stack_alphabet":["Z7","A7"],"start_state":"push7","bottom_symbol":"Z7","final_states":["accept7"],"transitions":[["push7","a7","Z7","push7",["Z7","A7"]],["push7","a7","A7","push7",["A7","A7"]],["push7","b7","A7","pop7",[]],["pop7","b7","A7","pop7",[]],["push7",null,"Z7","accept7",["Z7"]],["pop7",null,"Z7","accept7",["Z7"]]],"input":["a7","a7","a7","b7","b7","b7"],"trace":[["push7",0,["Z7"]],["push7",1,["Z7","A7"]],["push7",2,["Z7","A7","A7"]],["push7",3,["Z7","A7","A7","A7"]],["pop7",4,["Z7","A7","A7"]],["pop7",5,["Z7","A7"]],["pop7",6,["Z7"]],["accept7",6,["Z7"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a7, a7, a7, b7, b7, b7], [[push7, 0, [Z7]], [push7, 1, [Z7, A7]], [push7, 2, [Z7, A7, A7]], [push7, 3, [Z7, A7, A7, A7]], [pop7, 4, [Z7, A7, A7]], [pop7, 5, [Z7, A7]], [pop7, 6, [Z7]], [accept7, 6, [Z7]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a7, a7, a7, b7, b7, b7], [[push7, 0, [Z7]], [push7, 1, [Z7, A7]], [push7, 2, [Z7, A7, A7]], [push7, 3, [Z7, A7, A7, A7]], [pop7, 4, [Z7, A7, A7]], [pop7, 5, [Z7, A7]], [pop7, 6, [Z7]], [accept7, 6, [Z7]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
34. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push8","pop8","accept8"],"input_alphabet":["a8","b8"],"stack_alphabet":["Z8","A8"],"start_state":"push8","bottom_symbol":"Z8","final_states":["accept8"],"transitions":[["push8","a8","Z8","push8",["Z8","A8"]],["push8","a8","A8","push8",["A8","A8"]],["push8","b8","A8","pop8",[]],["pop8","b8","A8","pop8",[]],["push8",null,"Z8","accept8",["Z8"]],["pop8",null,"Z8","accept8",["Z8"]]],"input":[],"trace":[["push8",0,["Z8"]],["accept8",0,["Z8"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([], [[push8, 0, [Z8]], [accept8, 0, [Z8]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([], [[push8, 0, [Z8]], [accept8, 0, [Z8]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
35. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push9","pop9","accept9"],"input_alphabet":["a9","b9"],"stack_alphabet":["Z9","A9"],"start_state":"push9","bottom_symbol":"Z9","final_states":["accept9"],"transitions":[["push9","a9","Z9","push9",["Z9","A9"]],["push9","a9","A9","push9",["A9","A9"]],["push9","b9","A9","pop9",[]],["pop9","b9","A9","pop9",[]],["push9",null,"Z9","accept9",["Z9"]],["pop9",null,"Z9","accept9",["Z9"]]],"input":["a9","b9"],"trace":[["push9",0,["Z9"]],["push9",1,["Z9","A9"]],["pop9",2,["Z9"]],["accept9",2,["Z9"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a9, b9], [[push9, 0, [Z9]], [push9, 1, [Z9, A9]], [pop9, 2, [Z9]], [accept9, 2, [Z9]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a9, b9], [[push9, 0, [Z9]], [push9, 1, [Z9, A9]], [pop9, 2, [Z9]], [accept9, 2, [Z9]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
36. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push10","pop10","accept10"],"input_alphabet":["a10","b10"],"stack_alphabet":["Z10","A10"],"start_state":"push10","bottom_symbol":"Z10","final_states":["accept10"],"transitions":[["push10","a10","Z10","push10",["Z10","A10"]],["push10","a10","A10","push10",["A10","A10"]],["push10","b10","A10","pop10",[]],["pop10","b10","A10","pop10",[]],["push10",null,"Z10","accept10",["Z10"]],["pop10",null,"Z10","accept10",["Z10"]]],"input":["a10","a10","b10","b10"],"trace":[["push10",0,["Z10"]],["push10",1,["Z10","A10"]],["push10",2,["Z10","A10","A10"]],["pop10",3,["Z10","A10"]],["pop10",4,["Z10"]],["accept10",4,["Z10"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a10, a10, b10, b10], [[push10, 0, [Z10]], [push10, 1, [Z10, A10]], [push10, 2, [Z10, A10, A10]], [pop10, 3, [Z10, A10]], [pop10, 4, [Z10]], [accept10, 4, [Z10]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a10, a10, b10, b10], [[push10, 0, [Z10]], [push10, 1, [Z10, A10]], [push10, 2, [Z10, A10, A10]], [pop10, 3, [Z10, A10]], [pop10, 4, [Z10]], [accept10, 4, [Z10]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
37. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push11","pop11","accept11"],"input_alphabet":["a11","b11"],"stack_alphabet":["Z11","A11"],"start_state":"push11","bottom_symbol":"Z11","final_states":["accept11"],"transitions":[["push11","a11","Z11","push11",["Z11","A11"]],["push11","a11","A11","push11",["A11","A11"]],["push11","b11","A11","pop11",[]],["pop11","b11","A11","pop11",[]],["push11",null,"Z11","accept11",["Z11"]],["pop11",null,"Z11","accept11",["Z11"]]],"input":["a11","a11","a11","b11","b11","b11"],"trace":[["push11",0,["Z11"]],["push11",1,["Z11","A11"]],["push11",2,["Z11","A11","A11"]],["push11",3,["Z11","A11","A11","A11"]],["pop11",4,["Z11","A11","A11"]],["pop11",5,["Z11","A11"]],["pop11",6,["Z11"]],["accept11",6,["Z11"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a11, a11, a11, b11, b11, b11], [[push11, 0, [Z11]], [push11, 1, [Z11, A11]], [push11, 2, [Z11, A11, A11]], [push11, 3, [Z11, A11, A11, A11]], [pop11, 4, [Z11, A11, A11]], [pop11, 5, [Z11, A11]], [pop11, 6, [Z11]], [accept11, 6, [Z11]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a11, a11, a11, b11, b11, b11], [[push11, 0, [Z11]], [push11, 1, [Z11, A11]], [push11, 2, [Z11, A11, A11]], [push11, 3, [Z11, A11, A11, A11]], [pop11, 4, [Z11, A11, A11]], [pop11, 5, [Z11, A11]], [pop11, 6, [Z11]], [accept11, 6, [Z11]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
38. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push12","pop12","accept12"],"input_alphabet":["a12","b12"],"stack_alphabet":["Z12","A12"],"start_state":"push12","bottom_symbol":"Z12","final_states":["accept12"],"transitions":[["push12","a12","Z12","push12",["Z12","A12"]],["push12","a12","A12","push12",["A12","A12"]],["push12","b12","A12","pop12",[]],["pop12","b12","A12","pop12",[]],["push12",null,"Z12","accept12",["Z12"]],["pop12",null,"Z12","accept12",["Z12"]]],"input":[],"trace":[["push12",0,["Z12"]],["accept12",0,["Z12"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([], [[push12, 0, [Z12]], [accept12, 0, [Z12]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([], [[push12, 0, [Z12]], [accept12, 0, [Z12]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
39. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push13","pop13","accept13"],"input_alphabet":["a13","b13"],"stack_alphabet":["Z13","A13"],"start_state":"push13","bottom_symbol":"Z13","final_states":["accept13"],"transitions":[["push13","a13","Z13","push13",["Z13","A13"]],["push13","a13","A13","push13",["A13","A13"]],["push13","b13","A13","pop13",[]],["pop13","b13","A13","pop13",[]],["push13",null,"Z13","accept13",["Z13"]],["pop13",null,"Z13","accept13",["Z13"]]],"input":["a13","b13"],"trace":[["push13",0,["Z13"]],["push13",1,["Z13","A13"]],["pop13",2,["Z13"]],["accept13",2,["Z13"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a13, b13], [[push13, 0, [Z13]], [push13, 1, [Z13, A13]], [pop13, 2, [Z13]], [accept13, 2, [Z13]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a13, b13], [[push13, 0, [Z13]], [push13, 1, [Z13, A13]], [pop13, 2, [Z13]], [accept13, 2, [Z13]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
40. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push14","pop14","accept14"],"input_alphabet":["a14","b14"],"stack_alphabet":["Z14","A14"],"start_state":"push14","bottom_symbol":"Z14","final_states":["accept14"],"transitions":[["push14","a14","Z14","push14",["Z14","A14"]],["push14","a14","A14","push14",["A14","A14"]],["push14","b14","A14","pop14",[]],["pop14","b14","A14","pop14",[]],["push14",null,"Z14","accept14",["Z14"]],["pop14",null,"Z14","accept14",["Z14"]]],"input":["a14","a14","b14","b14"],"trace":[["push14",0,["Z14"]],["push14",1,["Z14","A14"]],["push14",2,["Z14","A14","A14"]],["pop14",3,["Z14","A14"]],["pop14",4,["Z14"]],["accept14",4,["Z14"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a14, a14, b14, b14], [[push14, 0, [Z14]], [push14, 1, [Z14, A14]], [push14, 2, [Z14, A14, A14]], [pop14, 3, [Z14, A14]], [pop14, 4, [Z14]], [accept14, 4, [Z14]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a14, a14, b14, b14], [[push14, 0, [Z14]], [push14, 1, [Z14, A14]], [push14, 2, [Z14, A14, A14]], [pop14, 3, [Z14, A14]], [pop14, 4, [Z14]], [accept14, 4, [Z14]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
41. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push15","pop15","accept15"],"input_alphabet":["a15","b15"],"stack_alphabet":["Z15","A15"],"start_state":"push15","bottom_symbol":"Z15","final_states":["accept15"],"transitions":[["push15","a15","Z15","push15",["Z15","A15"]],["push15","a15","A15","push15",["A15","A15"]],["push15","b15","A15","pop15",[]],["pop15","b15","A15","pop15",[]],["push15",null,"Z15","accept15",["Z15"]],["pop15",null,"Z15","accept15",["Z15"]]],"input":["a15","a15","a15","b15","b15","b15"],"trace":[["push15",0,["Z15"]],["push15",1,["Z15","A15"]],["push15",2,["Z15","A15","A15"]],["push15",3,["Z15","A15","A15","A15"]],["pop15",4,["Z15","A15","A15"]],["pop15",5,["Z15","A15"]],["pop15",6,["Z15"]],["accept15",6,["Z15"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a15, a15, a15, b15, b15, b15], [[push15, 0, [Z15]], [push15, 1, [Z15, A15]], [push15, 2, [Z15, A15, A15]], [push15, 3, [Z15, A15, A15, A15]], [pop15, 4, [Z15, A15, A15]], [pop15, 5, [Z15, A15]], [pop15, 6, [Z15]], [accept15, 6, [Z15]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a15, a15, a15, b15, b15, b15], [[push15, 0, [Z15]], [push15, 1, [Z15, A15]], [push15, 2, [Z15, A15, A15]], [push15, 3, [Z15, A15, A15, A15]], [pop15, 4, [Z15, A15, A15]], [pop15, 5, [Z15, A15]], [pop15, 6, [Z15]], [accept15, 6, [Z15]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
42. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push16","pop16","accept16"],"input_alphabet":["a16","b16"],"stack_alphabet":["Z16","A16"],"start_state":"push16","bottom_symbol":"Z16","final_states":["accept16"],"transitions":[["push16","a16","Z16","push16",["Z16","A16"]],["push16","a16","A16","push16",["A16","A16"]],["push16","b16","A16","pop16",[]],["pop16","b16","A16","pop16",[]],["push16",null,"Z16","accept16",["Z16"]],["pop16",null,"Z16","accept16",["Z16"]]],"input":[],"trace":[["push16",0,["Z16"]],["accept16",0,["Z16"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([], [[push16, 0, [Z16]], [accept16, 0, [Z16]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([], [[push16, 0, [Z16]], [accept16, 0, [Z16]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
43. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push17","pop17","accept17"],"input_alphabet":["a17","b17"],"stack_alphabet":["Z17","A17"],"start_state":"push17","bottom_symbol":"Z17","final_states":["accept17"],"transitions":[["push17","a17","Z17","push17",["Z17","A17"]],["push17","a17","A17","push17",["A17","A17"]],["push17","b17","A17","pop17",[]],["pop17","b17","A17","pop17",[]],["push17",null,"Z17","accept17",["Z17"]],["pop17",null,"Z17","accept17",["Z17"]]],"input":["a17","b17"],"trace":[["push17",0,["Z17"]],["push17",1,["Z17","A17"]],["pop17",2,["Z17"]],["accept17",2,["Z17"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a17, b17], [[push17, 0, [Z17]], [push17, 1, [Z17, A17]], [pop17, 2, [Z17]], [accept17, 2, [Z17]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a17, b17], [[push17, 0, [Z17]], [push17, 1, [Z17, A17]], [pop17, 2, [Z17]], [accept17, 2, [Z17]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
44. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push18","pop18","accept18"],"input_alphabet":["a18","b18"],"stack_alphabet":["Z18","A18"],"start_state":"push18","bottom_symbol":"Z18","final_states":["accept18"],"transitions":[["push18","a18","Z18","push18",["Z18","A18"]],["push18","a18","A18","push18",["A18","A18"]],["push18","b18","A18","pop18",[]],["pop18","b18","A18","pop18",[]],["push18",null,"Z18","accept18",["Z18"]],["pop18",null,"Z18","accept18",["Z18"]]],"input":["a18","a18","b18","b18"],"trace":[["push18",0,["Z18"]],["push18",1,["Z18","A18"]],["push18",2,["Z18","A18","A18"]],["pop18",3,["Z18","A18"]],["pop18",4,["Z18"]],["accept18",4,["Z18"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a18, a18, b18, b18], [[push18, 0, [Z18]], [push18, 1, [Z18, A18]], [push18, 2, [Z18, A18, A18]], [pop18, 3, [Z18, A18]], [pop18, 4, [Z18]], [accept18, 4, [Z18]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a18, a18, b18, b18], [[push18, 0, [Z18]], [push18, 1, [Z18, A18]], [push18, 2, [Z18, A18, A18]], [pop18, 3, [Z18, A18]], [pop18, 4, [Z18]], [accept18, 4, [Z18]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
45. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push19","pop19","accept19"],"input_alphabet":["a19","b19"],"stack_alphabet":["Z19","A19"],"start_state":"push19","bottom_symbol":"Z19","final_states":["accept19"],"transitions":[["push19","a19","Z19","push19",["Z19","A19"]],["push19","a19","A19","push19",["A19","A19"]],["push19","b19","A19","pop19",[]],["pop19","b19","A19","pop19",[]],["push19",null,"Z19","accept19",["Z19"]],["pop19",null,"Z19","accept19",["Z19"]]],"input":["a19","a19","a19","b19","b19","b19"],"trace":[["push19",0,["Z19"]],["push19",1,["Z19","A19"]],["push19",2,["Z19","A19","A19"]],["push19",3,["Z19","A19","A19","A19"]],["pop19",4,["Z19","A19","A19"]],["pop19",5,["Z19","A19"]],["pop19",6,["Z19"]],["accept19",6,["Z19"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a19, a19, a19, b19, b19, b19], [[push19, 0, [Z19]], [push19, 1, [Z19, A19]], [push19, 2, [Z19, A19, A19]], [push19, 3, [Z19, A19, A19, A19]], [pop19, 4, [Z19, A19, A19]], [pop19, 5, [Z19, A19]], [pop19, 6, [Z19]], [accept19, 6, [Z19]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a19, a19, a19, b19, b19, b19], [[push19, 0, [Z19]], [push19, 1, [Z19, A19]], [push19, 2, [Z19, A19, A19]], [push19, 3, [Z19, A19, A19, A19]], [pop19, 4, [Z19, A19, A19]], [pop19, 5, [Z19, A19]], [pop19, 6, [Z19]], [accept19, 6, [Z19]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
46. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push20","pop20","accept20"],"input_alphabet":["a20","b20"],"stack_alphabet":["Z20","A20"],"start_state":"push20","bottom_symbol":"Z20","final_states":["accept20"],"transitions":[["push20","a20","Z20","push20",["Z20","A20"]],["push20","a20","A20","push20",["A20","A20"]],["push20","b20","A20","pop20",[]],["pop20","b20","A20","pop20",[]],["push20",null,"Z20","accept20",["Z20"]],["pop20",null,"Z20","accept20",["Z20"]]],"input":[],"trace":[["push20",0,["Z20"]],["accept20",0,["Z20"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([], [[push20, 0, [Z20]], [accept20, 0, [Z20]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([], [[push20, 0, [Z20]], [accept20, 0, [Z20]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
47. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push21","pop21","accept21"],"input_alphabet":["a21","b21"],"stack_alphabet":["Z21","A21"],"start_state":"push21","bottom_symbol":"Z21","final_states":["accept21"],"transitions":[["push21","a21","Z21","push21",["Z21","A21"]],["push21","a21","A21","push21",["A21","A21"]],["push21","b21","A21","pop21",[]],["pop21","b21","A21","pop21",[]],["push21",null,"Z21","accept21",["Z21"]],["pop21",null,"Z21","accept21",["Z21"]]],"input":["a21","b21"],"trace":[["push21",0,["Z21"]],["push21",1,["Z21","A21"]],["pop21",2,["Z21"]],["accept21",2,["Z21"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a21, b21], [[push21, 0, [Z21]], [push21, 1, [Z21, A21]], [pop21, 2, [Z21]], [accept21, 2, [Z21]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a21, b21], [[push21, 0, [Z21]], [push21, 1, [Z21, A21]], [pop21, 2, [Z21]], [accept21, 2, [Z21]]], [0, 2, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
48. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push22","pop22","accept22"],"input_alphabet":["a22","b22"],"stack_alphabet":["Z22","A22"],"start_state":"push22","bottom_symbol":"Z22","final_states":["accept22"],"transitions":[["push22","a22","Z22","push22",["Z22","A22"]],["push22","a22","A22","push22",["A22","A22"]],["push22","b22","A22","pop22",[]],["pop22","b22","A22","pop22",[]],["push22",null,"Z22","accept22",["Z22"]],["pop22",null,"Z22","accept22",["Z22"]]],"input":["a22","a22","b22","b22"],"trace":[["push22",0,["Z22"]],["push22",1,["Z22","A22"]],["push22",2,["Z22","A22","A22"]],["pop22",3,["Z22","A22"]],["pop22",4,["Z22"]],["accept22",4,["Z22"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a22, a22, b22, b22], [[push22, 0, [Z22]], [push22, 1, [Z22, A22]], [push22, 2, [Z22, A22, A22]], [pop22, 3, [Z22, A22]], [pop22, 4, [Z22]], [accept22, 4, [Z22]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a22, a22, b22, b22], [[push22, 0, [Z22]], [push22, 1, [Z22, A22]], [push22, 2, [Z22, A22, A22]], [pop22, 3, [Z22, A22]], [pop22, 4, [Z22]], [accept22, 4, [Z22]]], [0, 1, 2, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
49. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push23","pop23","accept23"],"input_alphabet":["a23","b23"],"stack_alphabet":["Z23","A23"],"start_state":"push23","bottom_symbol":"Z23","final_states":["accept23"],"transitions":[["push23","a23","Z23","push23",["Z23","A23"]],["push23","a23","A23","push23",["A23","A23"]],["push23","b23","A23","pop23",[]],["pop23","b23","A23","pop23",[]],["push23",null,"Z23","accept23",["Z23"]],["pop23",null,"Z23","accept23",["Z23"]]],"input":["a23","a23","a23","b23","b23","b23"],"trace":[["push23",0,["Z23"]],["push23",1,["Z23","A23"]],["push23",2,["Z23","A23","A23"]],["push23",3,["Z23","A23","A23","A23"]],["pop23",4,["Z23","A23","A23"]],["pop23",5,["Z23","A23"]],["pop23",6,["Z23"]],["accept23",6,["Z23"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([a23, a23, a23, b23, b23, b23], [[push23, 0, [Z23]], [push23, 1, [Z23, A23]], [push23, 2, [Z23, A23, A23]], [push23, 3, [Z23, A23, A23, A23]], [pop23, 4, [Z23, A23, A23]], [pop23, 5, [Z23, A23]], [pop23, 6, [Z23]], [accept23, 6, [Z23]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([a23, a23, a23, b23, b23, b23], [[push23, 0, [Z23]], [push23, 1, [Z23, A23]], [push23, 2, [Z23, A23, A23]], [push23, 3, [Z23, A23, A23, A23]], [pop23, 4, [Z23, A23, A23]], [pop23, 5, [Z23, A23]], [pop23, 6, [Z23]], [accept23, 6, [Z23]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
50. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-trace-audit；資料={"states":["push24","pop24","accept24"],"input_alphabet":["a24","b24"],"stack_alphabet":["Z24","A24"],"start_state":"push24","bottom_symbol":"Z24","final_states":["accept24"],"transitions":[["push24","a24","Z24","push24",["Z24","A24"]],["push24","a24","A24","push24",["A24","A24"]],["push24","b24","A24","pop24",[]],["pop24","b24","A24","pop24",[]],["push24",null,"Z24","accept24",["Z24"]],["pop24",null,"Z24","accept24",["Z24"]]],"input":[],"trace":[["push24",0,["Z24"]],["accept24",0,["Z24"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, certificate] 欄序回答。
valid_run與accepted分開：到final state但input尚未讀完不算接受；stack保留bottom，不採empty-stack acceptance。
查看答案與解釋
([], [[push24, 0, [Z24]], [accept24, 0, [Z24]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)
Wave6第四層核對=([], [[push24, 0, [Z24]], [accept24, 0, [Z24]]], [4], 是, 是, epsilon_moves_consume_no_input_and_each_stack_update_is_explicit)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-trace-audit · candidate
51. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push0","pop0","accept0"],"input_alphabet":["a0","b0"],"stack_alphabet":["Z0","A0"],"start_state":"push0","bottom_symbol":"Z0","final_states":["accept0"],"transitions":[["push0","a0","Z0","push0",["Z0","A0"]],["push0","a0","A0","push0",["A0","A0"]],["push0","b0","A0","pop0",[]],["pop0","b0","A0","pop0",[]],["push0",null,"Z0","accept0",["Z0"]],["pop0",null,"Z0","accept0",["Z0"]]],"input":[],"trace":[["push0",0,["Z0"]],["accept0",0,["Z0"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([], [[push0, 0, [Z0]], [accept0, 0, [Z0]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([], [[push0, 0, [Z0]], [accept0, 0, [Z0]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
52. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push1","pop1","accept1"],"input_alphabet":["a1","b1"],"stack_alphabet":["Z1","A1"],"start_state":"push1","bottom_symbol":"Z1","final_states":["accept1"],"transitions":[["push1","a1","Z1","push1",["Z1","A1"]],["push1","a1","A1","push1",["A1","A1"]],["push1","b1","A1","pop1",[]],["pop1","b1","A1","pop1",[]],["push1",null,"Z1","accept1",["Z1"]],["pop1",null,"Z1","accept1",["Z1"]]],"input":["a1","b1"],"trace":[["push1",0,["Z1"]],["push1",1,["Z1","A1"]],["pop1",2,["Z1"]],["accept1",2,["Z1"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a1, b1], [[push1, 0, [Z1]], [push1, 1, [Z1, A1]], [pop1, 2, [Z1]], [accept1, 2, [Z1]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a1, b1], [[push1, 0, [Z1]], [push1, 1, [Z1, A1]], [pop1, 2, [Z1]], [accept1, 2, [Z1]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
53. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push2","pop2","accept2"],"input_alphabet":["a2","b2"],"stack_alphabet":["Z2","A2"],"start_state":"push2","bottom_symbol":"Z2","final_states":["accept2"],"transitions":[["push2","a2","Z2","push2",["Z2","A2"]],["push2","a2","A2","push2",["A2","A2"]],["push2","b2","A2","pop2",[]],["pop2","b2","A2","pop2",[]],["push2",null,"Z2","accept2",["Z2"]],["pop2",null,"Z2","accept2",["Z2"]]],"input":["a2","a2","b2","b2"],"trace":[["push2",0,["Z2"]],["push2",1,["Z2","A2"]],["push2",2,["Z2","A2","A2"]],["pop2",3,["Z2","A2"]],["pop2",4,["Z2"]],["accept2",4,["Z2"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a2, a2, b2, b2], [[push2, 0, [Z2]], [push2, 1, [Z2, A2]], [push2, 2, [Z2, A2, A2]], [pop2, 3, [Z2, A2]], [pop2, 4, [Z2]], [accept2, 4, [Z2]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a2, a2, b2, b2], [[push2, 0, [Z2]], [push2, 1, [Z2, A2]], [push2, 2, [Z2, A2, A2]], [pop2, 3, [Z2, A2]], [pop2, 4, [Z2]], [accept2, 4, [Z2]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
54. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push3","pop3","accept3"],"input_alphabet":["a3","b3"],"stack_alphabet":["Z3","A3"],"start_state":"push3","bottom_symbol":"Z3","final_states":["accept3"],"transitions":[["push3","a3","Z3","push3",["Z3","A3"]],["push3","a3","A3","push3",["A3","A3"]],["push3","b3","A3","pop3",[]],["pop3","b3","A3","pop3",[]],["push3",null,"Z3","accept3",["Z3"]],["pop3",null,"Z3","accept3",["Z3"]]],"input":["a3","a3","a3","b3","b3","b3"],"trace":[["push3",0,["Z3"]],["push3",1,["Z3","A3"]],["push3",2,["Z3","A3","A3"]],["push3",3,["Z3","A3","A3","A3"]],["pop3",4,["Z3","A3","A3"]],["pop3",5,["Z3","A3"]],["pop3",6,["Z3"]],["accept3",6,["Z3"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a3, a3, a3, b3, b3, b3], [[push3, 0, [Z3]], [push3, 1, [Z3, A3]], [push3, 2, [Z3, A3, A3]], [push3, 3, [Z3, A3, A3, A3]], [pop3, 4, [Z3, A3, A3]], [pop3, 5, [Z3, A3]], [pop3, 6, [Z3]], [accept3, 6, [Z3]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a3, a3, a3, b3, b3, b3], [[push3, 0, [Z3]], [push3, 1, [Z3, A3]], [push3, 2, [Z3, A3, A3]], [push3, 3, [Z3, A3, A3, A3]], [pop3, 4, [Z3, A3, A3]], [pop3, 5, [Z3, A3]], [pop3, 6, [Z3]], [accept3, 6, [Z3]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
55. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push4","pop4","accept4"],"input_alphabet":["a4","b4"],"stack_alphabet":["Z4","A4"],"start_state":"push4","bottom_symbol":"Z4","final_states":["accept4"],"transitions":[["push4","a4","Z4","push4",["Z4","A4"]],["push4","a4","A4","push4",["A4","A4"]],["push4","b4","A4","pop4",[]],["pop4","b4","A4","pop4",[]],["push4",null,"Z4","accept4",["Z4"]],["pop4",null,"Z4","accept4",["Z4"]]],"input":[],"trace":[["push4",0,["Z4"]],["accept4",0,["Z4"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([], [[push4, 0, [Z4]], [accept4, 0, [Z4]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([], [[push4, 0, [Z4]], [accept4, 0, [Z4]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
56. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push5","pop5","accept5"],"input_alphabet":["a5","b5"],"stack_alphabet":["Z5","A5"],"start_state":"push5","bottom_symbol":"Z5","final_states":["accept5"],"transitions":[["push5","a5","Z5","push5",["Z5","A5"]],["push5","a5","A5","push5",["A5","A5"]],["push5","b5","A5","pop5",[]],["pop5","b5","A5","pop5",[]],["push5",null,"Z5","accept5",["Z5"]],["pop5",null,"Z5","accept5",["Z5"]]],"input":["a5","b5"],"trace":[["push5",0,["Z5"]],["push5",1,["Z5","A5"]],["pop5",2,["Z5"]],["accept5",2,["Z5"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a5, b5], [[push5, 0, [Z5]], [push5, 1, [Z5, A5]], [pop5, 2, [Z5]], [accept5, 2, [Z5]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a5, b5], [[push5, 0, [Z5]], [push5, 1, [Z5, A5]], [pop5, 2, [Z5]], [accept5, 2, [Z5]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
57. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push6","pop6","accept6"],"input_alphabet":["a6","b6"],"stack_alphabet":["Z6","A6"],"start_state":"push6","bottom_symbol":"Z6","final_states":["accept6"],"transitions":[["push6","a6","Z6","push6",["Z6","A6"]],["push6","a6","A6","push6",["A6","A6"]],["push6","b6","A6","pop6",[]],["pop6","b6","A6","pop6",[]],["push6",null,"Z6","accept6",["Z6"]],["pop6",null,"Z6","accept6",["Z6"]]],"input":["a6","a6","b6","b6"],"trace":[["push6",0,["Z6"]],["push6",1,["Z6","A6"]],["push6",2,["Z6","A6","A6"]],["pop6",3,["Z6","A6"]],["pop6",4,["Z6"]],["accept6",4,["Z6"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a6, a6, b6, b6], [[push6, 0, [Z6]], [push6, 1, [Z6, A6]], [push6, 2, [Z6, A6, A6]], [pop6, 3, [Z6, A6]], [pop6, 4, [Z6]], [accept6, 4, [Z6]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a6, a6, b6, b6], [[push6, 0, [Z6]], [push6, 1, [Z6, A6]], [push6, 2, [Z6, A6, A6]], [pop6, 3, [Z6, A6]], [pop6, 4, [Z6]], [accept6, 4, [Z6]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
58. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push7","pop7","accept7"],"input_alphabet":["a7","b7"],"stack_alphabet":["Z7","A7"],"start_state":"push7","bottom_symbol":"Z7","final_states":["accept7"],"transitions":[["push7","a7","Z7","push7",["Z7","A7"]],["push7","a7","A7","push7",["A7","A7"]],["push7","b7","A7","pop7",[]],["pop7","b7","A7","pop7",[]],["push7",null,"Z7","accept7",["Z7"]],["pop7",null,"Z7","accept7",["Z7"]]],"input":["a7","a7","a7","b7","b7","b7"],"trace":[["push7",0,["Z7"]],["push7",1,["Z7","A7"]],["push7",2,["Z7","A7","A7"]],["push7",3,["Z7","A7","A7","A7"]],["pop7",4,["Z7","A7","A7"]],["pop7",5,["Z7","A7"]],["pop7",6,["Z7"]],["accept7",6,["Z7"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a7, a7, a7, b7, b7, b7], [[push7, 0, [Z7]], [push7, 1, [Z7, A7]], [push7, 2, [Z7, A7, A7]], [push7, 3, [Z7, A7, A7, A7]], [pop7, 4, [Z7, A7, A7]], [pop7, 5, [Z7, A7]], [pop7, 6, [Z7]], [accept7, 6, [Z7]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a7, a7, a7, b7, b7, b7], [[push7, 0, [Z7]], [push7, 1, [Z7, A7]], [push7, 2, [Z7, A7, A7]], [push7, 3, [Z7, A7, A7, A7]], [pop7, 4, [Z7, A7, A7]], [pop7, 5, [Z7, A7]], [pop7, 6, [Z7]], [accept7, 6, [Z7]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
59. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push8","pop8","accept8"],"input_alphabet":["a8","b8"],"stack_alphabet":["Z8","A8"],"start_state":"push8","bottom_symbol":"Z8","final_states":["accept8"],"transitions":[["push8","a8","Z8","push8",["Z8","A8"]],["push8","a8","A8","push8",["A8","A8"]],["push8","b8","A8","pop8",[]],["pop8","b8","A8","pop8",[]],["push8",null,"Z8","accept8",["Z8"]],["pop8",null,"Z8","accept8",["Z8"]]],"input":[],"trace":[["push8",0,["Z8"]],["accept8",0,["Z8"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([], [[push8, 0, [Z8]], [accept8, 0, [Z8]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([], [[push8, 0, [Z8]], [accept8, 0, [Z8]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
60. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push9","pop9","accept9"],"input_alphabet":["a9","b9"],"stack_alphabet":["Z9","A9"],"start_state":"push9","bottom_symbol":"Z9","final_states":["accept9"],"transitions":[["push9","a9","Z9","push9",["Z9","A9"]],["push9","a9","A9","push9",["A9","A9"]],["push9","b9","A9","pop9",[]],["pop9","b9","A9","pop9",[]],["push9",null,"Z9","accept9",["Z9"]],["pop9",null,"Z9","accept9",["Z9"]]],"input":["a9","b9"],"trace":[["push9",0,["Z9"]],["push9",1,["Z9","A9"]],["pop9",2,["Z9"]],["accept9",2,["Z9"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a9, b9], [[push9, 0, [Z9]], [push9, 1, [Z9, A9]], [pop9, 2, [Z9]], [accept9, 2, [Z9]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a9, b9], [[push9, 0, [Z9]], [push9, 1, [Z9, A9]], [pop9, 2, [Z9]], [accept9, 2, [Z9]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
61. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push10","pop10","accept10"],"input_alphabet":["a10","b10"],"stack_alphabet":["Z10","A10"],"start_state":"push10","bottom_symbol":"Z10","final_states":["accept10"],"transitions":[["push10","a10","Z10","push10",["Z10","A10"]],["push10","a10","A10","push10",["A10","A10"]],["push10","b10","A10","pop10",[]],["pop10","b10","A10","pop10",[]],["push10",null,"Z10","accept10",["Z10"]],["pop10",null,"Z10","accept10",["Z10"]]],"input":["a10","a10","b10","b10"],"trace":[["push10",0,["Z10"]],["push10",1,["Z10","A10"]],["push10",2,["Z10","A10","A10"]],["pop10",3,["Z10","A10"]],["pop10",4,["Z10"]],["accept10",4,["Z10"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a10, a10, b10, b10], [[push10, 0, [Z10]], [push10, 1, [Z10, A10]], [push10, 2, [Z10, A10, A10]], [pop10, 3, [Z10, A10]], [pop10, 4, [Z10]], [accept10, 4, [Z10]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a10, a10, b10, b10], [[push10, 0, [Z10]], [push10, 1, [Z10, A10]], [push10, 2, [Z10, A10, A10]], [pop10, 3, [Z10, A10]], [pop10, 4, [Z10]], [accept10, 4, [Z10]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
62. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push11","pop11","accept11"],"input_alphabet":["a11","b11"],"stack_alphabet":["Z11","A11"],"start_state":"push11","bottom_symbol":"Z11","final_states":["accept11"],"transitions":[["push11","a11","Z11","push11",["Z11","A11"]],["push11","a11","A11","push11",["A11","A11"]],["push11","b11","A11","pop11",[]],["pop11","b11","A11","pop11",[]],["push11",null,"Z11","accept11",["Z11"]],["pop11",null,"Z11","accept11",["Z11"]]],"input":["a11","a11","a11","b11","b11","b11"],"trace":[["push11",0,["Z11"]],["push11",1,["Z11","A11"]],["push11",2,["Z11","A11","A11"]],["push11",3,["Z11","A11","A11","A11"]],["pop11",4,["Z11","A11","A11"]],["pop11",5,["Z11","A11"]],["pop11",6,["Z11"]],["accept11",6,["Z11"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a11, a11, a11, b11, b11, b11], [[push11, 0, [Z11]], [push11, 1, [Z11, A11]], [push11, 2, [Z11, A11, A11]], [push11, 3, [Z11, A11, A11, A11]], [pop11, 4, [Z11, A11, A11]], [pop11, 5, [Z11, A11]], [pop11, 6, [Z11]], [accept11, 6, [Z11]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a11, a11, a11, b11, b11, b11], [[push11, 0, [Z11]], [push11, 1, [Z11, A11]], [push11, 2, [Z11, A11, A11]], [push11, 3, [Z11, A11, A11, A11]], [pop11, 4, [Z11, A11, A11]], [pop11, 5, [Z11, A11]], [pop11, 6, [Z11]], [accept11, 6, [Z11]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
63. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push12","pop12","accept12"],"input_alphabet":["a12","b12"],"stack_alphabet":["Z12","A12"],"start_state":"push12","bottom_symbol":"Z12","final_states":["accept12"],"transitions":[["push12","a12","Z12","push12",["Z12","A12"]],["push12","a12","A12","push12",["A12","A12"]],["push12","b12","A12","pop12",[]],["pop12","b12","A12","pop12",[]],["push12",null,"Z12","accept12",["Z12"]],["pop12",null,"Z12","accept12",["Z12"]]],"input":[],"trace":[["push12",0,["Z12"]],["accept12",0,["Z12"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([], [[push12, 0, [Z12]], [accept12, 0, [Z12]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([], [[push12, 0, [Z12]], [accept12, 0, [Z12]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
64. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push13","pop13","accept13"],"input_alphabet":["a13","b13"],"stack_alphabet":["Z13","A13"],"start_state":"push13","bottom_symbol":"Z13","final_states":["accept13"],"transitions":[["push13","a13","Z13","push13",["Z13","A13"]],["push13","a13","A13","push13",["A13","A13"]],["push13","b13","A13","pop13",[]],["pop13","b13","A13","pop13",[]],["push13",null,"Z13","accept13",["Z13"]],["pop13",null,"Z13","accept13",["Z13"]]],"input":["a13","b13"],"trace":[["push13",0,["Z13"]],["push13",1,["Z13","A13"]],["pop13",2,["Z13"]],["accept13",2,["Z13"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a13, b13], [[push13, 0, [Z13]], [push13, 1, [Z13, A13]], [pop13, 2, [Z13]], [accept13, 2, [Z13]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a13, b13], [[push13, 0, [Z13]], [push13, 1, [Z13, A13]], [pop13, 2, [Z13]], [accept13, 2, [Z13]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
65. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push14","pop14","accept14"],"input_alphabet":["a14","b14"],"stack_alphabet":["Z14","A14"],"start_state":"push14","bottom_symbol":"Z14","final_states":["accept14"],"transitions":[["push14","a14","Z14","push14",["Z14","A14"]],["push14","a14","A14","push14",["A14","A14"]],["push14","b14","A14","pop14",[]],["pop14","b14","A14","pop14",[]],["push14",null,"Z14","accept14",["Z14"]],["pop14",null,"Z14","accept14",["Z14"]]],"input":["a14","a14","b14","b14"],"trace":[["push14",0,["Z14"]],["push14",1,["Z14","A14"]],["push14",2,["Z14","A14","A14"]],["pop14",3,["Z14","A14"]],["pop14",4,["Z14"]],["accept14",4,["Z14"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a14, a14, b14, b14], [[push14, 0, [Z14]], [push14, 1, [Z14, A14]], [push14, 2, [Z14, A14, A14]], [pop14, 3, [Z14, A14]], [pop14, 4, [Z14]], [accept14, 4, [Z14]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a14, a14, b14, b14], [[push14, 0, [Z14]], [push14, 1, [Z14, A14]], [push14, 2, [Z14, A14, A14]], [pop14, 3, [Z14, A14]], [pop14, 4, [Z14]], [accept14, 4, [Z14]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
66. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push15","pop15","accept15"],"input_alphabet":["a15","b15"],"stack_alphabet":["Z15","A15"],"start_state":"push15","bottom_symbol":"Z15","final_states":["accept15"],"transitions":[["push15","a15","Z15","push15",["Z15","A15"]],["push15","a15","A15","push15",["A15","A15"]],["push15","b15","A15","pop15",[]],["pop15","b15","A15","pop15",[]],["push15",null,"Z15","accept15",["Z15"]],["pop15",null,"Z15","accept15",["Z15"]]],"input":["a15","a15","a15","b15","b15","b15"],"trace":[["push15",0,["Z15"]],["push15",1,["Z15","A15"]],["push15",2,["Z15","A15","A15"]],["push15",3,["Z15","A15","A15","A15"]],["pop15",4,["Z15","A15","A15"]],["pop15",5,["Z15","A15"]],["pop15",6,["Z15"]],["accept15",6,["Z15"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a15, a15, a15, b15, b15, b15], [[push15, 0, [Z15]], [push15, 1, [Z15, A15]], [push15, 2, [Z15, A15, A15]], [push15, 3, [Z15, A15, A15, A15]], [pop15, 4, [Z15, A15, A15]], [pop15, 5, [Z15, A15]], [pop15, 6, [Z15]], [accept15, 6, [Z15]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a15, a15, a15, b15, b15, b15], [[push15, 0, [Z15]], [push15, 1, [Z15, A15]], [push15, 2, [Z15, A15, A15]], [push15, 3, [Z15, A15, A15, A15]], [pop15, 4, [Z15, A15, A15]], [pop15, 5, [Z15, A15]], [pop15, 6, [Z15]], [accept15, 6, [Z15]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
67. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push16","pop16","accept16"],"input_alphabet":["a16","b16"],"stack_alphabet":["Z16","A16"],"start_state":"push16","bottom_symbol":"Z16","final_states":["accept16"],"transitions":[["push16","a16","Z16","push16",["Z16","A16"]],["push16","a16","A16","push16",["A16","A16"]],["push16","b16","A16","pop16",[]],["pop16","b16","A16","pop16",[]],["push16",null,"Z16","accept16",["Z16"]],["pop16",null,"Z16","accept16",["Z16"]]],"input":[],"trace":[["push16",0,["Z16"]],["accept16",0,["Z16"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([], [[push16, 0, [Z16]], [accept16, 0, [Z16]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([], [[push16, 0, [Z16]], [accept16, 0, [Z16]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
68. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push17","pop17","accept17"],"input_alphabet":["a17","b17"],"stack_alphabet":["Z17","A17"],"start_state":"push17","bottom_symbol":"Z17","final_states":["accept17"],"transitions":[["push17","a17","Z17","push17",["Z17","A17"]],["push17","a17","A17","push17",["A17","A17"]],["push17","b17","A17","pop17",[]],["pop17","b17","A17","pop17",[]],["push17",null,"Z17","accept17",["Z17"]],["pop17",null,"Z17","accept17",["Z17"]]],"input":["a17","b17"],"trace":[["push17",0,["Z17"]],["push17",1,["Z17","A17"]],["pop17",2,["Z17"]],["accept17",2,["Z17"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a17, b17], [[push17, 0, [Z17]], [push17, 1, [Z17, A17]], [pop17, 2, [Z17]], [accept17, 2, [Z17]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a17, b17], [[push17, 0, [Z17]], [push17, 1, [Z17, A17]], [pop17, 2, [Z17]], [accept17, 2, [Z17]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
69. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push18","pop18","accept18"],"input_alphabet":["a18","b18"],"stack_alphabet":["Z18","A18"],"start_state":"push18","bottom_symbol":"Z18","final_states":["accept18"],"transitions":[["push18","a18","Z18","push18",["Z18","A18"]],["push18","a18","A18","push18",["A18","A18"]],["push18","b18","A18","pop18",[]],["pop18","b18","A18","pop18",[]],["push18",null,"Z18","accept18",["Z18"]],["pop18",null,"Z18","accept18",["Z18"]]],"input":["a18","a18","b18","b18"],"trace":[["push18",0,["Z18"]],["push18",1,["Z18","A18"]],["push18",2,["Z18","A18","A18"]],["pop18",3,["Z18","A18"]],["pop18",4,["Z18"]],["accept18",4,["Z18"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a18, a18, b18, b18], [[push18, 0, [Z18]], [push18, 1, [Z18, A18]], [push18, 2, [Z18, A18, A18]], [pop18, 3, [Z18, A18]], [pop18, 4, [Z18]], [accept18, 4, [Z18]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a18, a18, b18, b18], [[push18, 0, [Z18]], [push18, 1, [Z18, A18]], [push18, 2, [Z18, A18, A18]], [pop18, 3, [Z18, A18]], [pop18, 4, [Z18]], [accept18, 4, [Z18]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
70. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push19","pop19","accept19"],"input_alphabet":["a19","b19"],"stack_alphabet":["Z19","A19"],"start_state":"push19","bottom_symbol":"Z19","final_states":["accept19"],"transitions":[["push19","a19","Z19","push19",["Z19","A19"]],["push19","a19","A19","push19",["A19","A19"]],["push19","b19","A19","pop19",[]],["pop19","b19","A19","pop19",[]],["push19",null,"Z19","accept19",["Z19"]],["pop19",null,"Z19","accept19",["Z19"]]],"input":["a19","a19","a19","b19","b19","b19"],"trace":[["push19",0,["Z19"]],["push19",1,["Z19","A19"]],["push19",2,["Z19","A19","A19"]],["push19",3,["Z19","A19","A19","A19"]],["pop19",4,["Z19","A19","A19"]],["pop19",5,["Z19","A19"]],["pop19",6,["Z19"]],["accept19",6,["Z19"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a19, a19, a19, b19, b19, b19], [[push19, 0, [Z19]], [push19, 1, [Z19, A19]], [push19, 2, [Z19, A19, A19]], [push19, 3, [Z19, A19, A19, A19]], [pop19, 4, [Z19, A19, A19]], [pop19, 5, [Z19, A19]], [pop19, 6, [Z19]], [accept19, 6, [Z19]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a19, a19, a19, b19, b19, b19], [[push19, 0, [Z19]], [push19, 1, [Z19, A19]], [push19, 2, [Z19, A19, A19]], [push19, 3, [Z19, A19, A19, A19]], [pop19, 4, [Z19, A19, A19]], [pop19, 5, [Z19, A19]], [pop19, 6, [Z19]], [accept19, 6, [Z19]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
71. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push20","pop20","accept20"],"input_alphabet":["a20","b20"],"stack_alphabet":["Z20","A20"],"start_state":"push20","bottom_symbol":"Z20","final_states":["accept20"],"transitions":[["push20","a20","Z20","push20",["Z20","A20"]],["push20","a20","A20","push20",["A20","A20"]],["push20","b20","A20","pop20",[]],["pop20","b20","A20","pop20",[]],["push20",null,"Z20","accept20",["Z20"]],["pop20",null,"Z20","accept20",["Z20"]]],"input":[],"trace":[["push20",0,["Z20"]],["accept20",0,["Z20"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([], [[push20, 0, [Z20]], [accept20, 0, [Z20]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([], [[push20, 0, [Z20]], [accept20, 0, [Z20]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
72. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push21","pop21","accept21"],"input_alphabet":["a21","b21"],"stack_alphabet":["Z21","A21"],"start_state":"push21","bottom_symbol":"Z21","final_states":["accept21"],"transitions":[["push21","a21","Z21","push21",["Z21","A21"]],["push21","a21","A21","push21",["A21","A21"]],["push21","b21","A21","pop21",[]],["pop21","b21","A21","pop21",[]],["push21",null,"Z21","accept21",["Z21"]],["pop21",null,"Z21","accept21",["Z21"]]],"input":["a21","b21"],"trace":[["push21",0,["Z21"]],["push21",1,["Z21","A21"]],["pop21",2,["Z21"]],["accept21",2,["Z21"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a21, b21], [[push21, 0, [Z21]], [push21, 1, [Z21, A21]], [pop21, 2, [Z21]], [accept21, 2, [Z21]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a21, b21], [[push21, 0, [Z21]], [push21, 1, [Z21, A21]], [pop21, 2, [Z21]], [accept21, 2, [Z21]]], [0, 2, 5], 是, 是, 3, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
73. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push22","pop22","accept22"],"input_alphabet":["a22","b22"],"stack_alphabet":["Z22","A22"],"start_state":"push22","bottom_symbol":"Z22","final_states":["accept22"],"transitions":[["push22","a22","Z22","push22",["Z22","A22"]],["push22","a22","A22","push22",["A22","A22"]],["push22","b22","A22","pop22",[]],["pop22","b22","A22","pop22",[]],["push22",null,"Z22","accept22",["Z22"]],["pop22",null,"Z22","accept22",["Z22"]]],"input":["a22","a22","b22","b22"],"trace":[["push22",0,["Z22"]],["push22",1,["Z22","A22"]],["push22",2,["Z22","A22","A22"]],["pop22",3,["Z22","A22"]],["pop22",4,["Z22"]],["accept22",4,["Z22"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a22, a22, b22, b22], [[push22, 0, [Z22]], [push22, 1, [Z22, A22]], [push22, 2, [Z22, A22, A22]], [pop22, 3, [Z22, A22]], [pop22, 4, [Z22]], [accept22, 4, [Z22]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a22, a22, b22, b22], [[push22, 0, [Z22]], [push22, 1, [Z22, A22]], [push22, 2, [Z22, A22, A22]], [pop22, 3, [Z22, A22]], [pop22, 4, [Z22]], [accept22, 4, [Z22]]], [0, 1, 2, 3, 5], 是, 是, 5, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
74. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push23","pop23","accept23"],"input_alphabet":["a23","b23"],"stack_alphabet":["Z23","A23"],"start_state":"push23","bottom_symbol":"Z23","final_states":["accept23"],"transitions":[["push23","a23","Z23","push23",["Z23","A23"]],["push23","a23","A23","push23",["A23","A23"]],["push23","b23","A23","pop23",[]],["pop23","b23","A23","pop23",[]],["push23",null,"Z23","accept23",["Z23"]],["pop23",null,"Z23","accept23",["Z23"]]],"input":["a23","a23","a23","b23","b23","b23"],"trace":[["push23",0,["Z23"]],["push23",1,["Z23","A23"]],["push23",2,["Z23","A23","A23"]],["push23",3,["Z23","A23","A23","A23"]],["pop23",4,["Z23","A23","A23"]],["pop23",5,["Z23","A23"]],["pop23",6,["Z23"]],["accept23",6,["Z23"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([a23, a23, a23, b23, b23, b23], [[push23, 0, [Z23]], [push23, 1, [Z23, A23]], [push23, 2, [Z23, A23, A23]], [push23, 3, [Z23, A23, A23, A23]], [pop23, 4, [Z23, A23, A23]], [pop23, 5, [Z23, A23]], [pop23, 6, [Z23]], [accept23, 6, [Z23]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([a23, a23, a23, b23, b23, b23], [[push23, 0, [Z23]], [push23, 1, [Z23, A23]], [push23, 2, [Z23, A23, A23]], [push23, 3, [Z23, A23, A23, A23]], [pop23, 4, [Z23, A23, A23]], [pop23, 5, [Z23, A23]], [pop23, 6, [Z23]], [accept23, 6, [Z23]]], [0, 1, 1, 2, 3, 3, 5], 是, 是, 7, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
75. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-accepting-run-witness；資料={"states":["push24","pop24","accept24"],"input_alphabet":["a24","b24"],"stack_alphabet":["Z24","A24"],"start_state":"push24","bottom_symbol":"Z24","final_states":["accept24"],"transitions":[["push24","a24","Z24","push24",["Z24","A24"]],["push24","a24","A24","push24",["A24","A24"]],["push24","b24","A24","pop24",[]],["pop24","b24","A24","pop24",[]],["push24",null,"Z24","accept24",["Z24"]],["pop24",null,"Z24","accept24",["Z24"]]],"input":[],"trace":[["push24",0,["Z24"]],["accept24",0,["Z24"]]]}。請依 [input, trace, transition_indices, valid_run, accepted, step_count, certificate] 欄序回答。
查看答案與解釋
([], [[push24, 0, [Z24]], [accept24, 0, [Z24]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)
Wave6第四層核對=([], [[push24, 0, [Z24]], [accept24, 0, [Z24]]], [4], 是, 是, 1, finite_full_run_witness_proves_acceptance_under_final_state_convention)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-accepting-run-witness · candidate
76. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push0","pop0","accept0"],"input_alphabet":["a0","b0"],"stack_alphabet":["Z0","A0"],"start_state":"push0","bottom_symbol":"Z0","final_states":["accept0"],"transitions":[["push0","a0","Z0","push0",["Z0","A0"]],["push0","a0","A0","push0",["A0","A0"]],["push0","b0","A0","pop0",[]],["pop0","b0","A0","pop0",[]],["push0",null,"Z0","accept0",["Z0"]],["pop0",null,"Z0","accept0",["Z0"]]],"input":["a0","b0"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a0, b0], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a0, b0], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
77. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push1","pop1","accept1"],"input_alphabet":["a1","b1"],"stack_alphabet":["Z1","A1"],"start_state":"push1","bottom_symbol":"Z1","final_states":["accept1"],"transitions":[["push1","a1","Z1","push1",["Z1","A1"]],["push1","a1","A1","push1",["A1","A1"]],["push1","b1","A1","pop1",[]],["pop1","b1","A1","pop1",[]],["push1",null,"Z1","accept1",["Z1"]],["pop1",null,"Z1","accept1",["Z1"]]],"input":["a1","a1","b1","b1"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a1, a1, b1, b1], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a1, a1, b1, b1], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
78. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push2","pop2","accept2"],"input_alphabet":["a2","b2"],"stack_alphabet":["Z2","A2"],"start_state":"push2","bottom_symbol":"Z2","final_states":["accept2"],"transitions":[["push2","a2","Z2","push2",["Z2","A2"]],["push2","a2","A2","push2",["A2","A2"]],["push2","b2","A2","pop2",[]],["pop2","b2","A2","pop2",[]],["push2",null,"Z2","accept2",["Z2"]],["pop2",null,"Z2","accept2",["Z2"]]],"input":["a2","a2","a2","b2","b2","b2"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a2, a2, a2, b2, b2, b2], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a2, a2, a2, b2, b2, b2], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
79. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push3","pop3","accept3"],"input_alphabet":["a3","b3"],"stack_alphabet":["Z3","A3"],"start_state":"push3","bottom_symbol":"Z3","final_states":["accept3"],"transitions":[["push3","a3","Z3","push3",["Z3","A3"]],["push3","a3","A3","push3",["A3","A3"]],["push3","b3","A3","pop3",[]],["pop3","b3","A3","pop3",[]],["push3",null,"Z3","accept3",["Z3"]],["pop3",null,"Z3","accept3",["Z3"]]],"input":["a3","a3","a3","a3","b3","b3","b3","b3"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a3, a3, a3, a3, b3, b3, b3, b3], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a3, a3, a3, a3, b3, b3, b3, b3], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
80. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push4","pop4","accept4"],"input_alphabet":["a4","b4"],"stack_alphabet":["Z4","A4"],"start_state":"push4","bottom_symbol":"Z4","final_states":["accept4"],"transitions":[["push4","a4","Z4","push4",["Z4","A4"]],["push4","a4","A4","push4",["A4","A4"]],["push4","b4","A4","pop4",[]],["pop4","b4","A4","pop4",[]],["push4",null,"Z4","accept4",["Z4"]],["pop4",null,"Z4","accept4",["Z4"]]],"input":["a4","b4"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a4, b4], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a4, b4], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
81. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push5","pop5","accept5"],"input_alphabet":["a5","b5"],"stack_alphabet":["Z5","A5"],"start_state":"push5","bottom_symbol":"Z5","final_states":["accept5"],"transitions":[["push5","a5","Z5","push5",["Z5","A5"]],["push5","a5","A5","push5",["A5","A5"]],["push5","b5","A5","pop5",[]],["pop5","b5","A5","pop5",[]],["push5",null,"Z5","accept5",["Z5"]],["pop5",null,"Z5","accept5",["Z5"]]],"input":["a5","a5","b5","b5"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a5, a5, b5, b5], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a5, a5, b5, b5], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
82. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push6","pop6","accept6"],"input_alphabet":["a6","b6"],"stack_alphabet":["Z6","A6"],"start_state":"push6","bottom_symbol":"Z6","final_states":["accept6"],"transitions":[["push6","a6","Z6","push6",["Z6","A6"]],["push6","a6","A6","push6",["A6","A6"]],["push6","b6","A6","pop6",[]],["pop6","b6","A6","pop6",[]],["push6",null,"Z6","accept6",["Z6"]],["pop6",null,"Z6","accept6",["Z6"]]],"input":["a6","a6","a6","b6","b6","b6"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a6, a6, a6, b6, b6, b6], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a6, a6, a6, b6, b6, b6], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
83. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push7","pop7","accept7"],"input_alphabet":["a7","b7"],"stack_alphabet":["Z7","A7"],"start_state":"push7","bottom_symbol":"Z7","final_states":["accept7"],"transitions":[["push7","a7","Z7","push7",["Z7","A7"]],["push7","a7","A7","push7",["A7","A7"]],["push7","b7","A7","pop7",[]],["pop7","b7","A7","pop7",[]],["push7",null,"Z7","accept7",["Z7"]],["pop7",null,"Z7","accept7",["Z7"]]],"input":["a7","a7","a7","a7","b7","b7","b7","b7"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a7, a7, a7, a7, b7, b7, b7, b7], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a7, a7, a7, a7, b7, b7, b7, b7], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
84. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push8","pop8","accept8"],"input_alphabet":["a8","b8"],"stack_alphabet":["Z8","A8"],"start_state":"push8","bottom_symbol":"Z8","final_states":["accept8"],"transitions":[["push8","a8","Z8","push8",["Z8","A8"]],["push8","a8","A8","push8",["A8","A8"]],["push8","b8","A8","pop8",[]],["pop8","b8","A8","pop8",[]],["push8",null,"Z8","accept8",["Z8"]],["pop8",null,"Z8","accept8",["Z8"]]],"input":["a8","b8"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a8, b8], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a8, b8], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
85. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push9","pop9","accept9"],"input_alphabet":["a9","b9"],"stack_alphabet":["Z9","A9"],"start_state":"push9","bottom_symbol":"Z9","final_states":["accept9"],"transitions":[["push9","a9","Z9","push9",["Z9","A9"]],["push9","a9","A9","push9",["A9","A9"]],["push9","b9","A9","pop9",[]],["pop9","b9","A9","pop9",[]],["push9",null,"Z9","accept9",["Z9"]],["pop9",null,"Z9","accept9",["Z9"]]],"input":["a9","a9","b9","b9"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a9, a9, b9, b9], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a9, a9, b9, b9], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
86. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push10","pop10","accept10"],"input_alphabet":["a10","b10"],"stack_alphabet":["Z10","A10"],"start_state":"push10","bottom_symbol":"Z10","final_states":["accept10"],"transitions":[["push10","a10","Z10","push10",["Z10","A10"]],["push10","a10","A10","push10",["A10","A10"]],["push10","b10","A10","pop10",[]],["pop10","b10","A10","pop10",[]],["push10",null,"Z10","accept10",["Z10"]],["pop10",null,"Z10","accept10",["Z10"]]],"input":["a10","a10","a10","b10","b10","b10"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a10, a10, a10, b10, b10, b10], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a10, a10, a10, b10, b10, b10], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
87. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push11","pop11","accept11"],"input_alphabet":["a11","b11"],"stack_alphabet":["Z11","A11"],"start_state":"push11","bottom_symbol":"Z11","final_states":["accept11"],"transitions":[["push11","a11","Z11","push11",["Z11","A11"]],["push11","a11","A11","push11",["A11","A11"]],["push11","b11","A11","pop11",[]],["pop11","b11","A11","pop11",[]],["push11",null,"Z11","accept11",["Z11"]],["pop11",null,"Z11","accept11",["Z11"]]],"input":["a11","a11","a11","a11","b11","b11","b11","b11"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a11, a11, a11, a11, b11, b11, b11, b11], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a11, a11, a11, a11, b11, b11, b11, b11], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
88. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push12","pop12","accept12"],"input_alphabet":["a12","b12"],"stack_alphabet":["Z12","A12"],"start_state":"push12","bottom_symbol":"Z12","final_states":["accept12"],"transitions":[["push12","a12","Z12","push12",["Z12","A12"]],["push12","a12","A12","push12",["A12","A12"]],["push12","b12","A12","pop12",[]],["pop12","b12","A12","pop12",[]],["push12",null,"Z12","accept12",["Z12"]],["pop12",null,"Z12","accept12",["Z12"]]],"input":["a12","b12"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a12, b12], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a12, b12], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
89. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push13","pop13","accept13"],"input_alphabet":["a13","b13"],"stack_alphabet":["Z13","A13"],"start_state":"push13","bottom_symbol":"Z13","final_states":["accept13"],"transitions":[["push13","a13","Z13","push13",["Z13","A13"]],["push13","a13","A13","push13",["A13","A13"]],["push13","b13","A13","pop13",[]],["pop13","b13","A13","pop13",[]],["push13",null,"Z13","accept13",["Z13"]],["pop13",null,"Z13","accept13",["Z13"]]],"input":["a13","a13","b13","b13"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a13, a13, b13, b13], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a13, a13, b13, b13], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
90. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push14","pop14","accept14"],"input_alphabet":["a14","b14"],"stack_alphabet":["Z14","A14"],"start_state":"push14","bottom_symbol":"Z14","final_states":["accept14"],"transitions":[["push14","a14","Z14","push14",["Z14","A14"]],["push14","a14","A14","push14",["A14","A14"]],["push14","b14","A14","pop14",[]],["pop14","b14","A14","pop14",[]],["push14",null,"Z14","accept14",["Z14"]],["pop14",null,"Z14","accept14",["Z14"]]],"input":["a14","a14","a14","b14","b14","b14"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a14, a14, a14, b14, b14, b14], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a14, a14, a14, b14, b14, b14], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
91. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push15","pop15","accept15"],"input_alphabet":["a15","b15"],"stack_alphabet":["Z15","A15"],"start_state":"push15","bottom_symbol":"Z15","final_states":["accept15"],"transitions":[["push15","a15","Z15","push15",["Z15","A15"]],["push15","a15","A15","push15",["A15","A15"]],["push15","b15","A15","pop15",[]],["pop15","b15","A15","pop15",[]],["push15",null,"Z15","accept15",["Z15"]],["pop15",null,"Z15","accept15",["Z15"]]],"input":["a15","a15","a15","a15","b15","b15","b15","b15"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a15, a15, a15, a15, b15, b15, b15, b15], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a15, a15, a15, a15, b15, b15, b15, b15], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
92. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push16","pop16","accept16"],"input_alphabet":["a16","b16"],"stack_alphabet":["Z16","A16"],"start_state":"push16","bottom_symbol":"Z16","final_states":["accept16"],"transitions":[["push16","a16","Z16","push16",["Z16","A16"]],["push16","a16","A16","push16",["A16","A16"]],["push16","b16","A16","pop16",[]],["pop16","b16","A16","pop16",[]],["push16",null,"Z16","accept16",["Z16"]],["pop16",null,"Z16","accept16",["Z16"]]],"input":["a16","b16"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a16, b16], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a16, b16], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
93. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push17","pop17","accept17"],"input_alphabet":["a17","b17"],"stack_alphabet":["Z17","A17"],"start_state":"push17","bottom_symbol":"Z17","final_states":["accept17"],"transitions":[["push17","a17","Z17","push17",["Z17","A17"]],["push17","a17","A17","push17",["A17","A17"]],["push17","b17","A17","pop17",[]],["pop17","b17","A17","pop17",[]],["push17",null,"Z17","accept17",["Z17"]],["pop17",null,"Z17","accept17",["Z17"]]],"input":["a17","a17","b17","b17"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a17, a17, b17, b17], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a17, a17, b17, b17], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
94. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push18","pop18","accept18"],"input_alphabet":["a18","b18"],"stack_alphabet":["Z18","A18"],"start_state":"push18","bottom_symbol":"Z18","final_states":["accept18"],"transitions":[["push18","a18","Z18","push18",["Z18","A18"]],["push18","a18","A18","push18",["A18","A18"]],["push18","b18","A18","pop18",[]],["pop18","b18","A18","pop18",[]],["push18",null,"Z18","accept18",["Z18"]],["pop18",null,"Z18","accept18",["Z18"]]],"input":["a18","a18","a18","b18","b18","b18"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a18, a18, a18, b18, b18, b18], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a18, a18, a18, b18, b18, b18], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
95. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push19","pop19","accept19"],"input_alphabet":["a19","b19"],"stack_alphabet":["Z19","A19"],"start_state":"push19","bottom_symbol":"Z19","final_states":["accept19"],"transitions":[["push19","a19","Z19","push19",["Z19","A19"]],["push19","a19","A19","push19",["A19","A19"]],["push19","b19","A19","pop19",[]],["pop19","b19","A19","pop19",[]],["push19",null,"Z19","accept19",["Z19"]],["pop19",null,"Z19","accept19",["Z19"]]],"input":["a19","a19","a19","a19","b19","b19","b19","b19"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a19, a19, a19, a19, b19, b19, b19, b19], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a19, a19, a19, a19, b19, b19, b19, b19], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
96. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push20","pop20","accept20"],"input_alphabet":["a20","b20"],"stack_alphabet":["Z20","A20"],"start_state":"push20","bottom_symbol":"Z20","final_states":["accept20"],"transitions":[["push20","a20","Z20","push20",["Z20","A20"]],["push20","a20","A20","push20",["A20","A20"]],["push20","b20","A20","pop20",[]],["pop20","b20","A20","pop20",[]],["push20",null,"Z20","accept20",["Z20"]],["pop20",null,"Z20","accept20",["Z20"]]],"input":["a20","b20"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a20, b20], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a20, b20], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
97. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push21","pop21","accept21"],"input_alphabet":["a21","b21"],"stack_alphabet":["Z21","A21"],"start_state":"push21","bottom_symbol":"Z21","final_states":["accept21"],"transitions":[["push21","a21","Z21","push21",["Z21","A21"]],["push21","a21","A21","push21",["A21","A21"]],["push21","b21","A21","pop21",[]],["pop21","b21","A21","pop21",[]],["push21",null,"Z21","accept21",["Z21"]],["pop21",null,"Z21","accept21",["Z21"]]],"input":["a21","a21","b21","b21"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a21, a21, b21, b21], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a21, a21, b21, b21], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
98. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push22","pop22","accept22"],"input_alphabet":["a22","b22"],"stack_alphabet":["Z22","A22"],"start_state":"push22","bottom_symbol":"Z22","final_states":["accept22"],"transitions":[["push22","a22","Z22","push22",["Z22","A22"]],["push22","a22","A22","push22",["A22","A22"]],["push22","b22","A22","pop22",[]],["pop22","b22","A22","pop22",[]],["push22",null,"Z22","accept22",["Z22"]],["pop22",null,"Z22","accept22",["Z22"]]],"input":["a22","a22","a22","b22","b22","b22"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a22, a22, a22, b22, b22, b22], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a22, a22, a22, b22, b22, b22], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
99. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push23","pop23","accept23"],"input_alphabet":["a23","b23"],"stack_alphabet":["Z23","A23"],"start_state":"push23","bottom_symbol":"Z23","final_states":["accept23"],"transitions":[["push23","a23","Z23","push23",["Z23","A23"]],["push23","a23","A23","push23",["A23","A23"]],["push23","b23","A23","pop23",[]],["pop23","b23","A23","pop23",[]],["push23",null,"Z23","accept23",["Z23"]],["pop23",null,"Z23","accept23",["Z23"]]],"input":["a23","a23","a23","a23","b23","b23","b23","b23"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a23, a23, a23, a23, b23, b23, b23, b23], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a23, a23, a23, a23, b23, b23, b23, b23], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
100. 下推自動機
transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-bounded-search-boundary；資料={"states":["push24","pop24","accept24"],"input_alphabet":["a24","b24"],"stack_alphabet":["Z24","A24"],"start_state":"push24","bottom_symbol":"Z24","final_states":["accept24"],"transitions":[["push24","a24","Z24","push24",["Z24","A24"]],["push24","a24","A24","push24",["A24","A24"]],["push24","b24","A24","pop24",[]],["pop24","b24","A24","pop24",[]],["push24",null,"Z24","accept24",["Z24"]],["pop24",null,"Z24","accept24",["Z24"]]],"input":["a24","b24"],"max_steps":1}。請依 [input, max_steps, found_accepting_run, rejection_or_nonmembership_claim, boundary] 欄序回答。
搜尋同時限制步數與stack長度；找不到不是reject或nonmembership證明，固定的否也不否定前面的found結果。
查看答案與解釋
([a24, b24], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)
Wave6第四層核對=([a24, b24], 1, 否, 否, bounded_nondeterministic_search_failure_cannot_prove_rejection_or_nonmembership)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。
本題逐步詳解（AI 二次覆核）
下推自動機 · qf-mod41-pda-bounded-search-boundary · candidate
原始題目 JSONL · 驗收報告