上下文無關文法基礎 · 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-20261109-r07-context-free-grammar-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. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S0","A0"],"terminals":["a0","b0"],"start":"S0","productions":[["S0",["a0","A0"]],["A0",["b0","A0"]],["A0",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S0, A0], [a0, b0], S0, [[S0, [a0, A0]], [A0, [b0, A0]], [A0, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S0, A0], [a0, b0], S0, [[S0, [a0, A0]], [A0, [b0, A0]], [A0, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
2. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S1","A1"],"terminals":["a1","b1"],"start":"S1","productions":[["S1",["a1","A1"]],["A1",["b1","A1"]],["A1",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S1, A1], [a1, b1], S1, [[S1, [a1, A1]], [A1, [b1, A1]], [A1, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S1, A1], [a1, b1], S1, [[S1, [a1, A1]], [A1, [b1, A1]], [A1, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
3. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S2","A2"],"terminals":["a2","b2"],"start":"S2","productions":[["S2",["a2","A2"]],["A2",["b2","A2"]],["A2",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S2, A2], [a2, b2], S2, [[S2, [a2, A2]], [A2, [b2, A2]], [A2, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S2, A2], [a2, b2], S2, [[S2, [a2, A2]], [A2, [b2, A2]], [A2, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
4. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S3","A3"],"terminals":["a3","b3"],"start":"S3","productions":[["S3",["a3","A3"]],["A3",["b3","A3"]],["A3",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S3, A3], [a3, b3], S3, [[S3, [a3, A3]], [A3, [b3, A3]], [A3, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S3, A3], [a3, b3], S3, [[S3, [a3, A3]], [A3, [b3, A3]], [A3, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
5. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S4","A4"],"terminals":["a4","b4"],"start":"S4","productions":[["S4",["a4","A4"]],["A4",["b4","A4"]],["A4",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S4, A4], [a4, b4], S4, [[S4, [a4, A4]], [A4, [b4, A4]], [A4, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S4, A4], [a4, b4], S4, [[S4, [a4, A4]], [A4, [b4, A4]], [A4, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
6. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S5","A5"],"terminals":["a5","b5"],"start":"S5","productions":[["S5",["a5","A5"]],["A5",["b5","A5"]],["A5",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S5, A5], [a5, b5], S5, [[S5, [a5, A5]], [A5, [b5, A5]], [A5, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S5, A5], [a5, b5], S5, [[S5, [a5, A5]], [A5, [b5, A5]], [A5, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
7. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S6","A6"],"terminals":["a6","b6"],"start":"S6","productions":[["S6",["a6","A6"]],["A6",["b6","A6"]],["A6",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S6, A6], [a6, b6], S6, [[S6, [a6, A6]], [A6, [b6, A6]], [A6, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S6, A6], [a6, b6], S6, [[S6, [a6, A6]], [A6, [b6, A6]], [A6, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
8. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S7","A7"],"terminals":["a7","b7"],"start":"S7","productions":[["S7",["a7","A7"]],["A7",["b7","A7"]],["A7",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S7, A7], [a7, b7], S7, [[S7, [a7, A7]], [A7, [b7, A7]], [A7, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S7, A7], [a7, b7], S7, [[S7, [a7, A7]], [A7, [b7, A7]], [A7, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
9. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S8","A8"],"terminals":["a8","b8"],"start":"S8","productions":[["S8",["a8","A8"]],["A8",["b8","A8"]],["A8",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S8, A8], [a8, b8], S8, [[S8, [a8, A8]], [A8, [b8, A8]], [A8, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S8, A8], [a8, b8], S8, [[S8, [a8, A8]], [A8, [b8, A8]], [A8, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
10. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S9","A9"],"terminals":["a9","b9"],"start":"S9","productions":[["S9",["a9","A9"]],["A9",["b9","A9"]],["A9",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S9, A9], [a9, b9], S9, [[S9, [a9, A9]], [A9, [b9, A9]], [A9, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S9, A9], [a9, b9], S9, [[S9, [a9, A9]], [A9, [b9, A9]], [A9, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
11. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S10","A10"],"terminals":["a10","b10"],"start":"S10","productions":[["S10",["a10","A10"]],["A10",["b10","A10"]],["A10",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S10, A10], [a10, b10], S10, [[S10, [a10, A10]], [A10, [b10, A10]], [A10, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S10, A10], [a10, b10], S10, [[S10, [a10, A10]], [A10, [b10, A10]], [A10, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
12. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S11","A11"],"terminals":["a11","b11"],"start":"S11","productions":[["S11",["a11","A11"]],["A11",["b11","A11"]],["A11",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S11, A11], [a11, b11], S11, [[S11, [a11, A11]], [A11, [b11, A11]], [A11, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S11, A11], [a11, b11], S11, [[S11, [a11, A11]], [A11, [b11, A11]], [A11, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
13. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S12","A12"],"terminals":["a12","b12"],"start":"S12","productions":[["S12",["a12","A12"]],["A12",["b12","A12"]],["A12",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S12, A12], [a12, b12], S12, [[S12, [a12, A12]], [A12, [b12, A12]], [A12, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S12, A12], [a12, b12], S12, [[S12, [a12, A12]], [A12, [b12, A12]], [A12, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
14. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S13","A13"],"terminals":["a13","b13"],"start":"S13","productions":[["S13",["a13","A13"]],["A13",["b13","A13"]],["A13",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S13, A13], [a13, b13], S13, [[S13, [a13, A13]], [A13, [b13, A13]], [A13, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S13, A13], [a13, b13], S13, [[S13, [a13, A13]], [A13, [b13, A13]], [A13, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
15. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S14","A14"],"terminals":["a14","b14"],"start":"S14","productions":[["S14",["a14","A14"]],["A14",["b14","A14"]],["A14",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S14, A14], [a14, b14], S14, [[S14, [a14, A14]], [A14, [b14, A14]], [A14, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S14, A14], [a14, b14], S14, [[S14, [a14, A14]], [A14, [b14, A14]], [A14, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
16. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S15","A15"],"terminals":["a15","b15"],"start":"S15","productions":[["S15",["a15","A15"]],["A15",["b15","A15"]],["A15",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S15, A15], [a15, b15], S15, [[S15, [a15, A15]], [A15, [b15, A15]], [A15, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S15, A15], [a15, b15], S15, [[S15, [a15, A15]], [A15, [b15, A15]], [A15, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
17. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S16","A16"],"terminals":["a16","b16"],"start":"S16","productions":[["S16",["a16","A16"]],["A16",["b16","A16"]],["A16",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S16, A16], [a16, b16], S16, [[S16, [a16, A16]], [A16, [b16, A16]], [A16, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S16, A16], [a16, b16], S16, [[S16, [a16, A16]], [A16, [b16, A16]], [A16, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
18. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S17","A17"],"terminals":["a17","b17"],"start":"S17","productions":[["S17",["a17","A17"]],["A17",["b17","A17"]],["A17",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S17, A17], [a17, b17], S17, [[S17, [a17, A17]], [A17, [b17, A17]], [A17, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S17, A17], [a17, b17], S17, [[S17, [a17, A17]], [A17, [b17, A17]], [A17, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
19. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S18","A18"],"terminals":["a18","b18"],"start":"S18","productions":[["S18",["a18","A18"]],["A18",["b18","A18"]],["A18",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S18, A18], [a18, b18], S18, [[S18, [a18, A18]], [A18, [b18, A18]], [A18, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S18, A18], [a18, b18], S18, [[S18, [a18, A18]], [A18, [b18, A18]], [A18, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
20. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S19","A19"],"terminals":["a19","b19"],"start":"S19","productions":[["S19",["a19","A19"]],["A19",["b19","A19"]],["A19",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S19, A19], [a19, b19], S19, [[S19, [a19, A19]], [A19, [b19, A19]], [A19, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S19, A19], [a19, b19], S19, [[S19, [a19, A19]], [A19, [b19, A19]], [A19, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
21. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S20","A20"],"terminals":["a20","b20"],"start":"S20","productions":[["S20",["a20","A20"]],["A20",["b20","A20"]],["A20",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S20, A20], [a20, b20], S20, [[S20, [a20, A20]], [A20, [b20, A20]], [A20, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S20, A20], [a20, b20], S20, [[S20, [a20, A20]], [A20, [b20, A20]], [A20, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
22. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S21","A21"],"terminals":["a21","b21"],"start":"S21","productions":[["S21",["a21","A21"]],["A21",["b21","A21"]],["A21",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S21, A21], [a21, b21], S21, [[S21, [a21, A21]], [A21, [b21, A21]], [A21, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S21, A21], [a21, b21], S21, [[S21, [a21, A21]], [A21, [b21, A21]], [A21, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
23. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S22","A22"],"terminals":["a22","b22"],"start":"S22","productions":[["S22",["a22","A22"]],["A22",["b22","A22"]],["A22",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S22, A22], [a22, b22], S22, [[S22, [a22, A22]], [A22, [b22, A22]], [A22, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S22, A22], [a22, b22], S22, [[S22, [a22, A22]], [A22, [b22, A22]], [A22, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
24. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S23","A23"],"terminals":["a23","b23"],"start":"S23","productions":[["S23",["a23","A23"]],["A23",["b23","A23"]],["A23",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S23, A23], [a23, b23], S23, [[S23, [a23, A23]], [A23, [b23, A23]], [A23, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S23, A23], [a23, b23], S23, [[S23, [a23, A23]], [A23, [b23, A23]], [A23, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
25. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-qualification；資料={"nonterminals":["S24","A24"],"terminals":["a24","b24"],"start":"S24","productions":[["S24",["a24","A24"]],["A24",["b24","A24"]],["A24",[]]],"allow_epsilon":true}。請依 [nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate] 欄序回答。
查看答案與解釋
([S24, A24], [a24, b24], S24, [[S24, [a24, A24]], [A24, [b24, A24]], [A24, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)
Wave6第三層核對=([S24, A24], [a24, b24], S24, [[S24, [a24, A24]], [A24, [b24, A24]], [A24, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-qualification · candidate
26. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S0","A0"],"terminals":["a0","b0"],"start":"S0","productions":[["S0",["a0","A0"]],["A0",["b0","A0"]],["A0",[]]],"allow_epsilon":true,"forms":[["S0"],["a0","A0"],["a0"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S0], [a0, A0], [a0]], [[0, 0, S0, [a0, A0]], [1, 2, A0, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S0], [a0, A0], [a0]], [[0, 0, S0, [a0, A0]], [1, 2, A0, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
27. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S1","A1"],"terminals":["a1","b1"],"start":"S1","productions":[["S1",["a1","A1"]],["A1",["b1","A1"]],["A1",[]]],"allow_epsilon":true,"forms":[["S1"],["a1","A1"],["a1","b1","A1"],["a1","b1"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S1], [a1, A1], [a1, b1, A1], [a1, b1]], [[0, 0, S1, [a1, A1]], [1, 1, A1, [b1, A1]], [2, 2, A1, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S1], [a1, A1], [a1, b1, A1], [a1, b1]], [[0, 0, S1, [a1, A1]], [1, 1, A1, [b1, A1]], [2, 2, A1, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
28. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S2","A2"],"terminals":["a2","b2"],"start":"S2","productions":[["S2",["a2","A2"]],["A2",["b2","A2"]],["A2",[]]],"allow_epsilon":true,"forms":[["S2"],["a2","A2"],["a2","b2","A2"],["a2","b2","b2","A2"],["a2","b2","b2"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S2], [a2, A2], [a2, b2, A2], [a2, b2, b2, A2], [a2, b2, b2]], [[0, 0, S2, [a2, A2]], [1, 1, A2, [b2, A2]], [2, 1, A2, [b2, A2]], [3, 2, A2, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S2], [a2, A2], [a2, b2, A2], [a2, b2, b2, A2], [a2, b2, b2]], [[0, 0, S2, [a2, A2]], [1, 1, A2, [b2, A2]], [2, 1, A2, [b2, A2]], [3, 2, A2, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
29. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S3","A3"],"terminals":["a3","b3"],"start":"S3","productions":[["S3",["a3","A3"]],["A3",["b3","A3"]],["A3",[]]],"allow_epsilon":true,"forms":[["S3"],["a3","A3"],["a3","b3","A3"],["a3","b3","b3","A3"],["a3","b3","b3","b3","A3"],["a3","b3","b3","b3"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S3], [a3, A3], [a3, b3, A3], [a3, b3, b3, A3], [a3, b3, b3, b3, A3], [a3, b3, b3, b3]], [[0, 0, S3, [a3, A3]], [1, 1, A3, [b3, A3]], [2, 1, A3, [b3, A3]], [3, 1, A3, [b3, A3]], [4, 2, A3, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S3], [a3, A3], [a3, b3, A3], [a3, b3, b3, A3], [a3, b3, b3, b3, A3], [a3, b3, b3, b3]], [[0, 0, S3, [a3, A3]], [1, 1, A3, [b3, A3]], [2, 1, A3, [b3, A3]], [3, 1, A3, [b3, A3]], [4, 2, A3, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
30. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S4","A4"],"terminals":["a4","b4"],"start":"S4","productions":[["S4",["a4","A4"]],["A4",["b4","A4"]],["A4",[]]],"allow_epsilon":true,"forms":[["S4"],["a4","A4"],["a4","b4","A4"],["a4","b4","b4","A4"],["a4","b4","b4","b4","A4"],["a4","b4","b4","b4","b4","A4"],["a4","b4","b4","b4","b4"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S4], [a4, A4], [a4, b4, A4], [a4, b4, b4, A4], [a4, b4, b4, b4, A4], [a4, b4, b4, b4, b4, A4], [a4, b4, b4, b4, b4]], [[0, 0, S4, [a4, A4]], [1, 1, A4, [b4, A4]], [2, 1, A4, [b4, A4]], [3, 1, A4, [b4, A4]], [4, 1, A4, [b4, A4]], [5, 2, A4, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S4], [a4, A4], [a4, b4, A4], [a4, b4, b4, A4], [a4, b4, b4, b4, A4], [a4, b4, b4, b4, b4, A4], [a4, b4, b4, b4, b4]], [[0, 0, S4, [a4, A4]], [1, 1, A4, [b4, A4]], [2, 1, A4, [b4, A4]], [3, 1, A4, [b4, A4]], [4, 1, A4, [b4, A4]], [5, 2, A4, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
31. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S5","A5"],"terminals":["a5","b5"],"start":"S5","productions":[["S5",["a5","A5"]],["A5",["b5","A5"]],["A5",[]]],"allow_epsilon":true,"forms":[["S5"],["a5","A5"],["a5"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S5], [a5, A5], [a5]], [[0, 0, S5, [a5, A5]], [1, 2, A5, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S5], [a5, A5], [a5]], [[0, 0, S5, [a5, A5]], [1, 2, A5, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
32. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S6","A6"],"terminals":["a6","b6"],"start":"S6","productions":[["S6",["a6","A6"]],["A6",["b6","A6"]],["A6",[]]],"allow_epsilon":true,"forms":[["S6"],["a6","A6"],["a6","b6","A6"],["a6","b6"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S6], [a6, A6], [a6, b6, A6], [a6, b6]], [[0, 0, S6, [a6, A6]], [1, 1, A6, [b6, A6]], [2, 2, A6, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S6], [a6, A6], [a6, b6, A6], [a6, b6]], [[0, 0, S6, [a6, A6]], [1, 1, A6, [b6, A6]], [2, 2, A6, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
33. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S7","A7"],"terminals":["a7","b7"],"start":"S7","productions":[["S7",["a7","A7"]],["A7",["b7","A7"]],["A7",[]]],"allow_epsilon":true,"forms":[["S7"],["a7","A7"],["a7","b7","A7"],["a7","b7","b7","A7"],["a7","b7","b7"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S7], [a7, A7], [a7, b7, A7], [a7, b7, b7, A7], [a7, b7, b7]], [[0, 0, S7, [a7, A7]], [1, 1, A7, [b7, A7]], [2, 1, A7, [b7, A7]], [3, 2, A7, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S7], [a7, A7], [a7, b7, A7], [a7, b7, b7, A7], [a7, b7, b7]], [[0, 0, S7, [a7, A7]], [1, 1, A7, [b7, A7]], [2, 1, A7, [b7, A7]], [3, 2, A7, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
34. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S8","A8"],"terminals":["a8","b8"],"start":"S8","productions":[["S8",["a8","A8"]],["A8",["b8","A8"]],["A8",[]]],"allow_epsilon":true,"forms":[["S8"],["a8","A8"],["a8","b8","A8"],["a8","b8","b8","A8"],["a8","b8","b8","b8","A8"],["a8","b8","b8","b8"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S8], [a8, A8], [a8, b8, A8], [a8, b8, b8, A8], [a8, b8, b8, b8, A8], [a8, b8, b8, b8]], [[0, 0, S8, [a8, A8]], [1, 1, A8, [b8, A8]], [2, 1, A8, [b8, A8]], [3, 1, A8, [b8, A8]], [4, 2, A8, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S8], [a8, A8], [a8, b8, A8], [a8, b8, b8, A8], [a8, b8, b8, b8, A8], [a8, b8, b8, b8]], [[0, 0, S8, [a8, A8]], [1, 1, A8, [b8, A8]], [2, 1, A8, [b8, A8]], [3, 1, A8, [b8, A8]], [4, 2, A8, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
35. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S9","A9"],"terminals":["a9","b9"],"start":"S9","productions":[["S9",["a9","A9"]],["A9",["b9","A9"]],["A9",[]]],"allow_epsilon":true,"forms":[["S9"],["a9","A9"],["a9","b9","A9"],["a9","b9","b9","A9"],["a9","b9","b9","b9","A9"],["a9","b9","b9","b9","b9","A9"],["a9","b9","b9","b9","b9"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S9], [a9, A9], [a9, b9, A9], [a9, b9, b9, A9], [a9, b9, b9, b9, A9], [a9, b9, b9, b9, b9, A9], [a9, b9, b9, b9, b9]], [[0, 0, S9, [a9, A9]], [1, 1, A9, [b9, A9]], [2, 1, A9, [b9, A9]], [3, 1, A9, [b9, A9]], [4, 1, A9, [b9, A9]], [5, 2, A9, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S9], [a9, A9], [a9, b9, A9], [a9, b9, b9, A9], [a9, b9, b9, b9, A9], [a9, b9, b9, b9, b9, A9], [a9, b9, b9, b9, b9]], [[0, 0, S9, [a9, A9]], [1, 1, A9, [b9, A9]], [2, 1, A9, [b9, A9]], [3, 1, A9, [b9, A9]], [4, 1, A9, [b9, A9]], [5, 2, A9, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
36. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S10","A10"],"terminals":["a10","b10"],"start":"S10","productions":[["S10",["a10","A10"]],["A10",["b10","A10"]],["A10",[]]],"allow_epsilon":true,"forms":[["S10"],["a10","A10"],["a10"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S10], [a10, A10], [a10]], [[0, 0, S10, [a10, A10]], [1, 2, A10, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S10], [a10, A10], [a10]], [[0, 0, S10, [a10, A10]], [1, 2, A10, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
37. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S11","A11"],"terminals":["a11","b11"],"start":"S11","productions":[["S11",["a11","A11"]],["A11",["b11","A11"]],["A11",[]]],"allow_epsilon":true,"forms":[["S11"],["a11","A11"],["a11","b11","A11"],["a11","b11"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S11], [a11, A11], [a11, b11, A11], [a11, b11]], [[0, 0, S11, [a11, A11]], [1, 1, A11, [b11, A11]], [2, 2, A11, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S11], [a11, A11], [a11, b11, A11], [a11, b11]], [[0, 0, S11, [a11, A11]], [1, 1, A11, [b11, A11]], [2, 2, A11, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
38. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S12","A12"],"terminals":["a12","b12"],"start":"S12","productions":[["S12",["a12","A12"]],["A12",["b12","A12"]],["A12",[]]],"allow_epsilon":true,"forms":[["S12"],["a12","A12"],["a12","b12","A12"],["a12","b12","b12","A12"],["a12","b12","b12"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S12], [a12, A12], [a12, b12, A12], [a12, b12, b12, A12], [a12, b12, b12]], [[0, 0, S12, [a12, A12]], [1, 1, A12, [b12, A12]], [2, 1, A12, [b12, A12]], [3, 2, A12, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S12], [a12, A12], [a12, b12, A12], [a12, b12, b12, A12], [a12, b12, b12]], [[0, 0, S12, [a12, A12]], [1, 1, A12, [b12, A12]], [2, 1, A12, [b12, A12]], [3, 2, A12, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
39. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S13","A13"],"terminals":["a13","b13"],"start":"S13","productions":[["S13",["a13","A13"]],["A13",["b13","A13"]],["A13",[]]],"allow_epsilon":true,"forms":[["S13"],["a13","A13"],["a13","b13","A13"],["a13","b13","b13","A13"],["a13","b13","b13","b13","A13"],["a13","b13","b13","b13"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S13], [a13, A13], [a13, b13, A13], [a13, b13, b13, A13], [a13, b13, b13, b13, A13], [a13, b13, b13, b13]], [[0, 0, S13, [a13, A13]], [1, 1, A13, [b13, A13]], [2, 1, A13, [b13, A13]], [3, 1, A13, [b13, A13]], [4, 2, A13, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S13], [a13, A13], [a13, b13, A13], [a13, b13, b13, A13], [a13, b13, b13, b13, A13], [a13, b13, b13, b13]], [[0, 0, S13, [a13, A13]], [1, 1, A13, [b13, A13]], [2, 1, A13, [b13, A13]], [3, 1, A13, [b13, A13]], [4, 2, A13, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
40. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S14","A14"],"terminals":["a14","b14"],"start":"S14","productions":[["S14",["a14","A14"]],["A14",["b14","A14"]],["A14",[]]],"allow_epsilon":true,"forms":[["S14"],["a14","A14"],["a14","b14","A14"],["a14","b14","b14","A14"],["a14","b14","b14","b14","A14"],["a14","b14","b14","b14","b14","A14"],["a14","b14","b14","b14","b14"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S14], [a14, A14], [a14, b14, A14], [a14, b14, b14, A14], [a14, b14, b14, b14, A14], [a14, b14, b14, b14, b14, A14], [a14, b14, b14, b14, b14]], [[0, 0, S14, [a14, A14]], [1, 1, A14, [b14, A14]], [2, 1, A14, [b14, A14]], [3, 1, A14, [b14, A14]], [4, 1, A14, [b14, A14]], [5, 2, A14, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S14], [a14, A14], [a14, b14, A14], [a14, b14, b14, A14], [a14, b14, b14, b14, A14], [a14, b14, b14, b14, b14, A14], [a14, b14, b14, b14, b14]], [[0, 0, S14, [a14, A14]], [1, 1, A14, [b14, A14]], [2, 1, A14, [b14, A14]], [3, 1, A14, [b14, A14]], [4, 1, A14, [b14, A14]], [5, 2, A14, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
41. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S15","A15"],"terminals":["a15","b15"],"start":"S15","productions":[["S15",["a15","A15"]],["A15",["b15","A15"]],["A15",[]]],"allow_epsilon":true,"forms":[["S15"],["a15","A15"],["a15"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S15], [a15, A15], [a15]], [[0, 0, S15, [a15, A15]], [1, 2, A15, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S15], [a15, A15], [a15]], [[0, 0, S15, [a15, A15]], [1, 2, A15, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
42. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S16","A16"],"terminals":["a16","b16"],"start":"S16","productions":[["S16",["a16","A16"]],["A16",["b16","A16"]],["A16",[]]],"allow_epsilon":true,"forms":[["S16"],["a16","A16"],["a16","b16","A16"],["a16","b16"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S16], [a16, A16], [a16, b16, A16], [a16, b16]], [[0, 0, S16, [a16, A16]], [1, 1, A16, [b16, A16]], [2, 2, A16, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S16], [a16, A16], [a16, b16, A16], [a16, b16]], [[0, 0, S16, [a16, A16]], [1, 1, A16, [b16, A16]], [2, 2, A16, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
43. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S17","A17"],"terminals":["a17","b17"],"start":"S17","productions":[["S17",["a17","A17"]],["A17",["b17","A17"]],["A17",[]]],"allow_epsilon":true,"forms":[["S17"],["a17","A17"],["a17","b17","A17"],["a17","b17","b17","A17"],["a17","b17","b17"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S17], [a17, A17], [a17, b17, A17], [a17, b17, b17, A17], [a17, b17, b17]], [[0, 0, S17, [a17, A17]], [1, 1, A17, [b17, A17]], [2, 1, A17, [b17, A17]], [3, 2, A17, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S17], [a17, A17], [a17, b17, A17], [a17, b17, b17, A17], [a17, b17, b17]], [[0, 0, S17, [a17, A17]], [1, 1, A17, [b17, A17]], [2, 1, A17, [b17, A17]], [3, 2, A17, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
44. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S18","A18"],"terminals":["a18","b18"],"start":"S18","productions":[["S18",["a18","A18"]],["A18",["b18","A18"]],["A18",[]]],"allow_epsilon":true,"forms":[["S18"],["a18","A18"],["a18","b18","A18"],["a18","b18","b18","A18"],["a18","b18","b18","b18","A18"],["a18","b18","b18","b18"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S18], [a18, A18], [a18, b18, A18], [a18, b18, b18, A18], [a18, b18, b18, b18, A18], [a18, b18, b18, b18]], [[0, 0, S18, [a18, A18]], [1, 1, A18, [b18, A18]], [2, 1, A18, [b18, A18]], [3, 1, A18, [b18, A18]], [4, 2, A18, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S18], [a18, A18], [a18, b18, A18], [a18, b18, b18, A18], [a18, b18, b18, b18, A18], [a18, b18, b18, b18]], [[0, 0, S18, [a18, A18]], [1, 1, A18, [b18, A18]], [2, 1, A18, [b18, A18]], [3, 1, A18, [b18, A18]], [4, 2, A18, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
45. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S19","A19"],"terminals":["a19","b19"],"start":"S19","productions":[["S19",["a19","A19"]],["A19",["b19","A19"]],["A19",[]]],"allow_epsilon":true,"forms":[["S19"],["a19","A19"],["a19","b19","A19"],["a19","b19","b19","A19"],["a19","b19","b19","b19","A19"],["a19","b19","b19","b19","b19","A19"],["a19","b19","b19","b19","b19"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S19], [a19, A19], [a19, b19, A19], [a19, b19, b19, A19], [a19, b19, b19, b19, A19], [a19, b19, b19, b19, b19, A19], [a19, b19, b19, b19, b19]], [[0, 0, S19, [a19, A19]], [1, 1, A19, [b19, A19]], [2, 1, A19, [b19, A19]], [3, 1, A19, [b19, A19]], [4, 1, A19, [b19, A19]], [5, 2, A19, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S19], [a19, A19], [a19, b19, A19], [a19, b19, b19, A19], [a19, b19, b19, b19, A19], [a19, b19, b19, b19, b19, A19], [a19, b19, b19, b19, b19]], [[0, 0, S19, [a19, A19]], [1, 1, A19, [b19, A19]], [2, 1, A19, [b19, A19]], [3, 1, A19, [b19, A19]], [4, 1, A19, [b19, A19]], [5, 2, A19, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
46. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S20","A20"],"terminals":["a20","b20"],"start":"S20","productions":[["S20",["a20","A20"]],["A20",["b20","A20"]],["A20",[]]],"allow_epsilon":true,"forms":[["S20"],["a20","A20"],["a20"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S20], [a20, A20], [a20]], [[0, 0, S20, [a20, A20]], [1, 2, A20, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S20], [a20, A20], [a20]], [[0, 0, S20, [a20, A20]], [1, 2, A20, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
47. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S21","A21"],"terminals":["a21","b21"],"start":"S21","productions":[["S21",["a21","A21"]],["A21",["b21","A21"]],["A21",[]]],"allow_epsilon":true,"forms":[["S21"],["a21","A21"],["a21","b21","A21"],["a21","b21"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S21], [a21, A21], [a21, b21, A21], [a21, b21]], [[0, 0, S21, [a21, A21]], [1, 1, A21, [b21, A21]], [2, 2, A21, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S21], [a21, A21], [a21, b21, A21], [a21, b21]], [[0, 0, S21, [a21, A21]], [1, 1, A21, [b21, A21]], [2, 2, A21, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
48. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S22","A22"],"terminals":["a22","b22"],"start":"S22","productions":[["S22",["a22","A22"]],["A22",["b22","A22"]],["A22",[]]],"allow_epsilon":true,"forms":[["S22"],["a22","A22"],["a22","b22","A22"],["a22","b22","b22","A22"],["a22","b22","b22"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S22], [a22, A22], [a22, b22, A22], [a22, b22, b22, A22], [a22, b22, b22]], [[0, 0, S22, [a22, A22]], [1, 1, A22, [b22, A22]], [2, 1, A22, [b22, A22]], [3, 2, A22, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S22], [a22, A22], [a22, b22, A22], [a22, b22, b22, A22], [a22, b22, b22]], [[0, 0, S22, [a22, A22]], [1, 1, A22, [b22, A22]], [2, 1, A22, [b22, A22]], [3, 2, A22, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
49. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S23","A23"],"terminals":["a23","b23"],"start":"S23","productions":[["S23",["a23","A23"]],["A23",["b23","A23"]],["A23",[]]],"allow_epsilon":true,"forms":[["S23"],["a23","A23"],["a23","b23","A23"],["a23","b23","b23","A23"],["a23","b23","b23","b23","A23"],["a23","b23","b23","b23"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S23], [a23, A23], [a23, b23, A23], [a23, b23, b23, A23], [a23, b23, b23, b23, A23], [a23, b23, b23, b23]], [[0, 0, S23, [a23, A23]], [1, 1, A23, [b23, A23]], [2, 1, A23, [b23, A23]], [3, 1, A23, [b23, A23]], [4, 2, A23, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S23], [a23, A23], [a23, b23, A23], [a23, b23, b23, A23], [a23, b23, b23, b23, A23], [a23, b23, b23, b23]], [[0, 0, S23, [a23, A23]], [1, 1, A23, [b23, A23]], [2, 1, A23, [b23, A23]], [3, 1, A23, [b23, A23]], [4, 2, A23, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
50. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={"nonterminals":["S24","A24"],"terminals":["a24","b24"],"start":"S24","productions":[["S24",["a24","A24"]],["A24",["b24","A24"]],["A24",[]]],"allow_epsilon":true,"forms":[["S24"],["a24","A24"],["a24","b24","A24"],["a24","b24","b24","A24"],["a24","b24","b24","b24","A24"],["a24","b24","b24","b24","b24","A24"],["a24","b24","b24","b24","b24"]]}。請依 [forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate] 欄序回答。
final_form_terminal_only單獨核最後形式；即使為是，也需要valid_derivation才構成由start推導的證書。
查看答案與解釋
([[S24], [a24, A24], [a24, b24, A24], [a24, b24, b24, A24], [a24, b24, b24, b24, A24], [a24, b24, b24, b24, b24, A24], [a24, b24, b24, b24, b24]], [[0, 0, S24, [a24, A24]], [1, 1, A24, [b24, A24]], [2, 1, A24, [b24, A24]], [3, 1, A24, [b24, A24]], [4, 1, A24, [b24, A24]], [5, 2, A24, []]], 是, 是, finite_production_sequence)
Wave6第三層核對=([[S24], [a24, A24], [a24, b24, A24], [a24, b24, b24, A24], [a24, b24, b24, b24, A24], [a24, b24, b24, b24, b24, A24], [a24, b24, b24, b24, b24]], [[0, 0, S24, [a24, A24]], [1, 1, A24, [b24, A24]], [2, 1, A24, [b24, A24]], [3, 1, A24, [b24, A24]], [4, 1, A24, [b24, A24]], [5, 2, A24, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-derivation-audit · candidate
51. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S0","A0"],"terminals":["a0","b0"],"start":"S0","productions":[["S0",["a0","A0"]],["A0",["b0","A0"]],["A0",[]]],"allow_epsilon":true,"word":["a0"],"forms":[["S0"],["a0","A0"],["a0"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a0], [[0, 0, S0, [a0, A0]], [1, 2, A0, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a0], [[0, 0, S0, [a0, A0]], [1, 2, A0, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
52. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S1","A1"],"terminals":["a1","b1"],"start":"S1","productions":[["S1",["a1","A1"]],["A1",["b1","A1"]],["A1",[]]],"allow_epsilon":true,"word":["a1","b1"],"forms":[["S1"],["a1","A1"],["a1","b1","A1"],["a1","b1"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a1, b1], [[0, 0, S1, [a1, A1]], [1, 1, A1, [b1, A1]], [2, 2, A1, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a1, b1], [[0, 0, S1, [a1, A1]], [1, 1, A1, [b1, A1]], [2, 2, A1, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
53. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S2","A2"],"terminals":["a2","b2"],"start":"S2","productions":[["S2",["a2","A2"]],["A2",["b2","A2"]],["A2",[]]],"allow_epsilon":true,"word":["a2","b2","b2"],"forms":[["S2"],["a2","A2"],["a2","b2","A2"],["a2","b2","b2","A2"],["a2","b2","b2"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a2, b2, b2], [[0, 0, S2, [a2, A2]], [1, 1, A2, [b2, A2]], [2, 1, A2, [b2, A2]], [3, 2, A2, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a2, b2, b2], [[0, 0, S2, [a2, A2]], [1, 1, A2, [b2, A2]], [2, 1, A2, [b2, A2]], [3, 2, A2, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
54. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S3","A3"],"terminals":["a3","b3"],"start":"S3","productions":[["S3",["a3","A3"]],["A3",["b3","A3"]],["A3",[]]],"allow_epsilon":true,"word":["a3","b3","b3","b3"],"forms":[["S3"],["a3","A3"],["a3","b3","A3"],["a3","b3","b3","A3"],["a3","b3","b3","b3","A3"],["a3","b3","b3","b3"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a3, b3, b3, b3], [[0, 0, S3, [a3, A3]], [1, 1, A3, [b3, A3]], [2, 1, A3, [b3, A3]], [3, 1, A3, [b3, A3]], [4, 2, A3, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a3, b3, b3, b3], [[0, 0, S3, [a3, A3]], [1, 1, A3, [b3, A3]], [2, 1, A3, [b3, A3]], [3, 1, A3, [b3, A3]], [4, 2, A3, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
55. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S4","A4"],"terminals":["a4","b4"],"start":"S4","productions":[["S4",["a4","A4"]],["A4",["b4","A4"]],["A4",[]]],"allow_epsilon":true,"word":["a4","b4","b4","b4","b4"],"forms":[["S4"],["a4","A4"],["a4","b4","A4"],["a4","b4","b4","A4"],["a4","b4","b4","b4","A4"],["a4","b4","b4","b4","b4","A4"],["a4","b4","b4","b4","b4"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a4, b4, b4, b4, b4], [[0, 0, S4, [a4, A4]], [1, 1, A4, [b4, A4]], [2, 1, A4, [b4, A4]], [3, 1, A4, [b4, A4]], [4, 1, A4, [b4, A4]], [5, 2, A4, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a4, b4, b4, b4, b4], [[0, 0, S4, [a4, A4]], [1, 1, A4, [b4, A4]], [2, 1, A4, [b4, A4]], [3, 1, A4, [b4, A4]], [4, 1, A4, [b4, A4]], [5, 2, A4, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
56. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S5","A5"],"terminals":["a5","b5"],"start":"S5","productions":[["S5",["a5","A5"]],["A5",["b5","A5"]],["A5",[]]],"allow_epsilon":true,"word":["a5"],"forms":[["S5"],["a5","A5"],["a5"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a5], [[0, 0, S5, [a5, A5]], [1, 2, A5, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a5], [[0, 0, S5, [a5, A5]], [1, 2, A5, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
57. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S6","A6"],"terminals":["a6","b6"],"start":"S6","productions":[["S6",["a6","A6"]],["A6",["b6","A6"]],["A6",[]]],"allow_epsilon":true,"word":["a6","b6"],"forms":[["S6"],["a6","A6"],["a6","b6","A6"],["a6","b6"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a6, b6], [[0, 0, S6, [a6, A6]], [1, 1, A6, [b6, A6]], [2, 2, A6, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a6, b6], [[0, 0, S6, [a6, A6]], [1, 1, A6, [b6, A6]], [2, 2, A6, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
58. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S7","A7"],"terminals":["a7","b7"],"start":"S7","productions":[["S7",["a7","A7"]],["A7",["b7","A7"]],["A7",[]]],"allow_epsilon":true,"word":["a7","b7","b7"],"forms":[["S7"],["a7","A7"],["a7","b7","A7"],["a7","b7","b7","A7"],["a7","b7","b7"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a7, b7, b7], [[0, 0, S7, [a7, A7]], [1, 1, A7, [b7, A7]], [2, 1, A7, [b7, A7]], [3, 2, A7, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a7, b7, b7], [[0, 0, S7, [a7, A7]], [1, 1, A7, [b7, A7]], [2, 1, A7, [b7, A7]], [3, 2, A7, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
59. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S8","A8"],"terminals":["a8","b8"],"start":"S8","productions":[["S8",["a8","A8"]],["A8",["b8","A8"]],["A8",[]]],"allow_epsilon":true,"word":["a8","b8","b8","b8"],"forms":[["S8"],["a8","A8"],["a8","b8","A8"],["a8","b8","b8","A8"],["a8","b8","b8","b8","A8"],["a8","b8","b8","b8"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a8, b8, b8, b8], [[0, 0, S8, [a8, A8]], [1, 1, A8, [b8, A8]], [2, 1, A8, [b8, A8]], [3, 1, A8, [b8, A8]], [4, 2, A8, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a8, b8, b8, b8], [[0, 0, S8, [a8, A8]], [1, 1, A8, [b8, A8]], [2, 1, A8, [b8, A8]], [3, 1, A8, [b8, A8]], [4, 2, A8, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
60. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S9","A9"],"terminals":["a9","b9"],"start":"S9","productions":[["S9",["a9","A9"]],["A9",["b9","A9"]],["A9",[]]],"allow_epsilon":true,"word":["a9","b9","b9","b9","b9"],"forms":[["S9"],["a9","A9"],["a9","b9","A9"],["a9","b9","b9","A9"],["a9","b9","b9","b9","A9"],["a9","b9","b9","b9","b9","A9"],["a9","b9","b9","b9","b9"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a9, b9, b9, b9, b9], [[0, 0, S9, [a9, A9]], [1, 1, A9, [b9, A9]], [2, 1, A9, [b9, A9]], [3, 1, A9, [b9, A9]], [4, 1, A9, [b9, A9]], [5, 2, A9, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a9, b9, b9, b9, b9], [[0, 0, S9, [a9, A9]], [1, 1, A9, [b9, A9]], [2, 1, A9, [b9, A9]], [3, 1, A9, [b9, A9]], [4, 1, A9, [b9, A9]], [5, 2, A9, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
61. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S10","A10"],"terminals":["a10","b10"],"start":"S10","productions":[["S10",["a10","A10"]],["A10",["b10","A10"]],["A10",[]]],"allow_epsilon":true,"word":["a10"],"forms":[["S10"],["a10","A10"],["a10"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a10], [[0, 0, S10, [a10, A10]], [1, 2, A10, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a10], [[0, 0, S10, [a10, A10]], [1, 2, A10, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
62. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S11","A11"],"terminals":["a11","b11"],"start":"S11","productions":[["S11",["a11","A11"]],["A11",["b11","A11"]],["A11",[]]],"allow_epsilon":true,"word":["a11","b11"],"forms":[["S11"],["a11","A11"],["a11","b11","A11"],["a11","b11"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a11, b11], [[0, 0, S11, [a11, A11]], [1, 1, A11, [b11, A11]], [2, 2, A11, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a11, b11], [[0, 0, S11, [a11, A11]], [1, 1, A11, [b11, A11]], [2, 2, A11, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
63. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S12","A12"],"terminals":["a12","b12"],"start":"S12","productions":[["S12",["a12","A12"]],["A12",["b12","A12"]],["A12",[]]],"allow_epsilon":true,"word":["a12","b12","b12"],"forms":[["S12"],["a12","A12"],["a12","b12","A12"],["a12","b12","b12","A12"],["a12","b12","b12"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a12, b12, b12], [[0, 0, S12, [a12, A12]], [1, 1, A12, [b12, A12]], [2, 1, A12, [b12, A12]], [3, 2, A12, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a12, b12, b12], [[0, 0, S12, [a12, A12]], [1, 1, A12, [b12, A12]], [2, 1, A12, [b12, A12]], [3, 2, A12, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
64. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S13","A13"],"terminals":["a13","b13"],"start":"S13","productions":[["S13",["a13","A13"]],["A13",["b13","A13"]],["A13",[]]],"allow_epsilon":true,"word":["a13","b13","b13","b13"],"forms":[["S13"],["a13","A13"],["a13","b13","A13"],["a13","b13","b13","A13"],["a13","b13","b13","b13","A13"],["a13","b13","b13","b13"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a13, b13, b13, b13], [[0, 0, S13, [a13, A13]], [1, 1, A13, [b13, A13]], [2, 1, A13, [b13, A13]], [3, 1, A13, [b13, A13]], [4, 2, A13, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a13, b13, b13, b13], [[0, 0, S13, [a13, A13]], [1, 1, A13, [b13, A13]], [2, 1, A13, [b13, A13]], [3, 1, A13, [b13, A13]], [4, 2, A13, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
65. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S14","A14"],"terminals":["a14","b14"],"start":"S14","productions":[["S14",["a14","A14"]],["A14",["b14","A14"]],["A14",[]]],"allow_epsilon":true,"word":["a14","b14","b14","b14","b14"],"forms":[["S14"],["a14","A14"],["a14","b14","A14"],["a14","b14","b14","A14"],["a14","b14","b14","b14","A14"],["a14","b14","b14","b14","b14","A14"],["a14","b14","b14","b14","b14"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a14, b14, b14, b14, b14], [[0, 0, S14, [a14, A14]], [1, 1, A14, [b14, A14]], [2, 1, A14, [b14, A14]], [3, 1, A14, [b14, A14]], [4, 1, A14, [b14, A14]], [5, 2, A14, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a14, b14, b14, b14, b14], [[0, 0, S14, [a14, A14]], [1, 1, A14, [b14, A14]], [2, 1, A14, [b14, A14]], [3, 1, A14, [b14, A14]], [4, 1, A14, [b14, A14]], [5, 2, A14, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
66. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S15","A15"],"terminals":["a15","b15"],"start":"S15","productions":[["S15",["a15","A15"]],["A15",["b15","A15"]],["A15",[]]],"allow_epsilon":true,"word":["a15"],"forms":[["S15"],["a15","A15"],["a15"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a15], [[0, 0, S15, [a15, A15]], [1, 2, A15, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a15], [[0, 0, S15, [a15, A15]], [1, 2, A15, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
67. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S16","A16"],"terminals":["a16","b16"],"start":"S16","productions":[["S16",["a16","A16"]],["A16",["b16","A16"]],["A16",[]]],"allow_epsilon":true,"word":["a16","b16"],"forms":[["S16"],["a16","A16"],["a16","b16","A16"],["a16","b16"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a16, b16], [[0, 0, S16, [a16, A16]], [1, 1, A16, [b16, A16]], [2, 2, A16, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a16, b16], [[0, 0, S16, [a16, A16]], [1, 1, A16, [b16, A16]], [2, 2, A16, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
68. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S17","A17"],"terminals":["a17","b17"],"start":"S17","productions":[["S17",["a17","A17"]],["A17",["b17","A17"]],["A17",[]]],"allow_epsilon":true,"word":["a17","b17","b17"],"forms":[["S17"],["a17","A17"],["a17","b17","A17"],["a17","b17","b17","A17"],["a17","b17","b17"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a17, b17, b17], [[0, 0, S17, [a17, A17]], [1, 1, A17, [b17, A17]], [2, 1, A17, [b17, A17]], [3, 2, A17, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a17, b17, b17], [[0, 0, S17, [a17, A17]], [1, 1, A17, [b17, A17]], [2, 1, A17, [b17, A17]], [3, 2, A17, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
69. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S18","A18"],"terminals":["a18","b18"],"start":"S18","productions":[["S18",["a18","A18"]],["A18",["b18","A18"]],["A18",[]]],"allow_epsilon":true,"word":["a18","b18","b18","b18"],"forms":[["S18"],["a18","A18"],["a18","b18","A18"],["a18","b18","b18","A18"],["a18","b18","b18","b18","A18"],["a18","b18","b18","b18"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a18, b18, b18, b18], [[0, 0, S18, [a18, A18]], [1, 1, A18, [b18, A18]], [2, 1, A18, [b18, A18]], [3, 1, A18, [b18, A18]], [4, 2, A18, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a18, b18, b18, b18], [[0, 0, S18, [a18, A18]], [1, 1, A18, [b18, A18]], [2, 1, A18, [b18, A18]], [3, 1, A18, [b18, A18]], [4, 2, A18, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
70. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S19","A19"],"terminals":["a19","b19"],"start":"S19","productions":[["S19",["a19","A19"]],["A19",["b19","A19"]],["A19",[]]],"allow_epsilon":true,"word":["a19","b19","b19","b19","b19"],"forms":[["S19"],["a19","A19"],["a19","b19","A19"],["a19","b19","b19","A19"],["a19","b19","b19","b19","A19"],["a19","b19","b19","b19","b19","A19"],["a19","b19","b19","b19","b19"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a19, b19, b19, b19, b19], [[0, 0, S19, [a19, A19]], [1, 1, A19, [b19, A19]], [2, 1, A19, [b19, A19]], [3, 1, A19, [b19, A19]], [4, 1, A19, [b19, A19]], [5, 2, A19, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a19, b19, b19, b19, b19], [[0, 0, S19, [a19, A19]], [1, 1, A19, [b19, A19]], [2, 1, A19, [b19, A19]], [3, 1, A19, [b19, A19]], [4, 1, A19, [b19, A19]], [5, 2, A19, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
71. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S20","A20"],"terminals":["a20","b20"],"start":"S20","productions":[["S20",["a20","A20"]],["A20",["b20","A20"]],["A20",[]]],"allow_epsilon":true,"word":["a20"],"forms":[["S20"],["a20","A20"],["a20"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a20], [[0, 0, S20, [a20, A20]], [1, 2, A20, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a20], [[0, 0, S20, [a20, A20]], [1, 2, A20, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
72. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S21","A21"],"terminals":["a21","b21"],"start":"S21","productions":[["S21",["a21","A21"]],["A21",["b21","A21"]],["A21",[]]],"allow_epsilon":true,"word":["a21","b21"],"forms":[["S21"],["a21","A21"],["a21","b21","A21"],["a21","b21"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a21, b21], [[0, 0, S21, [a21, A21]], [1, 1, A21, [b21, A21]], [2, 2, A21, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a21, b21], [[0, 0, S21, [a21, A21]], [1, 1, A21, [b21, A21]], [2, 2, A21, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
73. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S22","A22"],"terminals":["a22","b22"],"start":"S22","productions":[["S22",["a22","A22"]],["A22",["b22","A22"]],["A22",[]]],"allow_epsilon":true,"word":["a22","b22","b22"],"forms":[["S22"],["a22","A22"],["a22","b22","A22"],["a22","b22","b22","A22"],["a22","b22","b22"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a22, b22, b22], [[0, 0, S22, [a22, A22]], [1, 1, A22, [b22, A22]], [2, 1, A22, [b22, A22]], [3, 2, A22, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a22, b22, b22], [[0, 0, S22, [a22, A22]], [1, 1, A22, [b22, A22]], [2, 1, A22, [b22, A22]], [3, 2, A22, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
74. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S23","A23"],"terminals":["a23","b23"],"start":"S23","productions":[["S23",["a23","A23"]],["A23",["b23","A23"]],["A23",[]]],"allow_epsilon":true,"word":["a23","b23","b23","b23"],"forms":[["S23"],["a23","A23"],["a23","b23","A23"],["a23","b23","b23","A23"],["a23","b23","b23","b23","A23"],["a23","b23","b23","b23"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a23, b23, b23, b23], [[0, 0, S23, [a23, A23]], [1, 1, A23, [b23, A23]], [2, 1, A23, [b23, A23]], [3, 1, A23, [b23, A23]], [4, 2, A23, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a23, b23, b23, b23], [[0, 0, S23, [a23, A23]], [1, 1, A23, [b23, A23]], [2, 1, A23, [b23, A23]], [3, 1, A23, [b23, A23]], [4, 2, A23, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
75. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-membership-witness；資料={"nonterminals":["S24","A24"],"terminals":["a24","b24"],"start":"S24","productions":[["S24",["a24","A24"]],["A24",["b24","A24"]],["A24",[]]],"allow_epsilon":true,"word":["a24","b24","b24","b24","b24"],"forms":[["S24"],["a24","A24"],["a24","b24","A24"],["a24","b24","b24","A24"],["a24","b24","b24","b24","A24"],["a24","b24","b24","b24","b24","A24"],["a24","b24","b24","b24","b24"]]}。請依 [word, step_witnesses, valid_derivation, terminal_word, membership_certificate, certificate] 欄序回答。
查看答案與解釋
([a24, b24, b24, b24, b24], [[0, 0, S24, [a24, A24]], [1, 1, A24, [b24, A24]], [2, 1, A24, [b24, A24]], [3, 1, A24, [b24, A24]], [4, 1, A24, [b24, A24]], [5, 2, A24, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)
Wave6第三層核對=([a24, b24, b24, b24, b24], [[0, 0, S24, [a24, A24]], [1, 1, A24, [b24, A24]], [2, 1, A24, [b24, A24]], [3, 1, A24, [b24, A24]], [4, 1, A24, [b24, A24]], [5, 2, A24, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-membership-witness · candidate
76. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S0","A0"],"terminals":["a0","b0"],"start":"S0","productions":[["S0",["a0","A0"]],["A0",["b0","A0"]],["A0",[]]],"allow_epsilon":true,"word":["a0","b0"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a0, b0], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a0, b0], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
77. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S1","A1"],"terminals":["a1","b1"],"start":"S1","productions":[["S1",["a1","A1"]],["A1",["b1","A1"]],["A1",[]]],"allow_epsilon":true,"word":["a1","b1","b1"],"max_steps":2}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a1, b1, b1], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a1, b1, b1], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
78. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S2","A2"],"terminals":["a2","b2"],"start":"S2","productions":[["S2",["a2","A2"]],["A2",["b2","A2"]],["A2",[]]],"allow_epsilon":true,"word":["a2","b2","b2","b2"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a2, b2, b2, b2], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a2, b2, b2, b2], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
79. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S3","A3"],"terminals":["a3","b3"],"start":"S3","productions":[["S3",["a3","A3"]],["A3",["b3","A3"]],["A3",[]]],"allow_epsilon":true,"word":["a3","b3","b3","b3","b3"],"max_steps":2}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a3, b3, b3, b3, b3], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a3, b3, b3, b3, b3], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
80. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S4","A4"],"terminals":["a4","b4"],"start":"S4","productions":[["S4",["a4","A4"]],["A4",["b4","A4"]],["A4",[]]],"allow_epsilon":true,"word":["a4","b4","b4","b4","b4","b4"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a4, b4, b4, b4, b4, b4], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a4, b4, b4, b4, b4, b4], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
81. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S5","A5"],"terminals":["a5","b5"],"start":"S5","productions":[["S5",["a5","A5"]],["A5",["b5","A5"]],["A5",[]]],"allow_epsilon":true,"word":["a5","b5"],"max_steps":2}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a5, b5], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a5, b5], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
82. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S6","A6"],"terminals":["a6","b6"],"start":"S6","productions":[["S6",["a6","A6"]],["A6",["b6","A6"]],["A6",[]]],"allow_epsilon":true,"word":["a6","b6","b6"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a6, b6, b6], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a6, b6, b6], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
83. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S7","A7"],"terminals":["a7","b7"],"start":"S7","productions":[["S7",["a7","A7"]],["A7",["b7","A7"]],["A7",[]]],"allow_epsilon":true,"word":["a7","b7","b7","b7"],"max_steps":2}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a7, b7, b7, b7], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a7, b7, b7, b7], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
84. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S8","A8"],"terminals":["a8","b8"],"start":"S8","productions":[["S8",["a8","A8"]],["A8",["b8","A8"]],["A8",[]]],"allow_epsilon":true,"word":["a8","b8","b8","b8","b8"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a8, b8, b8, b8, b8], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a8, b8, b8, b8, b8], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
85. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S9","A9"],"terminals":["a9","b9"],"start":"S9","productions":[["S9",["a9","A9"]],["A9",["b9","A9"]],["A9",[]]],"allow_epsilon":true,"word":["a9","b9","b9","b9","b9","b9"],"max_steps":2}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a9, b9, b9, b9, b9, b9], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a9, b9, b9, b9, b9, b9], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
86. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S10","A10"],"terminals":["a10","b10"],"start":"S10","productions":[["S10",["a10","A10"]],["A10",["b10","A10"]],["A10",[]]],"allow_epsilon":true,"word":["a10","b10"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a10, b10], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a10, b10], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
87. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S11","A11"],"terminals":["a11","b11"],"start":"S11","productions":[["S11",["a11","A11"]],["A11",["b11","A11"]],["A11",[]]],"allow_epsilon":true,"word":["a11","b11","b11"],"max_steps":2}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a11, b11, b11], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a11, b11, b11], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
88. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S12","A12"],"terminals":["a12","b12"],"start":"S12","productions":[["S12",["a12","A12"]],["A12",["b12","A12"]],["A12",[]]],"allow_epsilon":true,"word":["a12","b12","b12","b12"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a12, b12, b12, b12], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a12, b12, b12, b12], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
89. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S13","A13"],"terminals":["a13","b13"],"start":"S13","productions":[["S13",["a13","A13"]],["A13",["b13","A13"]],["A13",[]]],"allow_epsilon":true,"word":["a13","b13","b13","b13","b13"],"max_steps":2}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a13, b13, b13, b13, b13], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a13, b13, b13, b13, b13], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
90. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S14","A14"],"terminals":["a14","b14"],"start":"S14","productions":[["S14",["a14","A14"]],["A14",["b14","A14"]],["A14",[]]],"allow_epsilon":true,"word":["a14","b14","b14","b14","b14","b14"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a14, b14, b14, b14, b14, b14], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a14, b14, b14, b14, b14, b14], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
91. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S15","A15"],"terminals":["a15","b15"],"start":"S15","productions":[["S15",["a15","A15"]],["A15",["b15","A15"]],["A15",[]]],"allow_epsilon":true,"word":["a15","b15"],"max_steps":2}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a15, b15], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a15, b15], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
92. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S16","A16"],"terminals":["a16","b16"],"start":"S16","productions":[["S16",["a16","A16"]],["A16",["b16","A16"]],["A16",[]]],"allow_epsilon":true,"word":["a16","b16","b16"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a16, b16, b16], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a16, b16, b16], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
93. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S17","A17"],"terminals":["a17","b17"],"start":"S17","productions":[["S17",["a17","A17"]],["A17",["b17","A17"]],["A17",[]]],"allow_epsilon":true,"word":["a17","b17","b17","b17"],"max_steps":2}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a17, b17, b17, b17], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a17, b17, b17, b17], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
94. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S18","A18"],"terminals":["a18","b18"],"start":"S18","productions":[["S18",["a18","A18"]],["A18",["b18","A18"]],["A18",[]]],"allow_epsilon":true,"word":["a18","b18","b18","b18","b18"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a18, b18, b18, b18, b18], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a18, b18, b18, b18, b18], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
95. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S19","A19"],"terminals":["a19","b19"],"start":"S19","productions":[["S19",["a19","A19"]],["A19",["b19","A19"]],["A19",[]]],"allow_epsilon":true,"word":["a19","b19","b19","b19","b19","b19"],"max_steps":2}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a19, b19, b19, b19, b19, b19], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a19, b19, b19, b19, b19, b19], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
96. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S20","A20"],"terminals":["a20","b20"],"start":"S20","productions":[["S20",["a20","A20"]],["A20",["b20","A20"]],["A20",[]]],"allow_epsilon":true,"word":["a20","b20"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a20, b20], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a20, b20], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
97. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S21","A21"],"terminals":["a21","b21"],"start":"S21","productions":[["S21",["a21","A21"]],["A21",["b21","A21"]],["A21",[]]],"allow_epsilon":true,"word":["a21","b21","b21"],"max_steps":2}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a21, b21, b21], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a21, b21, b21], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
98. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S22","A22"],"terminals":["a22","b22"],"start":"S22","productions":[["S22",["a22","A22"]],["A22",["b22","A22"]],["A22",[]]],"allow_epsilon":true,"word":["a22","b22","b22","b22"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a22, b22, b22, b22], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a22, b22, b22, b22], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
99. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S23","A23"],"terminals":["a23","b23"],"start":"S23","productions":[["S23",["a23","A23"]],["A23",["b23","A23"]],["A23",[]]],"allow_epsilon":true,"word":["a23","b23","b23","b23","b23"],"max_steps":2}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a23, b23, b23, b23, b23], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a23, b23, b23, b23, b23], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
100. 上下文無關文法
finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-bounded-search-boundary；資料={"nonterminals":["S24","A24"],"terminals":["a24","b24"],"start":"S24","productions":[["S24",["a24","A24"]],["A24",["b24","A24"]],["A24",[]]],"allow_epsilon":true,"word":["a24","b24","b24","b24","b24","b24"],"max_steps":1}。請依 [word, max_steps, found_in_bounded_search, nonmembership_claim, boundary] 欄序回答。
found只報本次深度及長度受限搜尋是否找到；固定的否不作nonmembership結論。搜尋失敗不是word不在language的證明。
查看答案與解釋
([a24, b24, b24, b24, b24, b24], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)
Wave6第三層核對=([a24, b24, b24, b24, b24, b24], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。
本題逐步詳解（AI 二次覆核）
上下文無關文法 · qf-mod40-cfg-bounded-search-boundary · candidate
原始題目 JSONL · 驗收報告