{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0001","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S0, A0], [a0, b0], S0, [[S0, [a0, A0]], [A0, [b0, A0]], [A0, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097001,"parameters":{"nonterminals":["S0","A0"],"terminals":["a0","b0"],"start":"S0","productions":[["S0",["a0","A0"]],["A0",["b0","A0"]],["A0",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A0\",\"S0\"],\"productions\":[[\"A0\",[\"b0\",\"A0\"]],[\"A0\",[]],[\"S0\",[\"a0\",\"A0\"]]],\"start\":\"S0\",\"terminals\":[\"a0\",\"b0\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0002","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S1, A1], [a1, b1], S1, [[S1, [a1, A1]], [A1, [b1, A1]], [A1, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097002,"parameters":{"nonterminals":["S1","A1"],"terminals":["a1","b1"],"start":"S1","productions":[["S1",["a1","A1"]],["A1",["b1","A1"]],["A1",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A1\",\"S1\"],\"productions\":[[\"A1\",[\"b1\",\"A1\"]],[\"A1\",[]],[\"S1\",[\"a1\",\"A1\"]]],\"start\":\"S1\",\"terminals\":[\"a1\",\"b1\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0003","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S2, A2], [a2, b2], S2, [[S2, [a2, A2]], [A2, [b2, A2]], [A2, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097003,"parameters":{"nonterminals":["S2","A2"],"terminals":["a2","b2"],"start":"S2","productions":[["S2",["a2","A2"]],["A2",["b2","A2"]],["A2",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A2\",\"S2\"],\"productions\":[[\"A2\",[\"b2\",\"A2\"]],[\"A2\",[]],[\"S2\",[\"a2\",\"A2\"]]],\"start\":\"S2\",\"terminals\":[\"a2\",\"b2\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0004","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S3, A3], [a3, b3], S3, [[S3, [a3, A3]], [A3, [b3, A3]], [A3, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097004,"parameters":{"nonterminals":["S3","A3"],"terminals":["a3","b3"],"start":"S3","productions":[["S3",["a3","A3"]],["A3",["b3","A3"]],["A3",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A3\",\"S3\"],\"productions\":[[\"A3\",[\"b3\",\"A3\"]],[\"A3\",[]],[\"S3\",[\"a3\",\"A3\"]]],\"start\":\"S3\",\"terminals\":[\"a3\",\"b3\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0005","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S4, A4], [a4, b4], S4, [[S4, [a4, A4]], [A4, [b4, A4]], [A4, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097005,"parameters":{"nonterminals":["S4","A4"],"terminals":["a4","b4"],"start":"S4","productions":[["S4",["a4","A4"]],["A4",["b4","A4"]],["A4",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A4\",\"S4\"],\"productions\":[[\"A4\",[\"b4\",\"A4\"]],[\"A4\",[]],[\"S4\",[\"a4\",\"A4\"]]],\"start\":\"S4\",\"terminals\":[\"a4\",\"b4\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0006","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S5, A5], [a5, b5], S5, [[S5, [a5, A5]], [A5, [b5, A5]], [A5, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097006,"parameters":{"nonterminals":["S5","A5"],"terminals":["a5","b5"],"start":"S5","productions":[["S5",["a5","A5"]],["A5",["b5","A5"]],["A5",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A5\",\"S5\"],\"productions\":[[\"A5\",[\"b5\",\"A5\"]],[\"A5\",[]],[\"S5\",[\"a5\",\"A5\"]]],\"start\":\"S5\",\"terminals\":[\"a5\",\"b5\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0007","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S6, A6], [a6, b6], S6, [[S6, [a6, A6]], [A6, [b6, A6]], [A6, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097007,"parameters":{"nonterminals":["S6","A6"],"terminals":["a6","b6"],"start":"S6","productions":[["S6",["a6","A6"]],["A6",["b6","A6"]],["A6",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A6\",\"S6\"],\"productions\":[[\"A6\",[\"b6\",\"A6\"]],[\"A6\",[]],[\"S6\",[\"a6\",\"A6\"]]],\"start\":\"S6\",\"terminals\":[\"a6\",\"b6\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0008","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S7, A7], [a7, b7], S7, [[S7, [a7, A7]], [A7, [b7, A7]], [A7, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097008,"parameters":{"nonterminals":["S7","A7"],"terminals":["a7","b7"],"start":"S7","productions":[["S7",["a7","A7"]],["A7",["b7","A7"]],["A7",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A7\",\"S7\"],\"productions\":[[\"A7\",[\"b7\",\"A7\"]],[\"A7\",[]],[\"S7\",[\"a7\",\"A7\"]]],\"start\":\"S7\",\"terminals\":[\"a7\",\"b7\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0009","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S8, A8], [a8, b8], S8, [[S8, [a8, A8]], [A8, [b8, A8]], [A8, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097009,"parameters":{"nonterminals":["S8","A8"],"terminals":["a8","b8"],"start":"S8","productions":[["S8",["a8","A8"]],["A8",["b8","A8"]],["A8",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A8\",\"S8\"],\"productions\":[[\"A8\",[\"b8\",\"A8\"]],[\"A8\",[]],[\"S8\",[\"a8\",\"A8\"]]],\"start\":\"S8\",\"terminals\":[\"a8\",\"b8\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0010","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S9, A9], [a9, b9], S9, [[S9, [a9, A9]], [A9, [b9, A9]], [A9, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097010,"parameters":{"nonterminals":["S9","A9"],"terminals":["a9","b9"],"start":"S9","productions":[["S9",["a9","A9"]],["A9",["b9","A9"]],["A9",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A9\",\"S9\"],\"productions\":[[\"A9\",[\"b9\",\"A9\"]],[\"A9\",[]],[\"S9\",[\"a9\",\"A9\"]]],\"start\":\"S9\",\"terminals\":[\"a9\",\"b9\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0011","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S10, A10], [a10, b10], S10, [[S10, [a10, A10]], [A10, [b10, A10]], [A10, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097011,"parameters":{"nonterminals":["S10","A10"],"terminals":["a10","b10"],"start":"S10","productions":[["S10",["a10","A10"]],["A10",["b10","A10"]],["A10",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A10\",\"S10\"],\"productions\":[[\"A10\",[\"b10\",\"A10\"]],[\"A10\",[]],[\"S10\",[\"a10\",\"A10\"]]],\"start\":\"S10\",\"terminals\":[\"a10\",\"b10\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0012","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S11, A11], [a11, b11], S11, [[S11, [a11, A11]], [A11, [b11, A11]], [A11, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097012,"parameters":{"nonterminals":["S11","A11"],"terminals":["a11","b11"],"start":"S11","productions":[["S11",["a11","A11"]],["A11",["b11","A11"]],["A11",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A11\",\"S11\"],\"productions\":[[\"A11\",[\"b11\",\"A11\"]],[\"A11\",[]],[\"S11\",[\"a11\",\"A11\"]]],\"start\":\"S11\",\"terminals\":[\"a11\",\"b11\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0013","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S12, A12], [a12, b12], S12, [[S12, [a12, A12]], [A12, [b12, A12]], [A12, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097013,"parameters":{"nonterminals":["S12","A12"],"terminals":["a12","b12"],"start":"S12","productions":[["S12",["a12","A12"]],["A12",["b12","A12"]],["A12",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A12\",\"S12\"],\"productions\":[[\"A12\",[\"b12\",\"A12\"]],[\"A12\",[]],[\"S12\",[\"a12\",\"A12\"]]],\"start\":\"S12\",\"terminals\":[\"a12\",\"b12\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0014","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S13, A13], [a13, b13], S13, [[S13, [a13, A13]], [A13, [b13, A13]], [A13, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097014,"parameters":{"nonterminals":["S13","A13"],"terminals":["a13","b13"],"start":"S13","productions":[["S13",["a13","A13"]],["A13",["b13","A13"]],["A13",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A13\",\"S13\"],\"productions\":[[\"A13\",[\"b13\",\"A13\"]],[\"A13\",[]],[\"S13\",[\"a13\",\"A13\"]]],\"start\":\"S13\",\"terminals\":[\"a13\",\"b13\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0015","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S14, A14], [a14, b14], S14, [[S14, [a14, A14]], [A14, [b14, A14]], [A14, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097015,"parameters":{"nonterminals":["S14","A14"],"terminals":["a14","b14"],"start":"S14","productions":[["S14",["a14","A14"]],["A14",["b14","A14"]],["A14",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A14\",\"S14\"],\"productions\":[[\"A14\",[\"b14\",\"A14\"]],[\"A14\",[]],[\"S14\",[\"a14\",\"A14\"]]],\"start\":\"S14\",\"terminals\":[\"a14\",\"b14\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0016","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S15, A15], [a15, b15], S15, [[S15, [a15, A15]], [A15, [b15, A15]], [A15, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097016,"parameters":{"nonterminals":["S15","A15"],"terminals":["a15","b15"],"start":"S15","productions":[["S15",["a15","A15"]],["A15",["b15","A15"]],["A15",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A15\",\"S15\"],\"productions\":[[\"A15\",[\"b15\",\"A15\"]],[\"A15\",[]],[\"S15\",[\"a15\",\"A15\"]]],\"start\":\"S15\",\"terminals\":[\"a15\",\"b15\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0017","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S16, A16], [a16, b16], S16, [[S16, [a16, A16]], [A16, [b16, A16]], [A16, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097017,"parameters":{"nonterminals":["S16","A16"],"terminals":["a16","b16"],"start":"S16","productions":[["S16",["a16","A16"]],["A16",["b16","A16"]],["A16",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A16\",\"S16\"],\"productions\":[[\"A16\",[\"b16\",\"A16\"]],[\"A16\",[]],[\"S16\",[\"a16\",\"A16\"]]],\"start\":\"S16\",\"terminals\":[\"a16\",\"b16\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0018","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S17, A17], [a17, b17], S17, [[S17, [a17, A17]], [A17, [b17, A17]], [A17, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097018,"parameters":{"nonterminals":["S17","A17"],"terminals":["a17","b17"],"start":"S17","productions":[["S17",["a17","A17"]],["A17",["b17","A17"]],["A17",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A17\",\"S17\"],\"productions\":[[\"A17\",[\"b17\",\"A17\"]],[\"A17\",[]],[\"S17\",[\"a17\",\"A17\"]]],\"start\":\"S17\",\"terminals\":[\"a17\",\"b17\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0019","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S18, A18], [a18, b18], S18, [[S18, [a18, A18]], [A18, [b18, A18]], [A18, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097019,"parameters":{"nonterminals":["S18","A18"],"terminals":["a18","b18"],"start":"S18","productions":[["S18",["a18","A18"]],["A18",["b18","A18"]],["A18",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A18\",\"S18\"],\"productions\":[[\"A18\",[\"b18\",\"A18\"]],[\"A18\",[]],[\"S18\",[\"a18\",\"A18\"]]],\"start\":\"S18\",\"terminals\":[\"a18\",\"b18\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0020","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S19, A19], [a19, b19], S19, [[S19, [a19, A19]], [A19, [b19, A19]], [A19, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097020,"parameters":{"nonterminals":["S19","A19"],"terminals":["a19","b19"],"start":"S19","productions":[["S19",["a19","A19"]],["A19",["b19","A19"]],["A19",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A19\",\"S19\"],\"productions\":[[\"A19\",[\"b19\",\"A19\"]],[\"A19\",[]],[\"S19\",[\"a19\",\"A19\"]]],\"start\":\"S19\",\"terminals\":[\"a19\",\"b19\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0021","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S20, A20], [a20, b20], S20, [[S20, [a20, A20]], [A20, [b20, A20]], [A20, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097021,"parameters":{"nonterminals":["S20","A20"],"terminals":["a20","b20"],"start":"S20","productions":[["S20",["a20","A20"]],["A20",["b20","A20"]],["A20",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A20\",\"S20\"],\"productions\":[[\"A20\",[\"b20\",\"A20\"]],[\"A20\",[]],[\"S20\",[\"a20\",\"A20\"]]],\"start\":\"S20\",\"terminals\":[\"a20\",\"b20\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0022","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S21, A21], [a21, b21], S21, [[S21, [a21, A21]], [A21, [b21, A21]], [A21, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097022,"parameters":{"nonterminals":["S21","A21"],"terminals":["a21","b21"],"start":"S21","productions":[["S21",["a21","A21"]],["A21",["b21","A21"]],["A21",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A21\",\"S21\"],\"productions\":[[\"A21\",[\"b21\",\"A21\"]],[\"A21\",[]],[\"S21\",[\"a21\",\"A21\"]]],\"start\":\"S21\",\"terminals\":[\"a21\",\"b21\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0023","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S22, A22], [a22, b22], S22, [[S22, [a22, A22]], [A22, [b22, A22]], [A22, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097023,"parameters":{"nonterminals":["S22","A22"],"terminals":["a22","b22"],"start":"S22","productions":[["S22",["a22","A22"]],["A22",["b22","A22"]],["A22",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A22\",\"S22\"],\"productions\":[[\"A22\",[\"b22\",\"A22\"]],[\"A22\",[]],[\"S22\",[\"a22\",\"A22\"]]],\"start\":\"S22\",\"terminals\":[\"a22\",\"b22\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0024","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S23, A23], [a23, b23], S23, [[S23, [a23, A23]], [A23, [b23, A23]], [A23, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097024,"parameters":{"nonterminals":["S23","A23"],"terminals":["a23","b23"],"start":"S23","productions":[["S23",["a23","A23"]],["A23",["b23","A23"]],["A23",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A23\",\"S23\"],\"productions\":[[\"A23\",[\"b23\",\"A23\"]],[\"A23\",[]],[\"S23\",[\"a23\",\"A23\"]]],\"start\":\"S23\",\"terminals\":[\"a23\",\"b23\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0025","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([S24, A24], [a24, b24], S24, [[S24, [a24, A24]], [A24, [b24, A24]], [A24, []]], 是, 是, finite_disjoint_alphabets_single_nonterminal_lhs)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-qualification","seed":202611097025,"parameters":{"nonterminals":["S24","A24"],"terminals":["a24","b24"],"start":"S24","productions":[["S24",["a24","A24"]],["A24",["b24","A24"]],["A24",[]]],"allow_epsilon":true,"domain":"Complete_finite_context_free_grammar","operation":"cfg-qualification","semantic_template":"qf-mod40-cfg-qualification/{\"allow_epsilon\":true,\"nonterminals\":[\"A24\",\"S24\"],\"productions\":[[\"A24\",[\"b24\",\"A24\"]],[\"A24\",[]],[\"S24\",[\"a24\",\"A24\"]]],\"start\":\"S24\",\"terminals\":[\"a24\",\"b24\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0026","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[S0], [a0, A0], [a0]], [[0, 0, S0, [a0, A0]], [1, 2, A0, []]], 是, 是, finite_production_sequence)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097026,"parameters":{"nonterminals":["S0","A0"],"terminals":["a0","b0"],"start":"S0","productions":[["S0",["a0","A0"]],["A0",["b0","A0"]],["A0",[]]],"allow_epsilon":true,"forms":[["S0"],["a0","A0"],["a0"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S0\"],[\"a0\",\"A0\"],[\"a0\"]],\"nonterminals\":[\"A0\",\"S0\"],\"productions\":[[\"A0\",[\"b0\",\"A0\"]],[\"A0\",[]],[\"S0\",[\"a0\",\"A0\"]]],\"start\":\"S0\",\"terminals\":[\"a0\",\"b0\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0027","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097027,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S1\"],[\"a1\",\"A1\"],[\"a1\",\"b1\",\"A1\"],[\"a1\",\"b1\"]],\"nonterminals\":[\"A1\",\"S1\"],\"productions\":[[\"A1\",[\"b1\",\"A1\"]],[\"A1\",[]],[\"S1\",[\"a1\",\"A1\"]]],\"start\":\"S1\",\"terminals\":[\"a1\",\"b1\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0028","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097028,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S2\"],[\"a2\",\"A2\"],[\"a2\",\"b2\",\"A2\"],[\"a2\",\"b2\",\"b2\",\"A2\"],[\"a2\",\"b2\",\"b2\"]],\"nonterminals\":[\"A2\",\"S2\"],\"productions\":[[\"A2\",[\"b2\",\"A2\"]],[\"A2\",[]],[\"S2\",[\"a2\",\"A2\"]]],\"start\":\"S2\",\"terminals\":[\"a2\",\"b2\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0029","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097029,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S3\"],[\"a3\",\"A3\"],[\"a3\",\"b3\",\"A3\"],[\"a3\",\"b3\",\"b3\",\"A3\"],[\"a3\",\"b3\",\"b3\",\"b3\",\"A3\"],[\"a3\",\"b3\",\"b3\",\"b3\"]],\"nonterminals\":[\"A3\",\"S3\"],\"productions\":[[\"A3\",[\"b3\",\"A3\"]],[\"A3\",[]],[\"S3\",[\"a3\",\"A3\"]]],\"start\":\"S3\",\"terminals\":[\"a3\",\"b3\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0030","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097030,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"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\"]],\"nonterminals\":[\"A4\",\"S4\"],\"productions\":[[\"A4\",[\"b4\",\"A4\"]],[\"A4\",[]],[\"S4\",[\"a4\",\"A4\"]]],\"start\":\"S4\",\"terminals\":[\"a4\",\"b4\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0031","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[S5], [a5, A5], [a5]], [[0, 0, S5, [a5, A5]], [1, 2, A5, []]], 是, 是, finite_production_sequence)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097031,"parameters":{"nonterminals":["S5","A5"],"terminals":["a5","b5"],"start":"S5","productions":[["S5",["a5","A5"]],["A5",["b5","A5"]],["A5",[]]],"allow_epsilon":true,"forms":[["S5"],["a5","A5"],["a5"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S5\"],[\"a5\",\"A5\"],[\"a5\"]],\"nonterminals\":[\"A5\",\"S5\"],\"productions\":[[\"A5\",[\"b5\",\"A5\"]],[\"A5\",[]],[\"S5\",[\"a5\",\"A5\"]]],\"start\":\"S5\",\"terminals\":[\"a5\",\"b5\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0032","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097032,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S6\"],[\"a6\",\"A6\"],[\"a6\",\"b6\",\"A6\"],[\"a6\",\"b6\"]],\"nonterminals\":[\"A6\",\"S6\"],\"productions\":[[\"A6\",[\"b6\",\"A6\"]],[\"A6\",[]],[\"S6\",[\"a6\",\"A6\"]]],\"start\":\"S6\",\"terminals\":[\"a6\",\"b6\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0033","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097033,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S7\"],[\"a7\",\"A7\"],[\"a7\",\"b7\",\"A7\"],[\"a7\",\"b7\",\"b7\",\"A7\"],[\"a7\",\"b7\",\"b7\"]],\"nonterminals\":[\"A7\",\"S7\"],\"productions\":[[\"A7\",[\"b7\",\"A7\"]],[\"A7\",[]],[\"S7\",[\"a7\",\"A7\"]]],\"start\":\"S7\",\"terminals\":[\"a7\",\"b7\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0034","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097034,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S8\"],[\"a8\",\"A8\"],[\"a8\",\"b8\",\"A8\"],[\"a8\",\"b8\",\"b8\",\"A8\"],[\"a8\",\"b8\",\"b8\",\"b8\",\"A8\"],[\"a8\",\"b8\",\"b8\",\"b8\"]],\"nonterminals\":[\"A8\",\"S8\"],\"productions\":[[\"A8\",[\"b8\",\"A8\"]],[\"A8\",[]],[\"S8\",[\"a8\",\"A8\"]]],\"start\":\"S8\",\"terminals\":[\"a8\",\"b8\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0035","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097035,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"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\"]],\"nonterminals\":[\"A9\",\"S9\"],\"productions\":[[\"A9\",[\"b9\",\"A9\"]],[\"A9\",[]],[\"S9\",[\"a9\",\"A9\"]]],\"start\":\"S9\",\"terminals\":[\"a9\",\"b9\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0036","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[S10], [a10, A10], [a10]], [[0, 0, S10, [a10, A10]], [1, 2, A10, []]], 是, 是, finite_production_sequence)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097036,"parameters":{"nonterminals":["S10","A10"],"terminals":["a10","b10"],"start":"S10","productions":[["S10",["a10","A10"]],["A10",["b10","A10"]],["A10",[]]],"allow_epsilon":true,"forms":[["S10"],["a10","A10"],["a10"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S10\"],[\"a10\",\"A10\"],[\"a10\"]],\"nonterminals\":[\"A10\",\"S10\"],\"productions\":[[\"A10\",[\"b10\",\"A10\"]],[\"A10\",[]],[\"S10\",[\"a10\",\"A10\"]]],\"start\":\"S10\",\"terminals\":[\"a10\",\"b10\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0037","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097037,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S11\"],[\"a11\",\"A11\"],[\"a11\",\"b11\",\"A11\"],[\"a11\",\"b11\"]],\"nonterminals\":[\"A11\",\"S11\"],\"productions\":[[\"A11\",[\"b11\",\"A11\"]],[\"A11\",[]],[\"S11\",[\"a11\",\"A11\"]]],\"start\":\"S11\",\"terminals\":[\"a11\",\"b11\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0038","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097038,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S12\"],[\"a12\",\"A12\"],[\"a12\",\"b12\",\"A12\"],[\"a12\",\"b12\",\"b12\",\"A12\"],[\"a12\",\"b12\",\"b12\"]],\"nonterminals\":[\"A12\",\"S12\"],\"productions\":[[\"A12\",[\"b12\",\"A12\"]],[\"A12\",[]],[\"S12\",[\"a12\",\"A12\"]]],\"start\":\"S12\",\"terminals\":[\"a12\",\"b12\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0039","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097039,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S13\"],[\"a13\",\"A13\"],[\"a13\",\"b13\",\"A13\"],[\"a13\",\"b13\",\"b13\",\"A13\"],[\"a13\",\"b13\",\"b13\",\"b13\",\"A13\"],[\"a13\",\"b13\",\"b13\",\"b13\"]],\"nonterminals\":[\"A13\",\"S13\"],\"productions\":[[\"A13\",[\"b13\",\"A13\"]],[\"A13\",[]],[\"S13\",[\"a13\",\"A13\"]]],\"start\":\"S13\",\"terminals\":[\"a13\",\"b13\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0040","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097040,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"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\"]],\"nonterminals\":[\"A14\",\"S14\"],\"productions\":[[\"A14\",[\"b14\",\"A14\"]],[\"A14\",[]],[\"S14\",[\"a14\",\"A14\"]]],\"start\":\"S14\",\"terminals\":[\"a14\",\"b14\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0041","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[S15], [a15, A15], [a15]], [[0, 0, S15, [a15, A15]], [1, 2, A15, []]], 是, 是, finite_production_sequence)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097041,"parameters":{"nonterminals":["S15","A15"],"terminals":["a15","b15"],"start":"S15","productions":[["S15",["a15","A15"]],["A15",["b15","A15"]],["A15",[]]],"allow_epsilon":true,"forms":[["S15"],["a15","A15"],["a15"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S15\"],[\"a15\",\"A15\"],[\"a15\"]],\"nonterminals\":[\"A15\",\"S15\"],\"productions\":[[\"A15\",[\"b15\",\"A15\"]],[\"A15\",[]],[\"S15\",[\"a15\",\"A15\"]]],\"start\":\"S15\",\"terminals\":[\"a15\",\"b15\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0042","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097042,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S16\"],[\"a16\",\"A16\"],[\"a16\",\"b16\",\"A16\"],[\"a16\",\"b16\"]],\"nonterminals\":[\"A16\",\"S16\"],\"productions\":[[\"A16\",[\"b16\",\"A16\"]],[\"A16\",[]],[\"S16\",[\"a16\",\"A16\"]]],\"start\":\"S16\",\"terminals\":[\"a16\",\"b16\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0043","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097043,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S17\"],[\"a17\",\"A17\"],[\"a17\",\"b17\",\"A17\"],[\"a17\",\"b17\",\"b17\",\"A17\"],[\"a17\",\"b17\",\"b17\"]],\"nonterminals\":[\"A17\",\"S17\"],\"productions\":[[\"A17\",[\"b17\",\"A17\"]],[\"A17\",[]],[\"S17\",[\"a17\",\"A17\"]]],\"start\":\"S17\",\"terminals\":[\"a17\",\"b17\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0044","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097044,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S18\"],[\"a18\",\"A18\"],[\"a18\",\"b18\",\"A18\"],[\"a18\",\"b18\",\"b18\",\"A18\"],[\"a18\",\"b18\",\"b18\",\"b18\",\"A18\"],[\"a18\",\"b18\",\"b18\",\"b18\"]],\"nonterminals\":[\"A18\",\"S18\"],\"productions\":[[\"A18\",[\"b18\",\"A18\"]],[\"A18\",[]],[\"S18\",[\"a18\",\"A18\"]]],\"start\":\"S18\",\"terminals\":[\"a18\",\"b18\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0045","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097045,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"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\"]],\"nonterminals\":[\"A19\",\"S19\"],\"productions\":[[\"A19\",[\"b19\",\"A19\"]],[\"A19\",[]],[\"S19\",[\"a19\",\"A19\"]]],\"start\":\"S19\",\"terminals\":[\"a19\",\"b19\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0046","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[S20], [a20, A20], [a20]], [[0, 0, S20, [a20, A20]], [1, 2, A20, []]], 是, 是, finite_production_sequence)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097046,"parameters":{"nonterminals":["S20","A20"],"terminals":["a20","b20"],"start":"S20","productions":[["S20",["a20","A20"]],["A20",["b20","A20"]],["A20",[]]],"allow_epsilon":true,"forms":[["S20"],["a20","A20"],["a20"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S20\"],[\"a20\",\"A20\"],[\"a20\"]],\"nonterminals\":[\"A20\",\"S20\"],\"productions\":[[\"A20\",[\"b20\",\"A20\"]],[\"A20\",[]],[\"S20\",[\"a20\",\"A20\"]]],\"start\":\"S20\",\"terminals\":[\"a20\",\"b20\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0047","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097047,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S21\"],[\"a21\",\"A21\"],[\"a21\",\"b21\",\"A21\"],[\"a21\",\"b21\"]],\"nonterminals\":[\"A21\",\"S21\"],\"productions\":[[\"A21\",[\"b21\",\"A21\"]],[\"A21\",[]],[\"S21\",[\"a21\",\"A21\"]]],\"start\":\"S21\",\"terminals\":[\"a21\",\"b21\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0048","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097048,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S22\"],[\"a22\",\"A22\"],[\"a22\",\"b22\",\"A22\"],[\"a22\",\"b22\",\"b22\",\"A22\"],[\"a22\",\"b22\",\"b22\"]],\"nonterminals\":[\"A22\",\"S22\"],\"productions\":[[\"A22\",[\"b22\",\"A22\"]],[\"A22\",[]],[\"S22\",[\"a22\",\"A22\"]]],\"start\":\"S22\",\"terminals\":[\"a22\",\"b22\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0049","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097049,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S23\"],[\"a23\",\"A23\"],[\"a23\",\"b23\",\"A23\"],[\"a23\",\"b23\",\"b23\",\"A23\"],[\"a23\",\"b23\",\"b23\",\"b23\",\"A23\"],[\"a23\",\"b23\",\"b23\",\"b23\"]],\"nonterminals\":[\"A23\",\"S23\"],\"productions\":[[\"A23\",[\"b23\",\"A23\"]],[\"A23\",[]],[\"S23\",[\"a23\",\"A23\"]]],\"start\":\"S23\",\"terminals\":[\"a23\",\"b23\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0050","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-derivation-audit","seed":202611097050,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-derivation-audit","semantic_template":"qf-mod40-cfg-derivation-audit/{\"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\"]],\"nonterminals\":[\"A24\",\"S24\"],\"productions\":[[\"A24\",[\"b24\",\"A24\"]],[\"A24\",[]],[\"S24\",[\"a24\",\"A24\"]]],\"start\":\"S24\",\"terminals\":[\"a24\",\"b24\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0051","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a0], [[0, 0, S0, [a0, A0]], [1, 2, A0, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097051,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S0\"],[\"a0\",\"A0\"],[\"a0\"]],\"nonterminals\":[\"A0\",\"S0\"],\"productions\":[[\"A0\",[\"b0\",\"A0\"]],[\"A0\",[]],[\"S0\",[\"a0\",\"A0\"]]],\"start\":\"S0\",\"terminals\":[\"a0\",\"b0\"],\"word\":[\"a0\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0052","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097052,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S1\"],[\"a1\",\"A1\"],[\"a1\",\"b1\",\"A1\"],[\"a1\",\"b1\"]],\"nonterminals\":[\"A1\",\"S1\"],\"productions\":[[\"A1\",[\"b1\",\"A1\"]],[\"A1\",[]],[\"S1\",[\"a1\",\"A1\"]]],\"start\":\"S1\",\"terminals\":[\"a1\",\"b1\"],\"word\":[\"a1\",\"b1\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0053","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097053,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S2\"],[\"a2\",\"A2\"],[\"a2\",\"b2\",\"A2\"],[\"a2\",\"b2\",\"b2\",\"A2\"],[\"a2\",\"b2\",\"b2\"]],\"nonterminals\":[\"A2\",\"S2\"],\"productions\":[[\"A2\",[\"b2\",\"A2\"]],[\"A2\",[]],[\"S2\",[\"a2\",\"A2\"]]],\"start\":\"S2\",\"terminals\":[\"a2\",\"b2\"],\"word\":[\"a2\",\"b2\",\"b2\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0054","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097054,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S3\"],[\"a3\",\"A3\"],[\"a3\",\"b3\",\"A3\"],[\"a3\",\"b3\",\"b3\",\"A3\"],[\"a3\",\"b3\",\"b3\",\"b3\",\"A3\"],[\"a3\",\"b3\",\"b3\",\"b3\"]],\"nonterminals\":[\"A3\",\"S3\"],\"productions\":[[\"A3\",[\"b3\",\"A3\"]],[\"A3\",[]],[\"S3\",[\"a3\",\"A3\"]]],\"start\":\"S3\",\"terminals\":[\"a3\",\"b3\"],\"word\":[\"a3\",\"b3\",\"b3\",\"b3\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0055","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097055,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"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\"]],\"nonterminals\":[\"A4\",\"S4\"],\"productions\":[[\"A4\",[\"b4\",\"A4\"]],[\"A4\",[]],[\"S4\",[\"a4\",\"A4\"]]],\"start\":\"S4\",\"terminals\":[\"a4\",\"b4\"],\"word\":[\"a4\",\"b4\",\"b4\",\"b4\",\"b4\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0056","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a5], [[0, 0, S5, [a5, A5]], [1, 2, A5, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097056,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S5\"],[\"a5\",\"A5\"],[\"a5\"]],\"nonterminals\":[\"A5\",\"S5\"],\"productions\":[[\"A5\",[\"b5\",\"A5\"]],[\"A5\",[]],[\"S5\",[\"a5\",\"A5\"]]],\"start\":\"S5\",\"terminals\":[\"a5\",\"b5\"],\"word\":[\"a5\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0057","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097057,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S6\"],[\"a6\",\"A6\"],[\"a6\",\"b6\",\"A6\"],[\"a6\",\"b6\"]],\"nonterminals\":[\"A6\",\"S6\"],\"productions\":[[\"A6\",[\"b6\",\"A6\"]],[\"A6\",[]],[\"S6\",[\"a6\",\"A6\"]]],\"start\":\"S6\",\"terminals\":[\"a6\",\"b6\"],\"word\":[\"a6\",\"b6\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0058","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097058,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S7\"],[\"a7\",\"A7\"],[\"a7\",\"b7\",\"A7\"],[\"a7\",\"b7\",\"b7\",\"A7\"],[\"a7\",\"b7\",\"b7\"]],\"nonterminals\":[\"A7\",\"S7\"],\"productions\":[[\"A7\",[\"b7\",\"A7\"]],[\"A7\",[]],[\"S7\",[\"a7\",\"A7\"]]],\"start\":\"S7\",\"terminals\":[\"a7\",\"b7\"],\"word\":[\"a7\",\"b7\",\"b7\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0059","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097059,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S8\"],[\"a8\",\"A8\"],[\"a8\",\"b8\",\"A8\"],[\"a8\",\"b8\",\"b8\",\"A8\"],[\"a8\",\"b8\",\"b8\",\"b8\",\"A8\"],[\"a8\",\"b8\",\"b8\",\"b8\"]],\"nonterminals\":[\"A8\",\"S8\"],\"productions\":[[\"A8\",[\"b8\",\"A8\"]],[\"A8\",[]],[\"S8\",[\"a8\",\"A8\"]]],\"start\":\"S8\",\"terminals\":[\"a8\",\"b8\"],\"word\":[\"a8\",\"b8\",\"b8\",\"b8\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0060","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097060,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"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\"]],\"nonterminals\":[\"A9\",\"S9\"],\"productions\":[[\"A9\",[\"b9\",\"A9\"]],[\"A9\",[]],[\"S9\",[\"a9\",\"A9\"]]],\"start\":\"S9\",\"terminals\":[\"a9\",\"b9\"],\"word\":[\"a9\",\"b9\",\"b9\",\"b9\",\"b9\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0061","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a10], [[0, 0, S10, [a10, A10]], [1, 2, A10, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097061,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S10\"],[\"a10\",\"A10\"],[\"a10\"]],\"nonterminals\":[\"A10\",\"S10\"],\"productions\":[[\"A10\",[\"b10\",\"A10\"]],[\"A10\",[]],[\"S10\",[\"a10\",\"A10\"]]],\"start\":\"S10\",\"terminals\":[\"a10\",\"b10\"],\"word\":[\"a10\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0062","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097062,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S11\"],[\"a11\",\"A11\"],[\"a11\",\"b11\",\"A11\"],[\"a11\",\"b11\"]],\"nonterminals\":[\"A11\",\"S11\"],\"productions\":[[\"A11\",[\"b11\",\"A11\"]],[\"A11\",[]],[\"S11\",[\"a11\",\"A11\"]]],\"start\":\"S11\",\"terminals\":[\"a11\",\"b11\"],\"word\":[\"a11\",\"b11\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0063","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097063,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S12\"],[\"a12\",\"A12\"],[\"a12\",\"b12\",\"A12\"],[\"a12\",\"b12\",\"b12\",\"A12\"],[\"a12\",\"b12\",\"b12\"]],\"nonterminals\":[\"A12\",\"S12\"],\"productions\":[[\"A12\",[\"b12\",\"A12\"]],[\"A12\",[]],[\"S12\",[\"a12\",\"A12\"]]],\"start\":\"S12\",\"terminals\":[\"a12\",\"b12\"],\"word\":[\"a12\",\"b12\",\"b12\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0064","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097064,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S13\"],[\"a13\",\"A13\"],[\"a13\",\"b13\",\"A13\"],[\"a13\",\"b13\",\"b13\",\"A13\"],[\"a13\",\"b13\",\"b13\",\"b13\",\"A13\"],[\"a13\",\"b13\",\"b13\",\"b13\"]],\"nonterminals\":[\"A13\",\"S13\"],\"productions\":[[\"A13\",[\"b13\",\"A13\"]],[\"A13\",[]],[\"S13\",[\"a13\",\"A13\"]]],\"start\":\"S13\",\"terminals\":[\"a13\",\"b13\"],\"word\":[\"a13\",\"b13\",\"b13\",\"b13\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0065","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097065,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"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\"]],\"nonterminals\":[\"A14\",\"S14\"],\"productions\":[[\"A14\",[\"b14\",\"A14\"]],[\"A14\",[]],[\"S14\",[\"a14\",\"A14\"]]],\"start\":\"S14\",\"terminals\":[\"a14\",\"b14\"],\"word\":[\"a14\",\"b14\",\"b14\",\"b14\",\"b14\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0066","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a15], [[0, 0, S15, [a15, A15]], [1, 2, A15, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097066,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S15\"],[\"a15\",\"A15\"],[\"a15\"]],\"nonterminals\":[\"A15\",\"S15\"],\"productions\":[[\"A15\",[\"b15\",\"A15\"]],[\"A15\",[]],[\"S15\",[\"a15\",\"A15\"]]],\"start\":\"S15\",\"terminals\":[\"a15\",\"b15\"],\"word\":[\"a15\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0067","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097067,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S16\"],[\"a16\",\"A16\"],[\"a16\",\"b16\",\"A16\"],[\"a16\",\"b16\"]],\"nonterminals\":[\"A16\",\"S16\"],\"productions\":[[\"A16\",[\"b16\",\"A16\"]],[\"A16\",[]],[\"S16\",[\"a16\",\"A16\"]]],\"start\":\"S16\",\"terminals\":[\"a16\",\"b16\"],\"word\":[\"a16\",\"b16\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0068","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097068,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S17\"],[\"a17\",\"A17\"],[\"a17\",\"b17\",\"A17\"],[\"a17\",\"b17\",\"b17\",\"A17\"],[\"a17\",\"b17\",\"b17\"]],\"nonterminals\":[\"A17\",\"S17\"],\"productions\":[[\"A17\",[\"b17\",\"A17\"]],[\"A17\",[]],[\"S17\",[\"a17\",\"A17\"]]],\"start\":\"S17\",\"terminals\":[\"a17\",\"b17\"],\"word\":[\"a17\",\"b17\",\"b17\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0069","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097069,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S18\"],[\"a18\",\"A18\"],[\"a18\",\"b18\",\"A18\"],[\"a18\",\"b18\",\"b18\",\"A18\"],[\"a18\",\"b18\",\"b18\",\"b18\",\"A18\"],[\"a18\",\"b18\",\"b18\",\"b18\"]],\"nonterminals\":[\"A18\",\"S18\"],\"productions\":[[\"A18\",[\"b18\",\"A18\"]],[\"A18\",[]],[\"S18\",[\"a18\",\"A18\"]]],\"start\":\"S18\",\"terminals\":[\"a18\",\"b18\"],\"word\":[\"a18\",\"b18\",\"b18\",\"b18\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0070","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097070,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"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\"]],\"nonterminals\":[\"A19\",\"S19\"],\"productions\":[[\"A19\",[\"b19\",\"A19\"]],[\"A19\",[]],[\"S19\",[\"a19\",\"A19\"]]],\"start\":\"S19\",\"terminals\":[\"a19\",\"b19\"],\"word\":[\"a19\",\"b19\",\"b19\",\"b19\",\"b19\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0071","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a20], [[0, 0, S20, [a20, A20]], [1, 2, A20, []]], 是, 是, 是, derivation_from_start_to_terminal_only_word_proves_membership)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097071,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S20\"],[\"a20\",\"A20\"],[\"a20\"]],\"nonterminals\":[\"A20\",\"S20\"],\"productions\":[[\"A20\",[\"b20\",\"A20\"]],[\"A20\",[]],[\"S20\",[\"a20\",\"A20\"]]],\"start\":\"S20\",\"terminals\":[\"a20\",\"b20\"],\"word\":[\"a20\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0072","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097072,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S21\"],[\"a21\",\"A21\"],[\"a21\",\"b21\",\"A21\"],[\"a21\",\"b21\"]],\"nonterminals\":[\"A21\",\"S21\"],\"productions\":[[\"A21\",[\"b21\",\"A21\"]],[\"A21\",[]],[\"S21\",[\"a21\",\"A21\"]]],\"start\":\"S21\",\"terminals\":[\"a21\",\"b21\"],\"word\":[\"a21\",\"b21\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0073","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097073,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S22\"],[\"a22\",\"A22\"],[\"a22\",\"b22\",\"A22\"],[\"a22\",\"b22\",\"b22\",\"A22\"],[\"a22\",\"b22\",\"b22\"]],\"nonterminals\":[\"A22\",\"S22\"],\"productions\":[[\"A22\",[\"b22\",\"A22\"]],[\"A22\",[]],[\"S22\",[\"a22\",\"A22\"]]],\"start\":\"S22\",\"terminals\":[\"a22\",\"b22\"],\"word\":[\"a22\",\"b22\",\"b22\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0074","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097074,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"allow_epsilon\":true,\"forms\":[[\"S23\"],[\"a23\",\"A23\"],[\"a23\",\"b23\",\"A23\"],[\"a23\",\"b23\",\"b23\",\"A23\"],[\"a23\",\"b23\",\"b23\",\"b23\",\"A23\"],[\"a23\",\"b23\",\"b23\",\"b23\"]],\"nonterminals\":[\"A23\",\"S23\"],\"productions\":[[\"A23\",[\"b23\",\"A23\"]],[\"A23\",[]],[\"S23\",[\"a23\",\"A23\"]]],\"start\":\"S23\",\"terminals\":[\"a23\",\"b23\"],\"word\":[\"a23\",\"b23\",\"b23\",\"b23\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0075","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-membership-witness","seed":202611097075,"parameters":{"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"]],"domain":"Complete_finite_context_free_grammar","operation":"cfg-membership-witness","semantic_template":"qf-mod40-cfg-membership-witness/{\"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\"]],\"nonterminals\":[\"A24\",\"S24\"],\"productions\":[[\"A24\",[\"b24\",\"A24\"]],[\"A24\",[]],[\"S24\",[\"a24\",\"A24\"]]],\"start\":\"S24\",\"terminals\":[\"a24\",\"b24\"],\"word\":[\"a24\",\"b24\",\"b24\",\"b24\",\"b24\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0076","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a0, b0], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097076,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A0\",\"S0\"],\"productions\":[[\"A0\",[\"b0\",\"A0\"]],[\"A0\",[]],[\"S0\",[\"a0\",\"A0\"]]],\"start\":\"S0\",\"terminals\":[\"a0\",\"b0\"],\"word\":[\"a0\",\"b0\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0077","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a1, b1, b1], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097077,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":2,\"nonterminals\":[\"A1\",\"S1\"],\"productions\":[[\"A1\",[\"b1\",\"A1\"]],[\"A1\",[]],[\"S1\",[\"a1\",\"A1\"]]],\"start\":\"S1\",\"terminals\":[\"a1\",\"b1\"],\"word\":[\"a1\",\"b1\",\"b1\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0078","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a2, b2, b2, b2], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097078,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A2\",\"S2\"],\"productions\":[[\"A2\",[\"b2\",\"A2\"]],[\"A2\",[]],[\"S2\",[\"a2\",\"A2\"]]],\"start\":\"S2\",\"terminals\":[\"a2\",\"b2\"],\"word\":[\"a2\",\"b2\",\"b2\",\"b2\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0079","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a3, b3, b3, b3, b3], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097079,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":2,\"nonterminals\":[\"A3\",\"S3\"],\"productions\":[[\"A3\",[\"b3\",\"A3\"]],[\"A3\",[]],[\"S3\",[\"a3\",\"A3\"]]],\"start\":\"S3\",\"terminals\":[\"a3\",\"b3\"],\"word\":[\"a3\",\"b3\",\"b3\",\"b3\",\"b3\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0080","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a4, b4, b4, b4, b4, b4], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097080,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A4\",\"S4\"],\"productions\":[[\"A4\",[\"b4\",\"A4\"]],[\"A4\",[]],[\"S4\",[\"a4\",\"A4\"]]],\"start\":\"S4\",\"terminals\":[\"a4\",\"b4\"],\"word\":[\"a4\",\"b4\",\"b4\",\"b4\",\"b4\",\"b4\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0081","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a5, b5], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097081,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":2,\"nonterminals\":[\"A5\",\"S5\"],\"productions\":[[\"A5\",[\"b5\",\"A5\"]],[\"A5\",[]],[\"S5\",[\"a5\",\"A5\"]]],\"start\":\"S5\",\"terminals\":[\"a5\",\"b5\"],\"word\":[\"a5\",\"b5\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0082","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a6, b6, b6], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097082,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A6\",\"S6\"],\"productions\":[[\"A6\",[\"b6\",\"A6\"]],[\"A6\",[]],[\"S6\",[\"a6\",\"A6\"]]],\"start\":\"S6\",\"terminals\":[\"a6\",\"b6\"],\"word\":[\"a6\",\"b6\",\"b6\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0083","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a7, b7, b7, b7], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097083,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":2,\"nonterminals\":[\"A7\",\"S7\"],\"productions\":[[\"A7\",[\"b7\",\"A7\"]],[\"A7\",[]],[\"S7\",[\"a7\",\"A7\"]]],\"start\":\"S7\",\"terminals\":[\"a7\",\"b7\"],\"word\":[\"a7\",\"b7\",\"b7\",\"b7\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0084","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a8, b8, b8, b8, b8], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097084,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A8\",\"S8\"],\"productions\":[[\"A8\",[\"b8\",\"A8\"]],[\"A8\",[]],[\"S8\",[\"a8\",\"A8\"]]],\"start\":\"S8\",\"terminals\":[\"a8\",\"b8\"],\"word\":[\"a8\",\"b8\",\"b8\",\"b8\",\"b8\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0085","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a9, b9, b9, b9, b9, b9], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097085,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":2,\"nonterminals\":[\"A9\",\"S9\"],\"productions\":[[\"A9\",[\"b9\",\"A9\"]],[\"A9\",[]],[\"S9\",[\"a9\",\"A9\"]]],\"start\":\"S9\",\"terminals\":[\"a9\",\"b9\"],\"word\":[\"a9\",\"b9\",\"b9\",\"b9\",\"b9\",\"b9\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0086","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a10, b10], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097086,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A10\",\"S10\"],\"productions\":[[\"A10\",[\"b10\",\"A10\"]],[\"A10\",[]],[\"S10\",[\"a10\",\"A10\"]]],\"start\":\"S10\",\"terminals\":[\"a10\",\"b10\"],\"word\":[\"a10\",\"b10\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0087","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a11, b11, b11], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097087,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":2,\"nonterminals\":[\"A11\",\"S11\"],\"productions\":[[\"A11\",[\"b11\",\"A11\"]],[\"A11\",[]],[\"S11\",[\"a11\",\"A11\"]]],\"start\":\"S11\",\"terminals\":[\"a11\",\"b11\"],\"word\":[\"a11\",\"b11\",\"b11\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0088","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a12, b12, b12, b12], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097088,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A12\",\"S12\"],\"productions\":[[\"A12\",[\"b12\",\"A12\"]],[\"A12\",[]],[\"S12\",[\"a12\",\"A12\"]]],\"start\":\"S12\",\"terminals\":[\"a12\",\"b12\"],\"word\":[\"a12\",\"b12\",\"b12\",\"b12\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0089","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a13, b13, b13, b13, b13], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097089,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":2,\"nonterminals\":[\"A13\",\"S13\"],\"productions\":[[\"A13\",[\"b13\",\"A13\"]],[\"A13\",[]],[\"S13\",[\"a13\",\"A13\"]]],\"start\":\"S13\",\"terminals\":[\"a13\",\"b13\"],\"word\":[\"a13\",\"b13\",\"b13\",\"b13\",\"b13\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0090","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a14, b14, b14, b14, b14, b14], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097090,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A14\",\"S14\"],\"productions\":[[\"A14\",[\"b14\",\"A14\"]],[\"A14\",[]],[\"S14\",[\"a14\",\"A14\"]]],\"start\":\"S14\",\"terminals\":[\"a14\",\"b14\"],\"word\":[\"a14\",\"b14\",\"b14\",\"b14\",\"b14\",\"b14\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0091","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a15, b15], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097091,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":2,\"nonterminals\":[\"A15\",\"S15\"],\"productions\":[[\"A15\",[\"b15\",\"A15\"]],[\"A15\",[]],[\"S15\",[\"a15\",\"A15\"]]],\"start\":\"S15\",\"terminals\":[\"a15\",\"b15\"],\"word\":[\"a15\",\"b15\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0092","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a16, b16, b16], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097092,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A16\",\"S16\"],\"productions\":[[\"A16\",[\"b16\",\"A16\"]],[\"A16\",[]],[\"S16\",[\"a16\",\"A16\"]]],\"start\":\"S16\",\"terminals\":[\"a16\",\"b16\"],\"word\":[\"a16\",\"b16\",\"b16\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0093","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a17, b17, b17, b17], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097093,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":2,\"nonterminals\":[\"A17\",\"S17\"],\"productions\":[[\"A17\",[\"b17\",\"A17\"]],[\"A17\",[]],[\"S17\",[\"a17\",\"A17\"]]],\"start\":\"S17\",\"terminals\":[\"a17\",\"b17\"],\"word\":[\"a17\",\"b17\",\"b17\",\"b17\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0094","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a18, b18, b18, b18, b18], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097094,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A18\",\"S18\"],\"productions\":[[\"A18\",[\"b18\",\"A18\"]],[\"A18\",[]],[\"S18\",[\"a18\",\"A18\"]]],\"start\":\"S18\",\"terminals\":[\"a18\",\"b18\"],\"word\":[\"a18\",\"b18\",\"b18\",\"b18\",\"b18\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0095","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a19, b19, b19, b19, b19, b19], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097095,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":2,\"nonterminals\":[\"A19\",\"S19\"],\"productions\":[[\"A19\",[\"b19\",\"A19\"]],[\"A19\",[]],[\"S19\",[\"a19\",\"A19\"]]],\"start\":\"S19\",\"terminals\":[\"a19\",\"b19\"],\"word\":[\"a19\",\"b19\",\"b19\",\"b19\",\"b19\",\"b19\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0096","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a20, b20], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097096,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A20\",\"S20\"],\"productions\":[[\"A20\",[\"b20\",\"A20\"]],[\"A20\",[]],[\"S20\",[\"a20\",\"A20\"]]],\"start\":\"S20\",\"terminals\":[\"a20\",\"b20\"],\"word\":[\"a20\",\"b20\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0097","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a21, b21, b21], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097097,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":2,\"nonterminals\":[\"A21\",\"S21\"],\"productions\":[[\"A21\",[\"b21\",\"A21\"]],[\"A21\",[]],[\"S21\",[\"a21\",\"A21\"]]],\"start\":\"S21\",\"terminals\":[\"a21\",\"b21\"],\"word\":[\"a21\",\"b21\",\"b21\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0098","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a22, b22, b22, b22], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097098,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A22\",\"S22\"],\"productions\":[[\"A22\",[\"b22\",\"A22\"]],[\"A22\",[]],[\"S22\",[\"a22\",\"A22\"]]],\"start\":\"S22\",\"terminals\":[\"a22\",\"b22\"],\"word\":[\"a22\",\"b22\",\"b22\",\"b22\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0099","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a23, b23, b23, b23, b23], 2, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097099,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":2,\"nonterminals\":[\"A23\",\"S23\"],\"productions\":[[\"A23\",[\"b23\",\"A23\"]],[\"A23\",[]],[\"S23\",[\"a23\",\"A23\"]]],\"start\":\"S23\",\"terminals\":[\"a23\",\"b23\"],\"word\":[\"a23\",\"b23\",\"b23\",\"b23\",\"b23\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r07-context-free-grammar-0100","batch_id":"batch-20261014-advance-20261109-r07-context-free-grammar-foundations","language":"zh-Hant","source_mko_ids":["mko-context-free-grammar"],"title_zh":"上下文無關文法","stem_zh":"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 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([a24, b24, b24, b24, b24, b24], 1, 否, 否, bounded_search_failure_cannot_prove_nonmembership_without_complete_bound)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["上下文無關文法"]},"variant":{"family_id":"qf-mod40-cfg-bounded-search-boundary","seed":202611097100,"parameters":{"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,"domain":"Complete_finite_context_free_grammar","operation":"cfg-bounded-search-boundary","semantic_template":"qf-mod40-cfg-bounded-search-boundary/{\"allow_epsilon\":true,\"max_steps\":1,\"nonterminals\":[\"A24\",\"S24\"],\"productions\":[[\"A24\",[\"b24\",\"A24\"]],[\"A24\",[]],[\"S24\",[\"a24\",\"A24\"]]],\"start\":\"S24\",\"terminals\":[\"a24\",\"b24\"],\"word\":[\"a24\",\"b24\",\"b24\",\"b24\",\"b24\",\"b24\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}