{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261015-advance-20261113-r05-turing-machine-decision-model-0039", "pilot_number": "R0048-24714", "number": 24714, "family_id": "qf-mod44-tm-exact-step-trace", "title": { "zh-Hant": "第 24714 題：Turing機判定模型", "en": "Question 24714: A Finite Configuration Trace Has Only Its Declared Input and Budget Scope" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261015-advance-20261113-r05-turing-machine-decision-model-0039", "batch_id": "batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-turing-machine-decision-model" ], "title_zh": "Turing機判定模型", "stem_zh": "deterministic single-tape signature、exact configuration semantics與decider total-correctness boundary。操作=tm-exact-step-trace；資料={\"states\":[\"q013\",\"q113\",\"qa13\",\"qr13\"],\"input_alphabet\":[\"013\"],\"tape_alphabet\":[\"013\",\"X13\",\"_13\"],\"blank\":\"_13\",\"start_state\":\"q013\",\"accept_state\":\"qa13\",\"reject_state\":\"qr13\",\"transitions\":[[\"q013\",\"013\",\"q113\",\"X13\",\"R\"],[\"q013\",\"_13\",\"qr13\",\"_13\",\"S\"],[\"q113\",\"_13\",\"qa13\",\"_13\",\"L\"]],\"input\":[\"013\"],\"steps\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "answer": { "kind": "expression", "value": "([013], 2, [[q013, 0, [[0, 013]]], [q113, 1, [[0, X13]]], [qa13, 0, [[0, X13]]]], [step, step], qa13, accept, 否, finite_trace_is_input_local_and_does_not_certify_a_global_decider)", "explanation_zh": "Wave6第七層核對=([013], 2, [[q013, 0, [[0, 013]]], [q113, 1, [[0, X13]]], [qa13, 0, [[0, X13]]]], [step, step], qa13, accept, 否, finite_trace_is_input_local_and_does_not_certify_a_global_decider)；依完整明示資料獨立重算；finite trace只證指定input；global decider需forall-input ranking/step-bound與answer correctness；recognizer可loop；bounded failure不證reject或nontermination，單一halt trace不證decider。" }, "difficulty": { "band": "undergraduate_core", "level": 2, "skills": [ "Turing機判定模型" ] }, "variant": { "family_id": "qf-mod44-tm-exact-step-trace", "seed": 202611135039, "parameters": { "states": [ "q013", "q113", "qa13", "qr13" ], "input_alphabet": [ "013" ], "tape_alphabet": [ "013", "X13", "_13" ], "blank": "_13", "start_state": "q013", "accept_state": "qa13", "reject_state": "qr13", "transitions": [ [ "q013", "013", "q113", "X13", "R" ], [ "q013", "_13", "qr13", "_13", "S" ], [ "q113", "_13", "qa13", "_13", "L" ] ], "input": [ "013" ], "steps": 2, "domain": "Deterministic_single_tape_Turing_decider", "operation": "tm-exact-step-trace", "semantic_template": "qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa13\",\"blank\":\"_13\",\"input\":[\"013\"],\"input_alphabet\":[\"013\"],\"reject_state\":\"qr13\",\"start_state\":\"q013\",\"states\":[\"q013\",\"q113\",\"qa13\",\"qr13\"],\"steps\":2,\"tape_alphabet\":[\"013\",\"X13\",\"_13\"],\"transitions\":[[\"q013\",\"_13\",\"qr13\",\"_13\",\"S\"],[\"q013\",\"013\",\"q113\",\"X13\",\"R\"],[\"q113\",\"_13\",\"qa13\",\"_13\",\"L\"]]}" } }, "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、sampled normality、finite-sum exponential、formal-only analytic equality、circular Euler criterion、finite-trace decider、stationary extremum、feasible maximum-flow、Lean或Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-15", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261015-advance-20261113-r05-turing-machine-decision-model-0039", "batch_id": "batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "1002b250b2baac38b65bffe1d8299803ed90b49f0e50058d7ae967cd484c6d53", "family_id": "qf-mod44-tm-exact-step-trace", "seed": 202611135039, "semantic_template": "qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa13\",\"blank\":\"_13\",\"input\":[\"013\"],\"input_alphabet\":[\"013\"],\"reject_state\":\"qr13\",\"start_state\":\"q013\",\"states\":[\"q013\",\"q113\",\"qa13\",\"qr13\"],\"steps\":2,\"tape_alphabet\":[\"013\",\"X13\",\"_13\"],\"transitions\":[[\"q013\",\"_13\",\"qr13\",\"_13\",\"S\"],[\"q013\",\"013\",\"q113\",\"X13\",\"R\"],[\"q113\",\"_13\",\"qa13\",\"_13\",\"L\"]]}" }, "fields": { "title": "A Finite Configuration Trace Has Only Its Declared Input and Budget Scope", "stem": "Use deterministic single-tape states=[q013, q113, qa13, qr13], input_alphabet=[013], tape_alphabet=[013, X13, _13], blank=_13, start=q013, accept=qa13, reject=qr13, transitions=[[q013, 013, q113, X13, R], [q013, _13, qr13, _13, S], [q113, _13, qa13, _13, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[013], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).", "answer": { "kind": "expression", "value": "([013], 2, [[q013, 0, [[0, 013]]], [q113, 1, [[0, X13]]], [qa13, 0, [[0, X13]]]], [step, step], qa13, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)", "explanation": "Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([013], 2, [[q013, 0, [[0, 013]]], [q113, 1, [[0, X13]]], [qa13, 0, [[0, X13]]]], [step, step], qa13, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)." }, "skills": [ "A Finite Configuration Trace Has Only Its Declared Input and Budget Scope" ], "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review." } }, "givens": [ { "id": "G001", "text": { "zh-Hant": "deterministic single-tape signature、exact configuration semantics與decider total-correctness boundary。操作=tm-exact-step-trace；資料={\"states\":[\"q013\",\"q113\",\"qa13\",\"qr13\"],\"input_alphabet\":[\"013\"],\"tape_alphabet\":[\"013\",\"X13\",\"_13\"],\"blank\":\"_13\",\"start_state\":\"q013\",\"accept_state\":\"qa13\",\"reject_state\":\"qr13\",\"transitions\":[[\"q013\",\"013\",\"q113\",\"X13\",\"R\"],[\"q013\",\"_13\",\"qr13\",\"_13\",\"S\"],[\"q113\",\"_13\",\"qa13\",\"_13\",\"L\"]],\"input\":[\"013\"],\"steps\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "en": "Use deterministic single-tape states=[q013, q113, qa13, qr13], input_alphabet=[013], tape_alphabet=[013, X13, _13], blank=_13, start=q013, accept=qa13, reject=qr13, transitions=[[q013, 013, q113, X13, R], [q013, _13, qr13, _13, S], [q113, _13, qa13, _13, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[013], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [tm-exact-step-trace]", "after": "derived = [[input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary]]", "relation": "implies", "rule_id": "source_ordered_fields_without_JS", "conditions": [], "explanation": { "zh-Hant": "直接列來源完整欄序，不需JavaScript；原題、布林旗標、數學物件與非聲稱保持分層。", "en": "List the full source field order without JavaScript,keeping original data,Boolean flags,mathematical objects and nonclaims distinct." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [[q013, q113, qa13, qr13], [013], [013, X13, _13], _13, q013, qa13, qr13, [[q013, 013, q113, X13, R], [q013, _13, qr13, _13, S], [q113, _13, qa13, _13, L]]]", "after": "derived = [[q013, q113, qa13, qr13], [013], [013, X13, _13], [[q013, _13, qr13, _13, S], [q013, 013, q113, X13, R], [q113, _13, qa13, _13, L]], 是]", "relation": "implies", "rule_id": "TM_complete_signature_partial_transition_table_allowed", "conditions": [], "explanation": { "zh-Hant": "三個清單皆非空且唯一；input是blank-free tape子集，但state與字母標籤不要求不相交。每個(from,read)的來源NUL-joined key唯一、halt無出邊。partial table合法，不補reject規則；canonical transition序與UTF16集合序分開。", "en": "All three lists are nonempty and unique;input is a blank-free tape subset,but state and alphabet labels may overlap.Source NUL-joined(from,read) keys are unique,and halting states have no outgoing rules.A partial table is legal,not filled with rejection;transition collation and UTF16 set order differ." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [[013], q013, _13]", "after": "derived = [[q013, 0, [[0, 013]]]]", "relation": "implies", "rule_id": "TM_exact_initial_configuration_blank_elsewhere", "conditions": [], "explanation": { "zh-Hant": "初始head0、input放0起的整數格，其餘全blank；稀疏記錄僅保非blank。tape可往負index伸展。", "en": "Initially head0,input occupies integer cells from0,and every other cell is blank.The sparse record contains nonblank cells only;negative indices are legal." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "TM exact integer head move0 := sum(0, 1)", "after": "TM exact integer head move0 = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色與已證中間量精確代值，分母先核非零，不用浮點近似。", "en": "Substitute original roles and established intermediates exactly,checking nonzero denominators without floats." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 TM exact integer head move0，不以小數近似替代。", "en": "Recompute TM exact integer head move0 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "0", "1" ], "output": "1", "label": "TM exact integer head move0" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "source roles = [0, [q013, 0, [[0, 013]]], 013, [q013, 013, q113, X13, R]]", "after": "derived = [step, [q113, 1, [[0, X13]]]]", "relation": "implies", "rule_id": "TM_source_rule_exact_read_write_state_move", "conditions": [], "explanation": { "zh-Hant": "先在舊head寫字（blank刪格），再換state及移head；全部L/R/S按原rule，不混成停機語意。", "en": "Write at the old head first,delete a blank cell,then update state and move exactly L/R/S according to the source rule." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "TM exact integer head move1 := sum(1, -1)", "after": "TM exact integer head move1 = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色與已證中間量精確代值，分母先核非零，不用浮點近似。", "en": "Substitute original roles and established intermediates exactly,checking nonzero denominators without floats." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 TM exact integer head move1，不以小數近似替代。", "en": "Recompute TM exact integer head move1 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1", "-1" ], "output": "0", "label": "TM exact integer head move1" } }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "source roles = [1, [q113, 1, [[0, X13]]], _13, [q113, _13, qa13, _13, L]]", "after": "derived = [step, [qa13, 0, [[0, X13]]]]", "relation": "implies", "rule_id": "TM_source_rule_exact_read_write_state_move", "conditions": [], "explanation": { "zh-Hant": "先在舊head寫字（blank刪格），再換state及移head；全部L/R/S按原rule，不混成停機語意。", "en": "Write at the old head first,delete a blank cell,then update state and move exactly L/R/S according to the source rule." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "source roles = [[013], 2, [[q013, 0, [[0, 013]]], [q113, 1, [[0, X13]]], [qa13, 0, [[0, X13]]]], [step, step]]", "after": "derived = [qa13, accept, 否]", "relation": "implies", "rule_id": "TM_finite_trace_input_budget_scope_NOT_global_decider", "conditions": [], "explanation": { "zh-Hant": "已halt才接受／拒絕；budget用盡或stuck不是普通reject，也不證永久不停止。一個input的有限trace不提供all-input decider證書。", "en": "Only actual halting states accept or reject.Exhaustion or stuck is neither ordinary rejection nor a proof of infinite running.One finite input trace supplies no all-input decider certificate." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null } ], "math_model": { "result": [ [ "013" ], 2, [ [ "q013", 0, [ [ 0, "013" ] ] ], [ "q113", 1, [ [ 0, "X13" ] ] ], [ "qa13", 0, [ [ 0, "X13" ] ] ] ], [ "step", "step" ], "qa13", "accept", false, "finite_trace_is_input_local_and_does_not_certify_a_global_decider" ] }, "conclusion": { "canonical_value": "([013], 2, [[q013, 0, [[0, 013]]], [q113, 1, [[0, X13]]], [qa13, 0, [[0, X13]]]], [step, step], qa13, accept, 否, finite_trace_is_input_local_and_does_not_certify_a_global_decider)", "explanation": { "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。", "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged." } }, "definition_note": { "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。", "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate." }, "source": { "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db", "question_binding": { "batch_id": "batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations", "batch_path": "public/data/questions/batches/batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations/questions.jsonl", "batch_sha256": "a757aec41a210d6e0f347486ce4764d71874fe1c8cea6f6c3322f2cc451d297e", "original_line": 39, "original_line_sha256": "c38d9e57d2b920c342e2fcfe63d9b0608d03d72fd6538f3a3558b5d1e6ed97d8", "question_compact_sha256": "1002b250b2baac38b65bffe1d8299803ed90b49f0e50058d7ae967cd484c6d53", "english_row_compact_sha256": "687b626ebad24d8c5785cd4d0b1287ecb02c94bb258d5339547b71eeb275142b", "english_manifest_path": "public/data/i18n/editions/batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations.en.jsonl" }, "mko_bindings": { "mko-turing-machine-decision-model": { "sha256": "9fc9700d03f68194f76ce7dec138e0b7fcac9e14deae2adf44f6dba00627308c", "english_sha256": "899d905d1fa2bb187a389fe647567c10b147f2cfd5df11725e625c35475d16e3", "original_path": "public/data/mko/turing-machine-decision-model.json", "english_path": "public/data/i18n/editions/mko-turing-machine-decision-model.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "7f1649723787c6d7cf1abe85636fd3740f2c3cc1784071db7e38069361c81fd4", "original_candidate_sha256": "2f1ff33f9d8f4841f30d8b7b23472f694dfddab4291428a17e943497470e4ccc", "original_candidate_line_sha256": "2f1ff33f9d8f4841f30d8b7b23472f694dfddab4291428a17e943497470e4ccc" }, "historical_source_state": { "review_state": { "derivation": "candidate_authored_and_locally_checked", "source_question_state": "candidate", "independent_AI_or_human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN" }, "scope_note": { "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。", "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged." }, "label": "Frozen producer metadata; current per-question review is separate below." }, "revision": { "id": "review-20261026-009-p49", "review_date": "2026-10-26", "owner_authorized_reader_publication": true, "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.", "review_receipts": { "semantic_review_sha256": "049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0", "question_first_witness_sha256": "0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 8, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "68e0ee97379a5efbead1ad60c37005c928cd0ba625578d563cded5b4bb4814e5", "arithmetic_steps": 2 }, "uses_answer_as_premise": false, "human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN", "Canonical_truth_promotion": false, "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged." } }