{
  "$schema": "../../../schemas/mko-v0.4.schema.json",
  "schema_version": "mko-v0.4",
  "id": "mko-turing-machine-decision-model",
  "semantic_family_id": "sf-turing-machine-decision-model",
  "type": "definition",
  "version": "0.10.0",
  "language": "zh-Hant",
  "titles": {
    "zh-Hant": "Turing機判定模型"
  },
  "summary": {
    "zh-Hant": "固定deterministic single-tape Turing機語義；decider必須對每個合法輸入停機並給正確accept/reject答案。"
  },
  "statement": {
    "zh-Hant": "machine明示finite states、input alphabet、tape alphabet、blank、start、accept、reject及deterministic transition [state,read,next,write,move]，tape未列cells皆為blank。configuration固定[state,head,sparse nonblank tape]。exact step與finite trace只證指定input。全域decider certificate須提供對所有input成立且每步嚴格下降的ranking或明示step bound，並同時有answer correctness。recognizer可在nonmember上loop；bounded simulation failure不證rejection或nontermination，單一halting trace也不證全域decider。"
  },
  "formula": {
    "tex": "T(M,w)=h",
    "mathml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mrow><mi>T</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>w</mi><mo>)</mo></mrow><mo>=</mo><mi>h</mi></mrow></math>",
    "semantic_ast": {
      "type": "equation",
      "lhs": {
        "type": "function_call",
        "callee": {
          "type": "symbol",
          "name": "T",
          "glyph": "T"
        },
        "arguments": [
          {
            "type": "symbol",
            "name": "M",
            "glyph": "M"
          },
          {
            "type": "symbol",
            "name": "w",
            "glyph": "w"
          }
        ]
      },
      "rhs": {
        "type": "symbol",
        "name": "h",
        "glyph": "h"
      }
    },
    "compiler": {
      "id": "ocme-formula-core",
      "version": "0.4.0",
      "source_sha256": "1fc111790aeaa7523dbd454703e77b9dc29f5569ff8760a71bb66ad099a95fa7"
    }
  },
  "assumptions": [
    {
      "id": "a1",
      "zh-Hant": "move convention固定為L/R/S，accept與reject states無outgoing transitions。"
    },
    {
      "id": "a2",
      "zh-Hant": "全域正向family固定scan-decider schema，其ranking為尚未掃描的input cells加一。"
    }
  ],
  "symbols": [
    {
      "token": "T",
      "role": "turing_execution_record",
      "role_zh": "Turing執行紀錄",
      "scope": "representative_formula"
    },
    {
      "token": "M",
      "role": "deterministic_single_tape_machine",
      "role_zh": "確定性單帶機",
      "scope": "representative_formula"
    },
    {
      "token": "w",
      "role": "input_word",
      "role_zh": "輸入字",
      "scope": "representative_formula"
    },
    {
      "token": "h",
      "role": "halting_outcome",
      "role_zh": "停機結果",
      "scope": "representative_formula"
    }
  ],
  "dependencies": [
    {
      "id": "mko-computational-model",
      "title_zh": "計算模型",
      "reason_zh": "有限控制與step semantics。"
    },
    {
      "id": "mko-decision-problem",
      "title_zh": "判定問題",
      "reason_zh": "yes/no語義。"
    },
    {
      "id": "mko-finite-automaton",
      "title_zh": "有限自動機",
      "reason_zh": "有限狀態控制背景。"
    },
    {
      "id": "mko-algorithm-correctness",
      "title_zh": "演算法正確性",
      "reason_zh": "decider total correctness。"
    }
  ],
  "explanation": {
    "paragraphs_zh": [
      "signature qualification與執行語義分開。",
      "有限trace是input-local evidence。",
      "decider需要termination與answer correctness的全域證書。"
    ],
    "common_misconception_zh": "從一個halt trace或有限step未halt便斷言整台機是decider或reject。"
  },
  "proofs": [],
  "computational_companions": [],
  "verification": {
    "computational_status": "not_evaluated_no_computational_claim",
    "warning_zh": "本輪不宣稱Church–Turing thesis的形式證明、複雜度上界或多帶等價。",
    "evidence_refs": [],
    "producers": [
      {
        "id": "lean-mathlib",
        "adapter": "formal_system",
        "config_path": "formal/lean/lakefile.toml",
        "status": "configured"
      }
    ]
  },
  "formalization": {
    "status": "not_formalized",
    "target_systems": [
      "Lean 4",
      "Mathlib"
    ],
    "next_obligation_zh": "加入many-one reduction、undecidability與complexity。"
  },
  "provenance": {
    "origin": "ocme_local_ai_materialization_candidate",
    "note_zh": "依 research/atlas-turing-machine-decision-model.md 整理；2026-10-15 脈衝 R05（使用者手動接續 2026-11-13 工作序列；實際日期仍為 2026-10-15），英文及 Lean 依使用者指示延後。",
    "content_license": "CC-BY-SA-4.0",
    "code_license": "MIT",
    "created_at": "2026-10-15"
  }
}