{
  "$schema": "../../../schemas/mko-v0.4.schema.json",
  "schema_version": "mko-v0.4",
  "id": "mko-computational-model",
  "semantic_family_id": "sf-computational-model",
  "type": "definition",
  "version": "0.10.0",
  "language": "zh-Hant",
  "titles": {
    "zh-Hant": "抽象計算模型"
  },
  "summary": {
    "zh-Hant": "有限狀態計算模型以狀態集、初始狀態集、步驟關係與停止狀態集描述可能執行。"
  },
  "statement": {
    "zh-Hant": "本條目的有限抽象模型為 (S,Init,Step,Halt)，其中 Init,Halt⊆S、Step⊆S×S。執行從 Init 中狀態開始並沿 Step 前進；無後繼的 stuck 狀態不因而自動屬於 Halt。"
  },
  "formula": {
    "tex": "R\\subseteq S",
    "mathml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>R</mi><mo>⊆</mo><mi>S</mi></mrow></math>",
    "semantic_ast": {
      "type": "set_subset",
      "subset": {
        "type": "symbol",
        "name": "R",
        "glyph": "R"
      },
      "superset": {
        "type": "symbol",
        "name": "S",
        "glyph": "S"
      }
    },
    "compiler": {
      "id": "ocme-formula-core",
      "version": "0.4.0",
      "source_sha256": "5a28c2120e6350a85e18b9b4ef34453bc18da27978d04745bf6512a25444e83e"
    }
  },
  "assumptions": [
    {
      "id": "a1",
      "zh-Hant": "S 是明示有限狀態集，Step 是有向關係，可具 nondeterminism。"
    },
    {
      "id": "a2",
      "zh-Hant": "到達 Halt 後本模型視為停止，不再沿其外出邊；若資料含外出邊仍在分析前截斷。"
    }
  ],
  "symbols": [
    {
      "token": "R",
      "role": "step_relation",
      "role_zh": "步驟關係",
      "scope": "representative_formula"
    },
    {
      "token": "S",
      "role": "state_set",
      "role_zh": "狀態集合",
      "scope": "representative_formula"
    }
  ],
  "dependencies": [
    {
      "id": "mko-set",
      "title_zh": "集合",
      "reason_zh": "狀態、初始與停止條件用集合表示。"
    },
    {
      "id": "mko-relation",
      "title_zh": "二元關係與集合投影",
      "reason_zh": "步驟語義是狀態間有向關係。"
    },
    {
      "id": "mko-natural-number",
      "title_zh": "自然數",
      "reason_zh": "有限 trace 長度與步數由自然數索引。"
    }
  ],
  "explanation": {
    "paragraphs_zh": [
      "可達性從全部初始狀態出發，沿 Step 的零步或多步閉包計算。",
      "合法 trace 必須首狀態在 Init、相鄰狀態成 Step；一旦進入 Halt 就結束，不能在同一執行繼續。",
      "有限深度沒有看到循環不代表所有執行終止；reachable 非停止 cycle 或 reachable stuck 非停止狀態都是終止性風險。"
    ],
    "common_misconception_zh": "把無外出邊自動叫做 halt，或以有限 execution prefix 斷言所有執行終止。"
  },
  "proofs": [],
  "computational_companions": [],
  "verification": {
    "computational_status": "not_evaluated_no_computational_claim",
    "warning_zh": "有限狀態圖可以完整枚舉可達結構；不外推未指定的 Turing 完備性或實際程式行為。",
    "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": "建立 deterministic／nondeterministic、stuck、maximal execution 與有效編碼的分層模型。"
  },
  "provenance": {
    "origin": "ocme_local_ai_materialization_candidate",
    "note_zh": "依 research/atlas-computational-model.md 整理；2026-10-13 脈衝 R04（使用者手動接續 2026-10-19 工作序列；實際日期仍為 2026-10-13），英文及 Lean 依使用者指示延後。",
    "content_license": "CC-BY-SA-4.0",
    "code_license": "MIT",
    "created_at": "2026-10-13"
  }
}