{
  "machine": "NDTM",
  "sigma": [
    "1"
  ],
  "stackAlpha": [
    "1",
    "#",
    "X",
    "x",
    "D",
    "⊔"
  ],
  "states": [
    {
      "id": "s1",
      "x": 120,
      "y": 150,
      "name": "seed"
    },
    {
      "id": "s2",
      "x": 340,
      "y": 150,
      "name": "guess p"
    },
    {
      "id": "s3",
      "x": 560,
      "y": 150,
      "name": "next X"
    },
    {
      "id": "s4",
      "x": 800,
      "y": 150,
      "name": "cross 1"
    },
    {
      "id": "s5",
      "x": 560,
      "y": 380,
      "name": "last cross"
    },
    {
      "id": "s6",
      "x": 800,
      "y": 380,
      "name": "reset ruler"
    },
    {
      "id": "s7",
      "x": 340,
      "y": 380,
      "name": "any 1s left?"
    },
    {
      "id": "s8",
      "x": 120,
      "y": 380,
      "name": "acc"
    }
  ],
  "startId": "s1",
  "accepts": [
    "s8"
  ],
  "transitions": [
    {
      "id": "t1",
      "from": "s1",
      "to": "s2",
      "symbol": "1",
      "write": "#",
      "dir": "R"
    },
    {
      "id": "t2",
      "from": "s2",
      "to": "s2",
      "symbol": "1",
      "write": "X",
      "dir": "R"
    },
    {
      "id": "t3",
      "from": "s2",
      "to": "s3",
      "symbol": "1",
      "write": "X",
      "dir": "R"
    },
    {
      "id": "t4",
      "from": "s3",
      "to": "s3",
      "symbol": "1",
      "write": "1",
      "dir": "L"
    },
    {
      "id": "t5",
      "from": "s3",
      "to": "s3",
      "symbol": "D",
      "write": "D",
      "dir": "L"
    },
    {
      "id": "t6",
      "from": "s3",
      "to": "s3",
      "symbol": "x",
      "write": "x",
      "dir": "L"
    },
    {
      "id": "t7",
      "from": "s3",
      "to": "s4",
      "symbol": "X",
      "write": "x",
      "dir": "R"
    },
    {
      "id": "t8",
      "from": "s3",
      "to": "s5",
      "symbol": "#",
      "write": "#",
      "dir": "R"
    },
    {
      "id": "t9",
      "from": "s4",
      "to": "s4",
      "symbol": "x",
      "write": "x",
      "dir": "R"
    },
    {
      "id": "t10",
      "from": "s4",
      "to": "s4",
      "symbol": "D",
      "write": "D",
      "dir": "R"
    },
    {
      "id": "t11",
      "from": "s4",
      "to": "s3",
      "symbol": "1",
      "write": "D",
      "dir": "L"
    },
    {
      "id": "t12",
      "from": "s5",
      "to": "s5",
      "symbol": "x",
      "write": "x",
      "dir": "R"
    },
    {
      "id": "t13",
      "from": "s5",
      "to": "s5",
      "symbol": "D",
      "write": "D",
      "dir": "R"
    },
    {
      "id": "t14",
      "from": "s5",
      "to": "s6",
      "symbol": "1",
      "write": "D",
      "dir": "L"
    },
    {
      "id": "t15",
      "from": "s6",
      "to": "s6",
      "symbol": "D",
      "write": "D",
      "dir": "L"
    },
    {
      "id": "t16",
      "from": "s6",
      "to": "s6",
      "symbol": "x",
      "write": "X",
      "dir": "L"
    },
    {
      "id": "t17",
      "from": "s6",
      "to": "s7",
      "symbol": "#",
      "write": "#",
      "dir": "R"
    },
    {
      "id": "t18",
      "from": "s7",
      "to": "s7",
      "symbol": "X",
      "write": "X",
      "dir": "R"
    },
    {
      "id": "t19",
      "from": "s7",
      "to": "s7",
      "symbol": "D",
      "write": "D",
      "dir": "R"
    },
    {
      "id": "t20",
      "from": "s7",
      "to": "s3",
      "symbol": "1",
      "write": "1",
      "dir": "L"
    },
    {
      "id": "t21",
      "from": "s7",
      "to": "s8",
      "symbol": "⊔",
      "write": "⊔",
      "dir": "S"
    }
  ],
  "notes": [
    {
      "id": "n1",
      "x": 30,
      "y": 40,
      "color": "blue",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Compositeness by guessing: on input 1ⁿ the machine nondeterministically marks a factor p ≥ 2 as a ruler (#X…X), then deals the remaining 1s into rounds of exactly p. Every round completes cleanly ⇔ p divides n ⇔ n is composite."
    },
    {
      "id": "n2",
      "x": 950,
      "y": 220,
      "color": "green",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "1s get crossed to D one per ruler cell; the ruler resets (x→X) between rounds. If the 1s run out mid-round, that guess dies — only a correct factor survives."
    },
    {
      "id": "n3",
      "x": 950,
      "y": 420,
      "color": "orange",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "The trace shows breadth-first exploration over ALL guesses of p at once, not a single run — that's what the N in NDTM means."
    }
  ],
  "meta": {
    "title": "Is n composite? Guess a factor",
    "blurb": "Accepts 1ⁿ exactly when n is composite: the machine guesses a factor p, then verifies it by dealing the remaining 1s into rounds of p. Primality by nondeterministic elimination.",
    "inputs": [
      {
        "w": "1111",
        "expect": "accept",
        "label": "4 = 2×2"
      },
      {
        "w": "111111",
        "expect": "accept",
        "label": "6 = 2×3"
      },
      {
        "w": "111111111",
        "expect": "accept",
        "label": "9 = 3×3"
      },
      {
        "w": "11111",
        "expect": "reject",
        "label": "5 is prime"
      },
      {
        "w": "1111111",
        "expect": "reject",
        "label": "7 is prime"
      }
    ],
    "library": {
      "author": {
        "login": "thethinkmachine"
      },
      "license": "CC-BY-4.0",
      "tags": [
        "showcase",
        "ndtm"
      ],
      "difficulty": "intermediate"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}