{
  "machine": "MTM",
  "sigma": [
    "0",
    "1"
  ],
  "stackAlpha": [
    "0",
    "1",
    "⊔"
  ],
  "tapeCount": 3,
  "states": [
    {
      "id": "s1",
      "x": 240,
      "y": 220,
      "name": "carry 0"
    },
    {
      "id": "s2",
      "x": 620,
      "y": 220,
      "name": "carry 1"
    },
    {
      "id": "s3",
      "x": 430,
      "y": 440,
      "name": "acc"
    }
  ],
  "startId": "s1",
  "accepts": [
    "s3"
  ],
  "transitions": [
    {
      "id": "t1",
      "from": "s1",
      "to": "s1",
      "symbol": "0",
      "tapeSyms": [
        "0",
        "0",
        "⊔"
      ],
      "tapeWrites": [
        "0",
        "0",
        "0"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t2",
      "from": "s1",
      "to": "s1",
      "symbol": "0",
      "tapeSyms": [
        "0",
        "1",
        "⊔"
      ],
      "tapeWrites": [
        "0",
        "1",
        "1"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t3",
      "from": "s1",
      "to": "s1",
      "symbol": "1",
      "tapeSyms": [
        "1",
        "0",
        "⊔"
      ],
      "tapeWrites": [
        "1",
        "0",
        "1"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t4",
      "from": "s1",
      "to": "s2",
      "symbol": "1",
      "tapeSyms": [
        "1",
        "1",
        "⊔"
      ],
      "tapeWrites": [
        "1",
        "1",
        "0"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t5",
      "from": "s1",
      "to": "s1",
      "symbol": "0",
      "tapeSyms": [
        "0",
        "⊔",
        "⊔"
      ],
      "tapeWrites": [
        "0",
        "⊔",
        "0"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t6",
      "from": "s1",
      "to": "s1",
      "symbol": "1",
      "tapeSyms": [
        "1",
        "⊔",
        "⊔"
      ],
      "tapeWrites": [
        "1",
        "⊔",
        "1"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t7",
      "from": "s1",
      "to": "s1",
      "symbol": "⊔",
      "tapeSyms": [
        "⊔",
        "0",
        "⊔"
      ],
      "tapeWrites": [
        "⊔",
        "0",
        "0"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t8",
      "from": "s1",
      "to": "s1",
      "symbol": "⊔",
      "tapeSyms": [
        "⊔",
        "1",
        "⊔"
      ],
      "tapeWrites": [
        "⊔",
        "1",
        "1"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t9",
      "from": "s1",
      "to": "s3",
      "symbol": "⊔",
      "tapeSyms": [
        "⊔",
        "⊔",
        "⊔"
      ],
      "tapeWrites": [
        "⊔",
        "⊔",
        "⊔"
      ],
      "tapeDirs": [
        "S",
        "S",
        "S"
      ]
    },
    {
      "id": "t10",
      "from": "s2",
      "to": "s1",
      "symbol": "0",
      "tapeSyms": [
        "0",
        "0",
        "⊔"
      ],
      "tapeWrites": [
        "0",
        "0",
        "1"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t11",
      "from": "s2",
      "to": "s2",
      "symbol": "0",
      "tapeSyms": [
        "0",
        "1",
        "⊔"
      ],
      "tapeWrites": [
        "0",
        "1",
        "0"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t12",
      "from": "s2",
      "to": "s2",
      "symbol": "1",
      "tapeSyms": [
        "1",
        "0",
        "⊔"
      ],
      "tapeWrites": [
        "1",
        "0",
        "0"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t13",
      "from": "s2",
      "to": "s2",
      "symbol": "1",
      "tapeSyms": [
        "1",
        "1",
        "⊔"
      ],
      "tapeWrites": [
        "1",
        "1",
        "1"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t14",
      "from": "s2",
      "to": "s1",
      "symbol": "0",
      "tapeSyms": [
        "0",
        "⊔",
        "⊔"
      ],
      "tapeWrites": [
        "0",
        "⊔",
        "1"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t15",
      "from": "s2",
      "to": "s2",
      "symbol": "1",
      "tapeSyms": [
        "1",
        "⊔",
        "⊔"
      ],
      "tapeWrites": [
        "1",
        "⊔",
        "0"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t16",
      "from": "s2",
      "to": "s1",
      "symbol": "⊔",
      "tapeSyms": [
        "⊔",
        "0",
        "⊔"
      ],
      "tapeWrites": [
        "⊔",
        "0",
        "1"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t17",
      "from": "s2",
      "to": "s2",
      "symbol": "⊔",
      "tapeSyms": [
        "⊔",
        "1",
        "⊔"
      ],
      "tapeWrites": [
        "⊔",
        "1",
        "0"
      ],
      "tapeDirs": [
        "R",
        "R",
        "R"
      ]
    },
    {
      "id": "t18",
      "from": "s2",
      "to": "s3",
      "symbol": "⊔",
      "tapeSyms": [
        "⊔",
        "⊔",
        "⊔"
      ],
      "tapeWrites": [
        "⊔",
        "⊔",
        "1"
      ],
      "tapeDirs": [
        "S",
        "S",
        "S"
      ]
    }
  ],
  "notes": [
    {
      "id": "n1",
      "x": 60,
      "y": 40,
      "color": "blue",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Binary addition in ONE pass: tape 1 holds a, tape 2 holds b (least-significant bit first, like a hardware adder), tape 3 receives the sum. Three heads march right in lockstep; the only memory is the carry — that's the two states."
    },
    {
      "id": "n2",
      "x": 60,
      "y": 440,
      "color": "green",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Input format: a,b,ε — one segment per tape. Compare with the single-tape TM adder, which shuttles back and forth per unit: more tapes are hardware acceleration."
    }
  ],
  "meta": {
    "title": "3-tape adder — one pass",
    "blurb": "Adds two binary numbers (written LSB-first) in a single sweep: three synchronized heads, and the carry bit is the only state. The same job costs the 1-tape TM a lap per unit.",
    "inputs": [
      {
        "w": "1101,111,ε",
        "expect": "accept",
        "tape": "01001",
        "label": "11+7=18"
      },
      {
        "w": "11,11,ε",
        "expect": "accept",
        "tape": "011",
        "label": "3+3=6"
      },
      {
        "w": "1,111,ε",
        "expect": "accept",
        "tape": "0001",
        "label": "1+7=8"
      }
    ],
    "library": {
      "author": {
        "login": "thethinkmachine"
      },
      "license": "CC-BY-4.0",
      "tags": [
        "showcase",
        "mtm"
      ],
      "difficulty": "intermediate"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}