{
  "machine": "2DFA",
  "sigma": [
    "a",
    "b"
  ],
  "states": [
    {
      "id": "s1",
      "x": 150,
      "y": 160,
      "name": "a_even"
    },
    {
      "id": "s2",
      "x": 430,
      "y": 160,
      "name": "a_odd"
    },
    {
      "id": "s3",
      "x": 430,
      "y": 380,
      "name": "b_even"
    },
    {
      "id": "s4",
      "x": 150,
      "y": 380,
      "name": "b_odd"
    },
    {
      "id": "s5",
      "x": 660,
      "y": 270,
      "name": "acc"
    }
  ],
  "startId": "s1",
  "accepts": [
    "s5"
  ],
  "transitions": [
    {
      "id": "t1",
      "from": "s1",
      "to": "s1",
      "symbol": "⊢",
      "dir": "R"
    },
    {
      "id": "t2",
      "from": "s1",
      "to": "s2",
      "symbol": "a",
      "dir": "R"
    },
    {
      "id": "t3",
      "from": "s1",
      "to": "s1",
      "symbol": "b",
      "dir": "R"
    },
    {
      "id": "t4",
      "from": "s1",
      "to": "s3",
      "symbol": "⊣",
      "dir": "L"
    },
    {
      "id": "t5",
      "from": "s2",
      "to": "s1",
      "symbol": "a",
      "dir": "R"
    },
    {
      "id": "t6",
      "from": "s2",
      "to": "s2",
      "symbol": "b",
      "dir": "R"
    },
    {
      "id": "t7",
      "from": "s3",
      "to": "s3",
      "symbol": "a",
      "dir": "L"
    },
    {
      "id": "t8",
      "from": "s3",
      "to": "s4",
      "symbol": "b",
      "dir": "L"
    },
    {
      "id": "t9",
      "from": "s4",
      "to": "s4",
      "symbol": "a",
      "dir": "L"
    },
    {
      "id": "t10",
      "from": "s4",
      "to": "s3",
      "symbol": "b",
      "dir": "L"
    },
    {
      "id": "t11",
      "from": "s4",
      "to": "s5",
      "symbol": "⊢",
      "dir": "S"
    }
  ],
  "notes": [
    {
      "id": "n1",
      "x": 620,
      "y": 60,
      "color": "blue",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "One head, two passes, zero memory cells. Pass 1 (top row) sweeps right counting a-parity; bouncing off ⊣ starts pass 2 (bottom row) sweeping left counting b-parity. Accepts: even number of a's AND odd number of b's."
    },
    {
      "id": "n2",
      "x": 620,
      "y": 400,
      "color": "green",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Watch the tape head in the tracker: it visibly bounces off the right end marker. Multiple passes replace extra states — the 2DFA trick."
    }
  ],
  "meta": {
    "title": "Two passes, one head",
    "blurb": "Checks even a's on the way out and odd b's on the way back — the head bounces off the end marker and re-reads the input. Multiple passes replace memory.",
    "inputs": [
      {
        "w": "aab",
        "expect": "accept"
      },
      {
        "w": "b",
        "expect": "accept"
      },
      {
        "w": "babab",
        "expect": "accept"
      },
      {
        "w": "ab",
        "expect": "reject",
        "label": "odd a's"
      },
      {
        "w": "aabb",
        "expect": "reject",
        "label": "even b's"
      }
    ],
    "library": {
      "author": {
        "login": "thethinkmachine"
      },
      "license": "CC-BY-4.0",
      "tags": [
        "showcase",
        "2dfa"
      ],
      "difficulty": "intermediate"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}