{
  "machine": "2DFT",
  "sigma": [
    "a",
    "b"
  ],
  "outputAlpha": [
    "a",
    "b"
  ],
  "states": [
    {
      "id": "s1",
      "x": 160,
      "y": 200,
      "name": "start"
    },
    {
      "id": "s2",
      "x": 460,
      "y": 200,
      "name": "scan right"
    },
    {
      "id": "s3",
      "x": 460,
      "y": 430,
      "name": "print left"
    },
    {
      "id": "s4",
      "x": 160,
      "y": 430,
      "name": "done"
    }
  ],
  "startId": "s1",
  "accepts": [
    "s4"
  ],
  "transitions": [
    {
      "id": "t1",
      "from": "s1",
      "to": "s2",
      "symbol": "⊢",
      "dir": "R",
      "output": ""
    },
    {
      "id": "t2",
      "from": "s2",
      "to": "s2",
      "symbol": "a",
      "dir": "R",
      "output": ""
    },
    {
      "id": "t3",
      "from": "s2",
      "to": "s2",
      "symbol": "b",
      "dir": "R",
      "output": ""
    },
    {
      "id": "t4",
      "from": "s2",
      "to": "s3",
      "symbol": "⊣",
      "dir": "L",
      "output": ""
    },
    {
      "id": "t5",
      "from": "s3",
      "to": "s3",
      "symbol": "a",
      "dir": "L",
      "output": "a"
    },
    {
      "id": "t6",
      "from": "s3",
      "to": "s3",
      "symbol": "b",
      "dir": "L",
      "output": "b"
    },
    {
      "id": "t7",
      "from": "s3",
      "to": "s4",
      "symbol": "⊢",
      "dir": "S",
      "output": ""
    }
  ],
  "notes": [
    {
      "id": "n1",
      "x": 140,
      "y": 70,
      "color": "purple",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Reversal without a stack. Run right to the ⊣ endmarker printing nothing, then walk back left printing each symbol as you pass it. Reading the tape backwards is all the machine needs — no memory beyond the current state."
    },
    {
      "id": "n2",
      "x": 140,
      "y": 540,
      "color": "orange",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Compare with the pushdown transducer example, which reverses the same words using a stack and ε-moves. Both compute w ↦ wᴿ; the 2DFT gets there with a finite state set and a head that can turn around, which is why reversal is a REGULAR transduction rather than a genuinely context-free one."
    }
  ],
  "config": {
    "transducerAccepts": true
  },
  "meta": {
    "title": "Classic: reverse the input",
    "blurb": "Scans right in silence, then prints on the way back — computing w ↦ wᴿ with a finite state set and a two-way head, no stack required.",
    "inputs": [
      {
        "w": "ab",
        "expect": "accept",
        "out": "ba"
      },
      {
        "w": "abb",
        "expect": "accept",
        "out": "bba"
      },
      {
        "w": "aab",
        "expect": "accept",
        "out": "baa"
      },
      {
        "w": "abab",
        "expect": "accept",
        "out": "baba"
      },
      {
        "w": "a",
        "expect": "accept",
        "out": "a"
      }
    ],
    "library": {
      "author": {
        "login": "thethinkmachine"
      },
      "license": "CC-BY-4.0",
      "tags": [
        "textbook",
        "2dft"
      ],
      "difficulty": "intro"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}