{
  "machine": "PDT",
  "sigma": [
    "a",
    "b"
  ],
  "stackAlpha": [
    "Z",
    "X"
  ],
  "outputAlpha": [
    "a",
    "b"
  ],
  "states": [
    {
      "id": "s1",
      "x": 200,
      "y": 280,
      "name": "reading a"
    },
    {
      "id": "s2",
      "x": 520,
      "y": 280,
      "name": "reading b"
    },
    {
      "id": "s3",
      "x": 820,
      "y": 280,
      "name": "balanced"
    }
  ],
  "startId": "s1",
  "accepts": [
    "s3"
  ],
  "transitions": [
    {
      "id": "t1",
      "from": "s1",
      "to": "s1",
      "symbol": "a",
      "pop": "ε",
      "push": "X",
      "output": "b"
    },
    {
      "id": "t2",
      "from": "s1",
      "to": "s2",
      "symbol": "b",
      "pop": "X",
      "push": "ε",
      "output": "a"
    },
    {
      "id": "t3",
      "from": "s2",
      "to": "s2",
      "symbol": "b",
      "pop": "X",
      "push": "ε",
      "output": "a"
    },
    {
      "id": "t4",
      "from": "s2",
      "to": "s3",
      "symbol": "ε",
      "pop": "Z",
      "push": "Z",
      "output": ""
    }
  ],
  "notes": [
    {
      "id": "n1",
      "x": 150,
      "y": 70,
      "color": "purple",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "aⁿbⁿ ↦ bⁿaⁿ. The stack does the counting that makes aⁿbⁿ context-free: one X pushed per a, one popped per b, and the final ε-move only succeeds when Z is back on top — i.e. when the counts matched. The output swaps the letters as it goes."
    },
    {
      "id": "n2",
      "x": 150,
      "y": 430,
      "color": "orange",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Two jobs at once: the stack decides membership in a context-free language while the output function computes a transduction over the accepting runs. Try aab (unbalanced) — the run cannot reach \"balanced\", so the pair is not in the relation and nothing is output."
    }
  ],
  "config": {
    "transducerAccepts": true,
    "pdaParadigm": "explicit"
  },
  "meta": {
    "title": "Classic: aⁿbⁿ ↦ bⁿaⁿ",
    "blurb": "Accepts aⁿbⁿ with the stack while printing b for every a and a for every b — so the output is bⁿaⁿ. Recognition and transduction in one machine.",
    "inputs": [
      {
        "w": "ab",
        "expect": "accept",
        "out": "ba"
      },
      {
        "w": "aabb",
        "expect": "accept",
        "out": "bbaa"
      },
      {
        "w": "aaabbb",
        "expect": "accept",
        "out": "bbbaaa"
      },
      {
        "w": "aab",
        "expect": "reject"
      },
      {
        "w": "abb",
        "expect": "reject"
      }
    ],
    "library": {
      "author": {
        "login": "thethinkmachine"
      },
      "license": "CC-BY-4.0",
      "tags": [
        "textbook",
        "pdt"
      ],
      "difficulty": "intro"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}