{
  "machine": "NPDA",
  "sigma": [
    "a",
    "b"
  ],
  "stackAlpha": [
    "a",
    "b",
    "Z"
  ],
  "states": [
    {
      "id": "s1",
      "x": 180,
      "y": 260,
      "name": "first half"
    },
    {
      "id": "s2",
      "x": 470,
      "y": 260,
      "name": "mirror"
    },
    {
      "id": "s3",
      "x": 740,
      "y": 260,
      "name": "acc"
    }
  ],
  "startId": "s1",
  "accepts": [
    "s3"
  ],
  "transitions": [
    {
      "id": "t1",
      "from": "s1",
      "to": "s1",
      "symbol": "a",
      "pop": "ε",
      "push": "a"
    },
    {
      "id": "t2",
      "from": "s1",
      "to": "s1",
      "symbol": "b",
      "pop": "ε",
      "push": "b"
    },
    {
      "id": "t3",
      "from": "s1",
      "to": "s2",
      "symbol": "ε",
      "pop": "ε",
      "push": "ε"
    },
    {
      "id": "t4",
      "from": "s2",
      "to": "s2",
      "symbol": "a",
      "pop": "a",
      "push": "ε"
    },
    {
      "id": "t5",
      "from": "s2",
      "to": "s2",
      "symbol": "b",
      "pop": "b",
      "push": "ε"
    },
    {
      "id": "t6",
      "from": "s2",
      "to": "s3",
      "symbol": "ε",
      "pop": "Z",
      "push": "Z"
    }
  ],
  "notes": [
    {
      "id": "n1",
      "x": 150,
      "y": 80,
      "color": "blue",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Even-length palindromes (w · wʳ): push the first half, GUESS the invisible middle with the ε jump, then check the rest is the mirror image. No deterministic machine can find the middle — that guess is pure nondeterminism."
    },
    {
      "id": "n2",
      "x": 150,
      "y": 400,
      "color": "green",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "The playback shows only the branch where the guess was right. Run abba, then abab — for abab every possible middle fails."
    }
  ],
  "config": {
    "pdaParadigm": "explicit"
  },
  "meta": {
    "title": "Palindromes: guess the middle",
    "blurb": "Accepts even-length palindromes over {a,b}. The machine pushes symbols, nondeterministically guesses where the middle is, then pops and matches the mirror half.",
    "inputs": [
      {
        "w": "abba",
        "expect": "accept"
      },
      {
        "w": "baab",
        "expect": "accept"
      },
      {
        "w": "abaaba",
        "expect": "accept"
      },
      {
        "w": "abab",
        "expect": "reject"
      },
      {
        "w": "aba",
        "expect": "reject",
        "label": "odd length"
      }
    ],
    "library": {
      "author": {
        "login": "thethinkmachine"
      },
      "license": "CC-BY-4.0",
      "tags": [
        "showcase",
        "npda"
      ],
      "difficulty": "intermediate"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}