{
  "machine": "QA",
  "sigma": [
    "a",
    "b",
    "#"
  ],
  "stackAlpha": [
    "A",
    "B"
  ],
  "states": [
    {
      "id": "s1",
      "x": 220,
      "y": 260,
      "name": "enqueue"
    },
    {
      "id": "s2",
      "x": 540,
      "y": 260,
      "name": "match"
    }
  ],
  "startId": "s1",
  "accepts": [],
  "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": "#",
      "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"
    }
  ],
  "notes": [
    {
      "id": "n1",
      "x": 160,
      "y": 80,
      "color": "blue",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "The copy language w#w — provably IMPOSSIBLE for any pushdown automaton: a stack hands back what it stored in reverse. A queue preserves order, so verifying a perfect copy is effortless: enqueue the left half, then match each symbol against the queue front."
    },
    {
      "id": "n2",
      "x": 160,
      "y": 400,
      "color": "green",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "ab#ab is accepted; ab#ba — the string a STACK would accept — is rejected. Acceptance: empty queue + input consumed."
    }
  ],
  "config": {
    "pdaParadigm": "empty"
  },
  "meta": {
    "title": "Perfect copy: w#w",
    "blurb": "Accepts w#w — an exact repetition. No PDA can do this (stacks reverse), but FIFO order makes it natural: the queue front always holds the next symbol the copy must produce.",
    "inputs": [
      {
        "w": "ab#ab",
        "expect": "accept"
      },
      {
        "w": "abb#abb",
        "expect": "accept"
      },
      {
        "w": "#",
        "expect": "accept",
        "label": "empty copy"
      },
      {
        "w": "ab#ba",
        "expect": "reject",
        "label": "mirrored, not copied"
      },
      {
        "w": "ab#a",
        "expect": "reject"
      }
    ],
    "library": {
      "author": {
        "login": "thethinkmachine"
      },
      "license": "CC-BY-4.0",
      "tags": [
        "showcase",
        "qa"
      ],
      "difficulty": "intermediate"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}