{
  "machine": "2PDA",
  "sigma": [
    "a",
    "b",
    "c"
  ],
  "stackAlpha": [
    "A",
    "B",
    "Z"
  ],
  "states": [
    {
      "id": "s1",
      "x": 140,
      "y": 200,
      "name": "count a"
    },
    {
      "id": "s2",
      "x": 400,
      "y": 200,
      "name": "a vs b"
    },
    {
      "id": "s3",
      "x": 660,
      "y": 200,
      "name": "b vs c"
    },
    {
      "id": "s4",
      "x": 400,
      "y": 420,
      "name": "acc"
    }
  ],
  "startId": "s1",
  "accepts": [
    "s4"
  ],
  "transitions": [
    {
      "id": "t1",
      "from": "s1",
      "to": "s1",
      "symbol": "a",
      "pop": "ε",
      "push": "A",
      "pop2": "ε",
      "push2": "ε"
    },
    {
      "id": "t2",
      "from": "s1",
      "to": "s2",
      "symbol": "b",
      "pop": "A",
      "push": "ε",
      "pop2": "ε",
      "push2": "B"
    },
    {
      "id": "t3",
      "from": "s2",
      "to": "s2",
      "symbol": "b",
      "pop": "A",
      "push": "ε",
      "pop2": "ε",
      "push2": "B"
    },
    {
      "id": "t4",
      "from": "s2",
      "to": "s3",
      "symbol": "c",
      "pop": "ε",
      "push": "ε",
      "pop2": "B",
      "push2": "ε"
    },
    {
      "id": "t5",
      "from": "s3",
      "to": "s3",
      "symbol": "c",
      "pop": "ε",
      "push": "ε",
      "pop2": "B",
      "push2": "ε"
    },
    {
      "id": "t6",
      "from": "s3",
      "to": "s4",
      "symbol": "ε",
      "pop": "Z",
      "push": "Z",
      "pop2": "Z",
      "push2": "Z"
    },
    {
      "id": "t7",
      "from": "s1",
      "to": "s4",
      "symbol": "ε",
      "pop": "Z",
      "push": "Z",
      "pop2": "Z",
      "push2": "Z"
    }
  ],
  "notes": [
    {
      "id": "n1",
      "x": 620,
      "y": 60,
      "color": "blue",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "aⁿbⁿcⁿ — the canonical language ONE stack can never recognize. Stack 1 checks a's = b's (push A per a, pop per b); stack 2 checks b's = c's (push B per b, pop per c). Two stacks equal a Turing machine."
    },
    {
      "id": "n2",
      "x": 620,
      "y": 340,
      "color": "green",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Acceptance needs BOTH stacks down to bottom Z with input consumed. Watch both stores in the tracker: one drains while the other fills, then the second drains."
    }
  ],
  "config": {
    "pdaParadigm": "explicit"
  },
  "meta": {
    "title": "aⁿbⁿcⁿ — beyond one stack",
    "blurb": "The language that defines the limit of context-free: equal runs of a, b, and c. Stack 1 matches a's to b's while stack 2 matches b's to c's — two stacks reach Turing power.",
    "inputs": [
      {
        "w": "abc",
        "expect": "accept"
      },
      {
        "w": "aabbcc",
        "expect": "accept"
      },
      {
        "w": "aaabbbccc",
        "expect": "accept"
      },
      {
        "w": "aabbc",
        "expect": "reject"
      },
      {
        "w": "abcc",
        "expect": "reject"
      },
      {
        "w": "acb",
        "expect": "reject"
      }
    ],
    "library": {
      "author": {
        "login": "thethinkmachine"
      },
      "license": "CC-BY-4.0",
      "tags": [
        "showcase",
        "2pda"
      ],
      "difficulty": "intermediate"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}