{
  "machine": "PDT",
  "sigma": [
    "a",
    "b"
  ],
  "stackAlpha": [
    "Z",
    "A",
    "B"
  ],
  "outputAlpha": [
    "a",
    "b"
  ],
  "states": [
    {
      "id": "s1",
      "x": 200,
      "y": 280,
      "name": "push"
    },
    {
      "id": "s2",
      "x": 500,
      "y": 280,
      "name": "pop"
    },
    {
      "id": "s3",
      "x": 800,
      "y": 280,
      "name": "done"
    }
  ],
  "startId": "s1",
  "accepts": [
    "s3"
  ],
  "transitions": [
    {
      "id": "t1",
      "from": "s1",
      "to": "s1",
      "symbol": "a",
      "pop": "ε",
      "push": "A",
      "output": ""
    },
    {
      "id": "t2",
      "from": "s1",
      "to": "s1",
      "symbol": "b",
      "pop": "ε",
      "push": "B",
      "output": ""
    },
    {
      "id": "t3",
      "from": "s1",
      "to": "s2",
      "symbol": "ε",
      "pop": "ε",
      "push": "ε",
      "output": ""
    },
    {
      "id": "t4",
      "from": "s2",
      "to": "s2",
      "symbol": "ε",
      "pop": "A",
      "push": "ε",
      "output": "a"
    },
    {
      "id": "t5",
      "from": "s2",
      "to": "s2",
      "symbol": "ε",
      "pop": "B",
      "push": "ε",
      "output": "b"
    },
    {
      "id": "t6",
      "from": "s2",
      "to": "s3",
      "symbol": "ε",
      "pop": "Z",
      "push": "Z",
      "output": ""
    }
  ],
  "notes": [
    {
      "id": "n1",
      "x": 150,
      "y": 70,
      "color": "blue",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Reversal — the canonical pushdown transduction. Phase 1 reads the whole input and pushes a marker per symbol, printing nothing. An ε-move guesses the end of the input; phase 2 pops the stack and prints each symbol as it comes off. LIFO does the reversing."
    },
    {
      "id": "n2",
      "x": 150,
      "y": 430,
      "color": "green",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "No one-way finite transducer can do this: printing the first output symbol requires knowing the last input symbol, which needs unbounded lookahead. A stack supplies exactly that. Note the ε-read pops in phase 2 — they emit output without consuming input, which is why the Out row keeps growing after In is exhausted."
    }
  ],
  "config": {
    "transducerAccepts": true,
    "pdaParadigm": "explicit"
  },
  "meta": {
    "title": "Reverse the input",
    "blurb": "Pushes every input symbol, then pops the stack printing as it goes — so the output is the input reversed. The transduction w ↦ wᴿ needs a stack; no one-way FST can compute it.",
    "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": [
        "showcase",
        "pdt"
      ],
      "difficulty": "intermediate"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}