{
  "machine": "NBA",
  "sigma": [
    "a",
    "b"
  ],
  "states": [
    {
      "id": "s1",
      "x": 240,
      "y": 280,
      "name": "waiting"
    },
    {
      "id": "s2",
      "x": 640,
      "y": 280,
      "name": "saw a"
    }
  ],
  "startId": "s1",
  "accepts": [
    "s2"
  ],
  "transitions": [
    {
      "id": "t1",
      "from": "s1",
      "to": "s1",
      "symbol": "b"
    },
    {
      "id": "t2",
      "from": "s1",
      "to": "s2",
      "symbol": "a"
    },
    {
      "id": "t3",
      "from": "s2",
      "to": "s2",
      "symbol": "a"
    },
    {
      "id": "t4",
      "from": "s2",
      "to": "s1",
      "symbol": "b"
    }
  ],
  "notes": [
    {
      "id": "n1",
      "x": 150,
      "y": 70,
      "color": "blue",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Büchi acceptance: a run is accepting when it visits F infinitely often — NOT when it ends in F, because an ω-word never ends. This machine sits in \"saw a\" exactly after each a, so a run passes through F infinitely often precisely when the word contains infinitely many a's. In LTL that is GF a."
    },
    {
      "id": "n2",
      "x": 150,
      "y": 430,
      "color": "green",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Type an infinite word as u(v): a finite prefix then the block that repeats forever. (a) is aaa…, ab(ba) is ab bababa…. The simulator finds a lasso — a path into a cycle that keeps revisiting F — and unrolls it twice so you can see the loop. a(b) is rejected: the single a is not infinitely many."
    }
  ],
  "meta": {
    "title": "Infinitely often a",
    "blurb": "The canonical Büchi automaton for GF a: accepts exactly those infinite words containing infinitely many a's. Acceptance is about the cycle the run settles into, not where it stops.",
    "inputs": [
      {
        "w": "(a)",
        "expect": "accept"
      },
      {
        "w": "(b)",
        "expect": "reject"
      },
      {
        "w": "(ab)",
        "expect": "accept"
      },
      {
        "w": "a(b)",
        "expect": "reject"
      },
      {
        "w": "b(a)",
        "expect": "accept"
      },
      {
        "w": "abab(ab)",
        "expect": "accept"
      }
    ],
    "library": {
      "author": {
        "login": "thethinkmachine"
      },
      "license": "CC-BY-4.0",
      "tags": [
        "showcase",
        "nba"
      ],
      "difficulty": "intermediate"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}