{
  "machine": "DcoBA",
  "sigma": [
    "a",
    "b"
  ],
  "states": [
    {
      "id": "s1",
      "x": 240,
      "y": 280,
      "name": "last was b"
    },
    {
      "id": "s2",
      "x": 640,
      "y": 280,
      "name": "last was 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": "purple",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Eventually always b — FG b, the language with no deterministic Büchi automaton. Here it is, deterministic. The machine is shaped exactly like the DBA for \"infinitely often a\"; the acceptance condition is what differs. Under co-Büchi the ringed states are the ones that must STOP happening: a run is accepting when inf(r) ∩ F = ∅."
    },
    {
      "id": "n2",
      "x": 150,
      "y": 430,
      "color": "orange",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "\"last was a\" is entered on exactly the a's, so visiting it finitely often means the word has finitely many a's. Compare the Büchi model's \"eventually always b\", which needs a nondeterministic guess to say the same thing. co-Büchi does not need the guess — nondeterminism buys it nothing at all, because NcoBA = DcoBA."
    }
  ],
  "meta": {
    "title": "Eventually always b",
    "blurb": "FG b as a deterministic co-Büchi automaton — the same language a Büchi automaton can only recognise by guessing. Swapping α from Büchi to co-Büchi is the entire difference.",
    "inputs": [
      {
        "w": "(b)",
        "expect": "accept"
      },
      {
        "w": "a(b)",
        "expect": "accept"
      },
      {
        "w": "ab(b)",
        "expect": "accept"
      },
      {
        "w": "aaaa(b)",
        "expect": "accept"
      },
      {
        "w": "(a)",
        "expect": "reject"
      },
      {
        "w": "(ab)",
        "expect": "reject"
      },
      {
        "w": "bbb(ab)",
        "expect": "reject"
      }
    ],
    "library": {
      "author": {
        "login": "thethinkmachine"
      },
      "license": "CC-BY-4.0",
      "tags": [
        "showcase",
        "dcoba"
      ],
      "difficulty": "intermediate"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}