{
  "machine": "NWA",
  "sigma": [
    "a",
    "b"
  ],
  "states": [
    {
      "id": "s1",
      "x": 220,
      "y": 250,
      "name": "ok"
    },
    {
      "id": "s2",
      "x": 620,
      "y": 250,
      "name": "just saw a"
    },
    {
      "id": "s4",
      "x": 220,
      "y": 500,
      "name": "ok (copy)"
    },
    {
      "id": "s3",
      "x": 620,
      "y": 500,
      "name": "dead"
    }
  ],
  "startId": "s1",
  "accepts": [
    "s1",
    "s2",
    "s4"
  ],
  "transitions": [
    {
      "id": "t1",
      "from": "s1",
      "to": "s1",
      "symbol": "b"
    },
    {
      "id": "t2",
      "from": "s1",
      "to": "s2",
      "symbol": "a"
    },
    {
      "id": "t3",
      "from": "s2",
      "to": "s1",
      "symbol": "b"
    },
    {
      "id": "t4",
      "from": "s2",
      "to": "s3",
      "symbol": "a"
    },
    {
      "id": "t5",
      "from": "s3",
      "to": "s3",
      "symbol": "a"
    },
    {
      "id": "t6",
      "from": "s3",
      "to": "s3",
      "symbol": "b"
    },
    {
      "id": "t7",
      "from": "s1",
      "to": "s4",
      "symbol": "b"
    },
    {
      "id": "t8",
      "from": "s4",
      "to": "s4",
      "symbol": "b"
    },
    {
      "id": "t9",
      "from": "s4",
      "to": "s2",
      "symbol": "a"
    }
  ],
  "notes": [
    {
      "id": "n1",
      "x": 140,
      "y": 60,
      "color": "blue",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Never two a's in a row, drawn nondeterministically: a b out of \"ok\" may stay put or slide into \"ok (copy)\", which behaves identically. The weakness constraint survives the branching — {ok, just saw a, ok (copy)} is one strongly connected component lying wholly inside F, and {dead} is one lying wholly outside."
    },
    {
      "id": "n2",
      "x": 140,
      "y": 700,
      "color": "orange",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Weakness constrains the shape of the automaton, so it survives nondeterminism unharmed — what matters is that no SCC straddles F, not how many choices leave a state. Redirect \"dead\" back into \"ok\" and the two components merge into one that straddles F; the app reports that before running and falls back to plain Büchi acceptance."
    }
  ],
  "meta": {
    "title": "Never two a's, with a needless guess",
    "blurb": "A nondeterministic weak automaton for the same safety property as the DWA, with a redundant branch that leaves the SCC constraint intact.",
    "inputs": [
      {
        "w": "(b)",
        "expect": "accept"
      },
      {
        "w": "(ab)",
        "expect": "accept"
      },
      {
        "w": "b(ab)",
        "expect": "accept"
      },
      {
        "w": "ba(b)",
        "expect": "accept"
      },
      {
        "w": "(a)",
        "expect": "reject"
      },
      {
        "w": "aa(b)",
        "expect": "reject"
      },
      {
        "w": "(aab)",
        "expect": "reject"
      }
    ],
    "library": {
      "author": {
        "login": "thethinkmachine"
      },
      "license": "CC-BY-4.0",
      "tags": [
        "showcase",
        "nwa"
      ],
      "difficulty": "intermediate"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}