{
  "machine": "LBA",
  "sigma": [
    "a"
  ],
  "stackAlpha": [
    "⊢",
    "a",
    "X",
    "⊔",
    "⊣"
  ],
  "tapeCount": 1,
  "states": [
    {
      "id": "s1",
      "x": 140,
      "y": 160,
      "name": "pass"
    },
    {
      "id": "s2",
      "x": 380,
      "y": 160,
      "name": "saw one"
    },
    {
      "id": "s3",
      "x": 620,
      "y": 160,
      "name": "even"
    },
    {
      "id": "s4",
      "x": 860,
      "y": 160,
      "name": "odd ≥ 3"
    },
    {
      "id": "s5",
      "x": 500,
      "y": 380,
      "name": "rewind"
    },
    {
      "id": "s6",
      "x": 180,
      "y": 380,
      "name": "acc"
    }
  ],
  "startId": "s1",
  "accepts": [
    "s6"
  ],
  "transitions": [
    {
      "id": "t1",
      "from": "s1",
      "to": "s1",
      "symbol": "⊢",
      "write": "⊢",
      "dir": "R"
    },
    {
      "id": "t2",
      "from": "s1",
      "to": "s1",
      "symbol": "X",
      "write": "X",
      "dir": "R"
    },
    {
      "id": "t3",
      "from": "s1",
      "to": "s2",
      "symbol": "a",
      "write": "a",
      "dir": "R"
    },
    {
      "id": "t4",
      "from": "s2",
      "to": "s2",
      "symbol": "X",
      "write": "X",
      "dir": "R"
    },
    {
      "id": "t5",
      "from": "s2",
      "to": "s3",
      "symbol": "a",
      "write": "X",
      "dir": "R"
    },
    {
      "id": "t6",
      "from": "s2",
      "to": "s6",
      "symbol": "⊣",
      "write": "⊣",
      "dir": "S"
    },
    {
      "id": "t7",
      "from": "s3",
      "to": "s3",
      "symbol": "X",
      "write": "X",
      "dir": "R"
    },
    {
      "id": "t8",
      "from": "s3",
      "to": "s4",
      "symbol": "a",
      "write": "a",
      "dir": "R"
    },
    {
      "id": "t9",
      "from": "s3",
      "to": "s5",
      "symbol": "⊣",
      "write": "⊣",
      "dir": "L"
    },
    {
      "id": "t10",
      "from": "s4",
      "to": "s4",
      "symbol": "X",
      "write": "X",
      "dir": "R"
    },
    {
      "id": "t11",
      "from": "s4",
      "to": "s3",
      "symbol": "a",
      "write": "X",
      "dir": "R"
    },
    {
      "id": "t12",
      "from": "s5",
      "to": "s5",
      "symbol": "X",
      "write": "X",
      "dir": "L"
    },
    {
      "id": "t13",
      "from": "s5",
      "to": "s5",
      "symbol": "a",
      "write": "a",
      "dir": "L"
    },
    {
      "id": "t14",
      "from": "s5",
      "to": "s1",
      "symbol": "⊢",
      "write": "⊢",
      "dir": "R"
    }
  ],
  "notes": [
    {
      "id": "n1",
      "x": 30,
      "y": 40,
      "color": "blue",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Accepts aⁿ exactly when n is a power of two. Each left-to-right pass crosses off every SECOND surviving a — halving n. If a pass ever ends on an odd count above 1, n wasn't a power of two. When a pass finds exactly one a, accept."
    },
    {
      "id": "n2",
      "x": 700,
      "y": 380,
      "color": "green",
      "anchorStates": [],
      "anchorTransitions": [],
      "text": "Run 16 a's and watch the tape get eaten: 16 → 8 → 4 → 2 → 1. All inside the input's own cells — that bounded tape is what makes it an LBA."
    }
  ],
  "meta": {
    "title": "Powers of two, by halving",
    "blurb": "Accepts aⁿ iff n = 2ᵏ. Each pass crosses off every second a, halving the count; a clean halving chain down to 1 is only possible for powers of two.",
    "inputs": [
      {
        "w": "a",
        "expect": "accept",
        "label": "2⁰"
      },
      {
        "w": "aaaa",
        "expect": "accept",
        "label": "2²"
      },
      {
        "w": "aaaaaaaa",
        "expect": "accept",
        "label": "2³"
      },
      {
        "w": "aaaaaaaaaaaaaaaa",
        "expect": "accept",
        "label": "2⁴ — hypnotic"
      },
      {
        "w": "aaaaaa",
        "expect": "reject",
        "label": "6"
      },
      {
        "w": "aaaaa",
        "expect": "reject",
        "label": "5"
      }
    ],
    "library": {
      "author": {
        "login": "thethinkmachine"
      },
      "license": "CC-BY-4.0",
      "tags": [
        "showcase",
        "lba"
      ],
      "difficulty": "intermediate"
    }
  },
  "format": "automata-studio/workspace",
  "schema": 1,
  "app": "dev"
}