{
  "id": "1912.06897",
  "version": "v1",
  "published": "2019-12-14T18:14:33.000Z",
  "updated": "2019-12-14T18:14:33.000Z",
  "title": "On Orbits and the Finiteness of Bounded Automaton Groups",
  "authors": [
    "Ievgen Bondarenko",
    "Jan Philipp Wächter"
  ],
  "categories": [
    "math.GR",
    "cs.FL"
  ],
  "abstract": "We devise an algorithm which, given a bounded automaton A, decides whether the group generated by A is finite. The solution comes from a description of the infinite sequences having an infinite A-orbit using a deterministic finite-state acceptor. This acceptor can also be used to decide whether the bounded automaton acts level-transitively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-14T18:14:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F10",
      "20M35",
      "F.4.m"
    ],
    "keywords": [
      "bounded automaton groups",
      "finiteness",
      "deterministic finite-state acceptor",
      "solution comes",
      "bounded automaton acts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}