{
  "id": "1603.07271",
  "version": "v1",
  "published": "2016-03-21T15:37:34.000Z",
  "updated": "2016-03-21T15:37:34.000Z",
  "title": "Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon Theorem",
  "authors": [
    "Simon Wacker"
  ],
  "categories": [
    "math.GR",
    "cs.FL"
  ],
  "abstract": "We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spaces acted on by isometries; vertex-transitive graphs, in particular, Cayley graphs, acted on by automorphisms; groups acting on themselves by multiplication; and integer lattices acted on by translations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-21T15:37:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniform curtis-hedlund-lyndon theorem",
      "cellular automata",
      "group sets",
      "left homogeneous spaces",
      "integer lattices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160307271W"
    }
  }
}