{
  "id": "0711.3841",
  "version": "v2",
  "published": "2007-11-26T15:13:26.000Z",
  "updated": "2008-06-16T15:44:59.000Z",
  "title": "On the Induction Operation for Shift Subspaces and Cellular Automata as Presentations of Dynamical Systems",
  "authors": [
    "Silvio Capobianco"
  ],
  "comment": "20 pages, no figures. Presented at LATA 2008. Extended version, submitted to Information and Computation",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider continuous, translation-commuting transformations of compact, translation-invariant families of mappingsfrom finitely generated groups into finite alphabets. It is well-known that such transformations and spaces can be described \"locally\" via families of patterns and finitary functions; such descriptions can be re-used on groups larger than the original, usually defining non-isomorphic structures. We show how some of the properties of the \"induced\" entities can be deduced from those of the original ones, and vice versa; then, we show how to \"simulate\" the smaller structure into the larger one, and obtain a characterization in terms of group actions for the dynamical systems admitting of presentations via structures as such. Special attention is given to the class of sofic shifts.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-06-16T15:44:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B15",
      "68Q80"
    ],
    "keywords": [
      "dynamical systems",
      "induction operation",
      "shift subspaces",
      "cellular automata",
      "presentations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.3841C"
    }
  }
}