{
  "id": "0705.0670",
  "version": "v3",
  "published": "2007-05-04T19:59:14.000Z",
  "updated": "2008-06-16T18:09:08.000Z",
  "title": "Surjunctivity for cellular automata in Besicovitch spaces",
  "authors": [
    "Silvio Capobianco"
  ],
  "comment": "9 pages, no figures, LaTeX. Shortened, some definition changed, proof of main lemma changed accordingly. Almost as submitted to Journal of Cellular Automata for special issue dedicated to Automata 2007 conference proceedings. Exceptions: one major error corrected in definition of surjunctivity; adapted for use of the article document class",
  "categories": [
    "math.DS"
  ],
  "abstract": "The Besicovitch pseudodistance measures the relative size of the set of points where two functions take different values; the quotient space modulo the induced equivalence relation is endowed with a natural metric. We study the behavior of cellular automata in the new topology and show that, under suitable additional hypotheses, they retain certain properties possessed in the usual product topology; in particular, that injectivity still implies surjectivity.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-06-16T18:09:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B15",
      "68Q80"
    ],
    "keywords": [
      "cellular automata",
      "besicovitch spaces",
      "surjunctivity",
      "besicovitch pseudodistance measures",
      "usual product topology"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.0670C"
    }
  }
}