{
  "id": "1602.06095",
  "version": "v1",
  "published": "2016-02-19T10:00:36.000Z",
  "updated": "2016-02-19T10:00:36.000Z",
  "title": "Simulation of Effective Subshifts by Two-dimensional Subshifts of Finite Type",
  "authors": [
    "Nathalie Aubrun",
    "Mathieu Sablik"
  ],
  "journal": "Acta Applicandae Mathematicae, Springer Verlag, 2013",
  "doi": "10.1007/s10440-013-9808-5",
  "categories": [
    "math.DS",
    "cs.DM",
    "cs.FL"
  ],
  "abstract": "In this article we study how a subshift can simulate another one, where the notion of simulation is given by operations on subshifts inspired by the dynamical systems theory (factor, projective subaction...). There exists a correspondence between the notion of simulation and the set of forbidden patterns. The main result of this paper states that any effective subshift of dimension d -- that is a subshift whose set of forbidden patterns can be generated by a Turing machine -- can be obtained by applying dynamical operations on a subshift of finite type of dimension d + 1 -- a subshift that can be defined by a finite set of forbidden patterns. This result improves Hochman's [Hoc09].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-19T10:00:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite type",
      "effective subshift",
      "two-dimensional subshifts",
      "simulation",
      "forbidden patterns"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160206095A"
    }
  }
}