{
  "id": "1307.7412",
  "version": "v2",
  "published": "2013-07-28T22:18:34.000Z",
  "updated": "2014-10-26T15:51:03.000Z",
  "title": "On continuing codes",
  "authors": [
    "Jisang Yoo"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We investigate what happens when we try to work with continuing block codes (i.e. left or right continuing factor maps) between shift spaces that may not be shifts of finite type. For example, we demonstrate that continuing block codes on strictly sofic shifts do not behave as well as those on shifts of finite type; a continuing block code on a sofic shift need not have a uniformly bounded retract, unlike one on a shift of finite type. A right eresolving code on a sofic shift can display any behavior arbitrary block codes can have. We also show that a right continuing factor of a shift of finite type is always a shift of finite type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-28T22:18:34.000Z",
      "abstract": "We demonstrate that continuing block codes on general sofic shifts do not behave as well as in the case of shifts of finite type; a continuing block code on a sofic shift need not have a uniformly bounded retract, unlike one on a shift of finite type. A right eresolving code on a sofic shift can display any behavior arbitrary block codes can have. We also show that a right continuing factor of a shift of finite type is necessarily a shift of finite type.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-26T15:51:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10"
    ],
    "keywords": [
      "finite type",
      "continuing codes",
      "continuing block code",
      "behavior arbitrary block codes",
      "general sofic shifts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.7412Y"
    }
  }
}