{
  "id": "1408.1463",
  "version": "v1",
  "published": "2014-08-07T02:05:23.000Z",
  "updated": "2014-08-07T02:05:23.000Z",
  "title": "Reversibility of additive CA as function of cylinder size",
  "authors": [
    "Valeriy Bulitko"
  ],
  "comment": "28 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Additive CA on a cylinder of size $n$ can be represented by 01-string $V$ of length $n$ which is its rule. We study a problem: a class $S$ of rules given, for any $V\\in S$ describe all sizes $n', n'>n,$ of cylinders such that extension of $V$ by zeros to length $n'$ represents reversible additive CA on a cylinder of size $n'$. Since all extensions of $V$ have the same collection of positions of units, it is convenient to say about classes of collections of positions instead of classes of rules. A criterion of reversibility is proven. The problem is completely solved for infinite class of \"block collections\", i.e. $\\{(0,1,\\dots,h)|h\\in\\mathbb Z^+\\}$. Results obtained for \"exponential collections\" $\\{(1,2,4,\\dots,2^h)|h\\in\\mathbb Z^+\\}$ essentially reduce the complexity of the problem for this class. Ways to transfer the results on other classes of rules/collections are described. A conjecture is formulated for class $\\{(0,1,2^m)|m\\in\\mathbb Z^+\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-07T02:05:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B15",
      "68Q80"
    ],
    "keywords": [
      "cylinder size",
      "reversibility",
      "exponential collections",
      "represents reversible additive ca"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.1463B"
    }
  }
}