{
  "id": "2005.10078",
  "version": "v1",
  "published": "2020-05-18T19:48:46.000Z",
  "updated": "2020-05-18T19:48:46.000Z",
  "title": "Algebraic Structure and Complexity of Bootstrap Percolation with External Inputs",
  "authors": [
    "Saptarshi Pal",
    "Chrystopher L. Nehaniv"
  ],
  "comment": "10 pages, 5 Figures, Accepted with Minor Changes at Recent Advances in Mathematical and Statistical Methods, Proceedings of AMMCS - 2019",
  "categories": [
    "math.DS",
    "math.GR",
    "nlin.AO"
  ],
  "abstract": "In this paper a modification of the standard Bootstrap Percolation model is introduced. In our modification a discrete time update rule is constructed that allows for non-monotonicity - unlike its classical counterpart. External inputs to drive the system into desirable states are also included in the model. The algebraic structure and complexity properties of the system are inferred by studying the system's holonomy decomposition. We introduce methods of inferring the pools of reversibility for the system. Dependence of system complexity on process parameters is presented and discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-18T19:48:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "external inputs",
      "algebraic structure",
      "complexity",
      "discrete time update rule",
      "standard bootstrap percolation model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}