{
  "id": "1808.06886",
  "version": "v1",
  "published": "2018-08-21T13:16:24.000Z",
  "updated": "2018-08-21T13:16:24.000Z",
  "title": "Compressed decision problems in hyperbolic groups",
  "authors": [
    "Derek Holt",
    "Markus Lohrey",
    "Saul Schleimer"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove that the compressed word problem and the compressed simultaneous conjugacy problem are solvable in polynomial time in hyperbolic groups. In such problems, group elements are input as words defined by straight line programs defined over a finite generating set for the group. We prove also that, for any infinite hyperbolic group $G$, the compressed knapsack problem in $G$ is ${\\mathsf{NP}}$-complete.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-21T13:16:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F10",
      "20F67"
    ],
    "keywords": [
      "compressed decision problems",
      "straight line programs",
      "infinite hyperbolic group",
      "polynomial time",
      "group elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}