{
  "id": "1811.00060",
  "version": "v1",
  "published": "2018-10-31T18:49:36.000Z",
  "updated": "2018-10-31T18:49:36.000Z",
  "title": "On the Complexity of Properties of Transformation Semigroups",
  "authors": [
    "Trevor Jack"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We investigate the computational complexity for determining various properties of a finite transformation semigroup $S$ given by generators. In particular, we show that checking whether an element of $S$ is regular is PSPACE-complete. We give polynomial time algorithms for enumerating left/right identities, finding a left/right zero, checking nilpotence, and checking if a semigroup satisfies a fixed equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-31T18:49:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M20"
    ],
    "keywords": [
      "properties",
      "polynomial time algorithms",
      "finite transformation semigroup",
      "computational complexity",
      "enumerating left/right identities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}