{
  "id": "0812.3499",
  "version": "v1",
  "published": "2008-12-18T10:14:34.000Z",
  "updated": "2008-12-18T10:14:34.000Z",
  "title": "An Effective Lower Bound for Group Complexity of Finite Semigroups and Automata",
  "authors": [
    "Karsten Henckell",
    "John Rhodes",
    "Benjamin Steinberg"
  ],
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, \\textit{Complexity of finite semigroups}, Annals of Mathematics (2) \\textbf{88} (1968), 128--160, motivated by the Prime Decomposition Theorem of K. Krohn and J. Rhodes, \\textit{Algebraic theory of machines, {I}: {P}rime decomposition theorem for finite semigroups and machines}, Transactions of the American Mathematical Society \\textbf{116} (1965), 450--464. Here we provide an effective lower bound for group complexity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-18T10:14:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M07"
    ],
    "keywords": [
      "finite semigroups",
      "effective lower bound",
      "group complexity",
      "prime decomposition theorem",
      "american mathematical society"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.3499H"
    }
  }
}