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Asymptotic enumeration of Minimal Automata

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Abstract

We determine the asymptotic proportion of minimal automata, within n-state accessible deterministic complete automata over a k-letter alphabet, with the uniform distribution over the possible transition structures, and a binomial distribution over terminal states, with arbitrary parameter b. It turns out that a fraction ~ 1-C(k,b) n^{-k+2} of automata is minimal, with C(k,b) a function, explicitly determined, involving the solution of a transcendental equation.

BibTeX - Entry

@InProceedings{bassino_et_al:LIPIcs:2012:3432,
  author =	{Fr{\'e}d{\'e}rique Bassino and Julien David and Andrea Sportiello},
  title =	{{Asymptotic enumeration of Minimal Automata}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{88--99},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{Christoph D{\"u}rr and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3432},
  URN =		{urn:nbn:de:0030-drops-34328},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2012.88},
  annote =	{Keywords: minimal automata, regular languages, enumeration of random structures}
}

Keywords: minimal automata, regular languages, enumeration of random structures
Seminar: 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Issue date: 2012
Date of publication: 2012


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