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On the Average Complexity of Moore's State Minimization Algorithm

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Abstract

We prove that, for any arbitrary finite alphabet and for the uniform distribution over deterministic and accessible automata with $n$ states, the average complexity of Moore's state minimization algorithm is in $\mathcal{O}(n \log n)$. Moreover this bound is tight in the case of unary automata.

BibTeX - Entry

@InProceedings{bassino_et_al:LIPIcs:2009:1822,
  author =	{Frederique Bassino and Julien David and Cyril Nicaud},
  title =	{{On the Average Complexity of Moore's State Minimization Algorithm}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{123--134},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Susanne Albers and Jean-Yves Marion},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/1822},
  URN =		{urn:nbn:de:0030-drops-18222},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2009.1822},
  annote =	{Keywords: Finite automata, State minimization, Moore’s algorithm, Average complexity}
}

Keywords: Finite automata, State minimization, Moore’s algorithm, Average complexity
Seminar: 26th International Symposium on Theoretical Aspects of Computer Science
Issue date: 2009
Date of publication: 2009


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