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DOI: 10.4230/LIPIcs.STACS.2008.1328
URN: urn:nbn:de:0030-drops-13286
URL: http://drops.dagstuhl.de/opus/volltexte/2008/1328/
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Valmari, Antti ; Lehtinen, Petri

Efficient Minimization of DFAs with Partial Transition

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Abstract

Let PT-DFA mean a deterministic finite automaton whose transition relation is a partial function. We present an algorithm for minimizing a PT-DFA in $O(m lg n)$ time and $O(m+n+alpha)$ memory, where $n$ is the number of states, $m$ is the number of defined transitions, and $alpha$ is the size of the alphabet. Time consumption does not depend on $alpha$, because the $alpha$ term arises from an array that is accessed at random and never initialized. It is not needed, if transitions are in a suitable order in the input. The algorithm uses two instances of an array-based data structure for maintaining a refinable partition. Its operations are all amortized constant time. One instance represents the classical blocks and the other a partition of transitions. Our measurements demonstrate the speed advantage of our algorithm on PT-DFAs over an $O(alpha n lg n)$ time, $O(alpha n)$ memory algorithm.

BibTeX - Entry

@InProceedings{valmari_et_al:LIPIcs:2008:1328,
  author =	{Antti Valmari and Petri Lehtinen},
  title =	{{Efficient Minimization of DFAs with Partial Transition}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{645--656},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Susanne Albers and Pascal Weil},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1328},
  URN =		{urn:nbn:de:0030-drops-13286},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2008.1328},
  annote =	{Keywords: Deterministic finite automaton, sparse adjacency matrix, partition refinement}
}

Keywords: Deterministic finite automaton, sparse adjacency matrix, partition refinement
Seminar: 25th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2008
Date of publication: 06.02.2008


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