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Average Analysis of Glushkov Automata under a BST-Like Model

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Abstract

We study the average number of transitions in Glushkov automata built from random regular expressions. This statistic highly depends on the probabilistic distribution set on the expressions. A recent work shows that, under the uniform distribution, regular expressions lead to automata with a linear number of transitions. However, uniform regular expressions are not necessarily a satisfying model. Therefore, we rather focus on an other model, inspired from random binary search trees (BST), which is widely used, in particular for testing. We establish that, in this case, the average number of transitions becomes quadratic according to the size of the regular expression.

BibTeX - Entry

@InProceedings{nicaud_et_al:LIPIcs:2010:2880,
  author =	{Cyril Nicaud and Carine Pivoteau and Benoît Razet},
  title =	{{Average Analysis of Glushkov Automata under a BST-Like Model}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
  pages =	{388--399},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-23-1},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{8},
  editor =	{Kamal Lodaya and Meena Mahajan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2880},
  URN =		{urn:nbn:de:0030-drops-28809},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2010.388},
  annote =	{Keywords: Glushkov automata, random binary search tree, regular expression}
}

Keywords: Glushkov automata, random binary search tree, regular expression
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)
Issue date: 2010
Date of publication: 2010


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