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Average Analysis of Glushkov Automata under a BST-Like Model

Authors Cyril Nicaud, Carine Pivoteau, Benoît Razet

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Cyril Nicaud
Carine Pivoteau
Benoît Razet

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Cyril Nicaud, Carine Pivoteau, and Benoît Razet. Average Analysis of Glushkov Automata under a BST-Like Model. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 388-399, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)


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.
  • Glushkov automata
  • random binary search tree
  • regular expression


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