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Multi-tilde-bar expressions and their automata

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Abstract

The aim of this paper is to extend the family of Glushkov automata. This is achieved by designing new operators, the so-called multi-tilde-bar operators, that allow us to compute Glushkov functions for the associated extended expressions. Conversely an extended Glushkov automaton with \(n+1\) states can be converted into an extended expression with \(n\) occurrences of symbols. It leads to a characterization in terms of graphs of the family of extended Glushkov automata. Moreover, extended expressions are shown to be superpolynomially more succinct than standard expressions.

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Acknowledgments

We wish to thank H. Gruber who pointed out the superpolynomial factorization of multi-tilde-bar expression.

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Authors and Affiliations

  1. LITIS, Université de Rouen, Saint-Étienne du Rouvray Cedex, 76801, France

    Pascal Caron, Jean-Marc Champarnaud & Ludovic Mignot

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  1. Pascal Caron
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  2. Jean-Marc Champarnaud
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  3. Ludovic Mignot
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Correspondence to Pascal Caron.

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Caron, P., Champarnaud, JM. & Mignot, L. Multi-tilde-bar expressions and their automata. Acta Informatica 49, 413–436 (2012). https://doi.org/10.1007/s00236-012-0167-x

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  • DOI: https://doi.org/10.1007/s00236-012-0167-x

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