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International Symposium on Mathematical Foundations of Computer Science

MFCS 2008: Mathematical Foundations of Computer Science 2008 pp 363–374Cite as

Succinctness of Regular Expressions with Interleaving, Intersection and Counting

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5162))

Abstract

Studying the impact of operations, such as intersection and interleaving, on the succinctness of regular expressions has recently received renewed attention [12,13,14]. In this paper, we study the succinctness of regular expressions (REs) extended with interleaving, intersection and counting operators. We show that in a translation from REs with interleaving to standard regular expressions a double exponential size increase can not be avoided. We also consider the complexity of translations to finite automata. We give a tight exponential lower bound on the translation of REs with intersection to NFAs, and, for each of the three classes of REs, we show that in a translation to a DFA a double exponential size increase can not be avoided. Together with known results, this gives a complete picture of the complexity of translating REs extended with interleaving, intersection or counting into (standard) regular expressions, NFAs, and DFAs.

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Authors and Affiliations

  1. School for Information Technology, Hasselt University and Transnational University of Limburg,  

    Wouter Gelade

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  1. Wouter Gelade
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Edward Ochmański Jerzy Tyszkiewicz

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Gelade, W. (2008). Succinctness of Regular Expressions with Interleaving, Intersection and Counting. In: Ochmański, E., Tyszkiewicz, J. (eds) Mathematical Foundations of Computer Science 2008. MFCS 2008. Lecture Notes in Computer Science, vol 5162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85238-4_29

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  • DOI: https://doi.org/10.1007/978-3-540-85238-4_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85237-7

  • Online ISBN: 978-3-540-85238-4

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