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International Conference on Implementation and Application of Automata

CIAA 2017: Implementation and Application of Automata pp 76–88Cite as

Complexity of Bifix-Free Regular Languages

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10329))

Abstract

We study descriptive complexity properties of the class of regular bifix-free languages, which is the intersection of prefix-free and suffix-free regular languages. We show that there exist universal bifix-free languages that meet all the bounds for the state complexity of basic operations (Boolean operations, product, star, and reversal). This is in contrast with suffix-free languages, where it is known that there does not exist such languages. Then we present a stream of bifix-free languages that is most complex in terms of all basic operations, syntactic complexity, and the number of atoms and their complexities, which requires a superexponential alphabet. We also complete the previous results by characterizing state complexity of product, star, and reversal, and establishing tight upper bounds for atom complexities of bifix-free languages. Moreover, we consider the problem of the minimal size of an alphabet required to meet the bounds, and the problem of attainable values of state complexities (magic numbers).

This work was supported in part by the National Science Centre, Poland under project number 2014/15/B/ST6/00615.

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Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, Wrocław, Poland

    Robert Ferens & Marek Szykuła

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  1. Robert Ferens
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  2. Marek Szykuła
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Correspondence to Marek Szykuła .

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Editors and Affiliations

  1. LIGM (UMR 8049), CNRS, Université Paris-Est, Marne-la-Vallée Cedex 2, France

    Arnaud Carayol

  2. LIGM (UMR 8049), Université Paris-Est, Marne-la-Vallée Cedex 2, France

    Cyril Nicaud

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Ferens, R., Szykuła, M. (2017). Complexity of Bifix-Free Regular Languages. In: Carayol, A., Nicaud, C. (eds) Implementation and Application of Automata. CIAA 2017. Lecture Notes in Computer Science(), vol 10329. Springer, Cham. https://doi.org/10.1007/978-3-319-60134-2_7

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  • DOI: https://doi.org/10.1007/978-3-319-60134-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60133-5

  • Online ISBN: 978-3-319-60134-2

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