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Syntactic Complexity of Prefix-, Suffix-, and Bifix-Free Regular Languages

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Descriptional Complexity of Formal Systems (DCFS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6808))

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Abstract

The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as a function of the state complexity n of these languages. We study the syntactic complexity of prefix-, suffix-, and bifix-free regular languages. We prove that n nā€‰āˆ’ā€‰2 is a tight upper bound for prefix-free regular languages. We present properties of the syntactic semigroups of suffix- and bifix-free regular languages, and conjecture tight upper bounds on their size.

This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant No. OGP0000871 and a Postgraduate Scholarship, and by a Graduate Award from the Department of Computer Science, University of Toronto.

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Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Janusz Brzozowski & Baiyu Li

  2. Department of Computer Science, University of Toronto, Toronto, ON, M5S 3G4, Canada

    Yuli Ye

Authors
  1. Janusz Brzozowski
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  2. Baiyu Li
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  3. Yuli Ye
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Editor information

Editors and Affiliations

  1. Institut fĆ¼r Informatik, UniversitƤt Giessen, ArndtstraƟe 2, 35392, Giessen, Germany

    Markus Holzer

  2. Institut fĆ¼r Informatik, UniversitƤt GieƟen, ArndtstraƟe 2, 35392, GieƟen, Germany

    Martin Kutrib

  3. Dipartimento di Informatica e Comunicazione, UniversitĆ  degli Studi di Milano, Via Comelico 39, 20135, Milano, Italy

    Giovanni Pighizzini

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Brzozowski, J., Li, B., Ye, Y. (2011). Syntactic Complexity of Prefix-, Suffix-, and Bifix-Free Regular Languages. In: Holzer, M., Kutrib, M., Pighizzini, G. (eds) Descriptional Complexity of Formal Systems. DCFS 2011. Lecture Notes in Computer Science, vol 6808. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22600-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-22600-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22599-4

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