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Syntactic Complexity of \({\mathcal R}\)- and \({\mathcal J}\)-Trivial Regular Languages

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Descriptional Complexity of Formal Systems (DCFS 2013)

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Abstract

The syntactic complexity of a subclass of the class of regular languages is the maximal cardinality of syntactic semigroups of languages in that class, taken as a function of the state complexity n of these languages. We prove that n! and \(\lfloor e(n-1)! \rfloor\) are tight upper bounds for the syntactic complexity of \({\mathcal R}\)- and \({\mathcal J}\)-trivial regular languages, respectively.

This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant No. OGP0000871 and a Postgraduate Scholarship.

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Author information

Authors and Affiliations

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

    Janusz Brzozowski & Baiyu Li

Authors
  1. Janusz Brzozowski
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  2. Baiyu Li
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Middlesex College, Western University, N6A 5B7, London, ON, Canada

    Helmut Jurgensen

  2. Departamento de Ciência de Computadores, Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre 1021-1055,, 4169-007, Porto, Portugal

    Rogério Reis

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Brzozowski, J., Li, B. (2013). Syntactic Complexity of \({\mathcal R}\)- and \({\mathcal J}\)-Trivial Regular Languages. In: Jurgensen, H., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2013. Lecture Notes in Computer Science, vol 8031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39310-5_16

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  • DOI: https://doi.org/10.1007/978-3-642-39310-5_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39309-9

  • Online ISBN: 978-3-642-39310-5

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