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On Brzozowski’s Conjecture for the Free Burnside Semigroup Satisfying x 2 = x 3

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Developments in Language Theory (DLT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6795))

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Abstract

In this paper we examine Brzozowski’s conjecture for the two-generated free Burnside semigroup satisfying x 2 = x 3. The elements of this semigroup are classes of equivalent words, and the conjecture claims that all elements are regular languages. The case of the identity x 2 = x 3 is the only one, for which Brzozowski’s conjecture is neither proved nor disproved. We prove the conjecture for all the elements containing an overlap-free or an “almost” overlap-free word. In addition, we show that all but finitely many of these elements are “big” languages in terms of growth rate.

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Authors and Affiliations

  1. Ural State University, Ekaterinburg, Russia

    Andrey N. Plyushchenko & Arseny M. Shur

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  1. Andrey N. Plyushchenko
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  2. Arseny M. Shur
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  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Viale Sarca 336, Edificio U14, 20126, Milano, Italy

    Giancarlo Mauri  & Alberto Leporati  & 

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Plyushchenko, A.N., Shur, A.M. (2011). On Brzozowski’s Conjecture for the Free Burnside Semigroup Satisfying x 2 = x 3 . In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_31

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  • DOI: https://doi.org/10.1007/978-3-642-22321-1_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22320-4

  • Online ISBN: 978-3-642-22321-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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