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On Decidability of Regular Languages Theories

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Computer Science – Theory and Applications (CSR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11532))

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Abstract

This paper is dedicated to studying decidability properties of some regular languages theories. We prove that the regular languages theory with the Kleene star only is decidable. If we use union and concatenation simultaneously then the theory becomes both \(\varSigma _1\)- and \(\varPi _1\)-hard over the one-symbol alphabet. Finally, we prove that the regular languages theory over one-symbol alphabet with union and the Kleene star is equivalent to arithmetic. The Kleene star is definable with union and concatenation, hence, the previous theory is equivalent to arithmetic also.

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Authors and Affiliations

  1. CS Department, Tver State University, Zhelyabova Str., 33, Tver, 170100, Russia

    Sergey Dudakov & Boris Karlov

Authors
  1. Sergey Dudakov
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  2. Boris Karlov
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Correspondence to Boris Karlov .

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Editors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    René van Bevern

  2. Laboratoire d'Informatique Gaspard-Monge, Marne-la-Vallée, France

    Gregory Kucherov

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Dudakov, S., Karlov, B. (2019). On Decidability of Regular Languages Theories. In: van Bevern, R., Kucherov, G. (eds) Computer Science – Theory and Applications. CSR 2019. Lecture Notes in Computer Science(), vol 11532. Springer, Cham. https://doi.org/10.1007/978-3-030-19955-5_11

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  • DOI: https://doi.org/10.1007/978-3-030-19955-5_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-19954-8

  • Online ISBN: 978-3-030-19955-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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