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On Theory of Regular Languages with the Kleene Star Operation

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Abstract

This paper is dedicated to studying model-theoretic and complexity properties of the theory of regular languages with the Kleene star operation. We construct a ‘‘natural’’ infinite set of axioms for this theory, and we prove that it is not finitely axiomatizable. We establish that this theory is countably categorical, but it is not categorical in any uncountable cardinality. Also, we find the exact amount of non-isomorphic models of given cardinality. Finally, we prove that the theory of regular languages with the Kleene star is PSPACE-complete.

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Authors and Affiliations

  1. Department of Computer Science, Tver State University, 170000, Tver, Russia

    B. Karlov

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  1. B. Karlov
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Correspondence to B. Karlov.

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(Submitted by M. M. Arslanov)

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Karlov, B. On Theory of Regular Languages with the Kleene Star Operation. Lobachevskii J Math 41, 1660–1665 (2020). https://doi.org/10.1134/S1995080220090164

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  • DOI: https://doi.org/10.1134/S1995080220090164

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