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On Varieties of Ordered Automata

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Language and Automata Theory and Applications (LATA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11417))

Abstract

The Eilenberg correspondence relates varieties of regular languages with pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of more complex algebraic structures on the other hand. It is also possible to consider classes of automata instead of algebraic structures as a natural counterpart of classes of languages. Here we deal with the correspondence relating positive \(\mathcal C\)-varieties of languages to positive \(\mathcal C\)-varieties of ordered automata and we demonstrate various specific instances of this correspondence. These bring certain well-known results from a new perspective and also some new observations. Moreover, complexity aspects of the membership problem are discussed both in the particular examples and in a general setting.

The paper was supported by grant GA15-02862S of the Czech Science Foundation.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic

    Ondřej Klíma & Libor Polák

Authors
  1. Ondřej Klíma
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  2. Libor Polák
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Correspondence to Ondřej Klíma .

Editor information

Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  2. Saint Petersburg State University, St. Petersburg, Russia

    Alexander Okhotin

  3. Ariel University, Ariel, Israel

    Dana Shapira

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Klíma, O., Polák, L. (2019). On Varieties of Ordered Automata. In: Martín-Vide, C., Okhotin, A., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2019. Lecture Notes in Computer Science(), vol 11417. Springer, Cham. https://doi.org/10.1007/978-3-030-13435-8_8

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  • DOI: https://doi.org/10.1007/978-3-030-13435-8_8

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  • Print ISBN: 978-3-030-13434-1

  • Online ISBN: 978-3-030-13435-8

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