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On Varieties of Ordered Automata

  • Ondřej KlímaEmail author
  • Libor Polák
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Algebraic language theory Ordered automata 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMasaryk UniversityBrnoCzech Republic

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