Equational description of pseudovarieties of homomorphisms

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Authors

KUNC Michal

Year of publication 2003
Type Article in Periodical
Magazine / Source RAIRO - Theoretical Informatics and Applications
MU Faculty or unit

Faculty of Science

Citation
Web http://www.edpsciences.org/articles/ita/abs/2003/03/ita0311/ita0311.html
Field General mathematics
Keywords Pseudovariety; Pseudoidentity; Implicit operation; Variety of regular languages; Syntactic homomorphism
Description The notion of pseudovarieties of homomorphisms onto finite monoids was recently introduced by Straubing as an algebraic characterization for certain classes of regular languages. In this paper we provide a mechanism of equational description of these pseudovarieties based on an appropriate generalization of the notion of implicit operations. We show that the resulting metric monoids of implicit operations coincide with the standard ones, the only difference being the actual interpretation of pseudoidentities. As an example, an equational characterization of the pseudovariety corresponding to the class of regular languages in AC0 is given.
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