Geodesic
Equational description of pseudovarieties of homomorphisms
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 3, pp. 243-254

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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 AC 0 is given.

DOI : 10.1051/ita:2003018
Classification : 20M35, 68Q70
Keywords: pseudovariety, pseudoidentity, implicit operation, variety of regular languages, syntactic homomorphism 
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     author = {Kunc, Michal},
     title = {Equational description of pseudovarieties of homomorphisms},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {243--254},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {3},
     year = {2003},
     doi = {10.1051/ita:2003018},
     mrnumber = {2021316},
     zbl = {1045.20049},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2003018/}
}
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Kunc, Michal. Equational description of pseudovarieties of homomorphisms. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 3, pp. 243-254. doi: 10.1051/ita:2003018

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