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 is given.
Mots-clés : pseudovariety, pseudoidentity, implicit operation, variety of regular languages, syntactic homomorphism
@article{ITA_2003__37_3_243_0, 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://archive.numdam.org/articles/10.1051/ita:2003018/} }
TY - JOUR AU - Kunc, Michal TI - Equational description of pseudovarieties of homomorphisms JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2003 SP - 243 EP - 254 VL - 37 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2003018/ DO - 10.1051/ita:2003018 LA - en ID - ITA_2003__37_3_243_0 ER -
%0 Journal Article %A Kunc, Michal %T Equational description of pseudovarieties of homomorphisms %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2003 %P 243-254 %V 37 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2003018/ %R 10.1051/ita:2003018 %G en %F ITA_2003__37_3_243_0
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. http://archive.numdam.org/articles/10.1051/ita:2003018/
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