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

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
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/

[1] J. Almeida, Finite Semigroups and Universal Algebra. World Scientific, Singapore (1995). | MR | Zbl

[2] D. Mix Barrington, K. Compton, H. Straubing and D. Thérien, Regular languages in NC 1 . J. Comput. System Sci. 44 (1992) 478-499. | Zbl

[3] S. Eilenberg, Automata, Languages and Machines. vol. B, Academic Press, New York (1976). | MR | Zbl

[4] J.E. Pin, A variety theorem without complementation. Russian Math. (Iz. VUZ) 39 (1995) 74-83.

[5] J. Reiterman, The Birkhoff theorem for finite algebras. Algebra Universalis 14 (1982) 1-10. | Zbl

[6] M.P. Schützenberger, On finite monoids having only trivial subgroups. Inform. and Control 8 (1965) 190-194. | Zbl

[7] H. Straubing, On the logical description of regular languages. in Proc. 5th Latin American Sympos. on Theoretical Informatics (LATIN 2002), edited by S. Rajsbaum, Lecture Notes in Comput. Sci., vol. 2286, Springer, Berlin (2002) 528-538. | Zbl

Cité par Sources :