# Equational description of pseudovarieties of homomorphisms

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2003)

- Volume: 37, Issue: 3, page 243-254
- ISSN: 0988-3754

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topKunc, Michal. "Equational description of pseudovarieties of homomorphisms." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 37.3 (2003): 243-254. <http://eudml.org/doc/246082>.

@article{Kunc2003,

abstract = {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.},

author = {Kunc, Michal},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {pseudovariety; pseudoidentity; implicit operation; variety of regular languages; syntactic homomorphism; pseudovarieties; bases of pseudoidentities; implicit operations; varieties of regular languages; syntactic homomorphisms},

language = {eng},

number = {3},

pages = {243-254},

publisher = {EDP-Sciences},

title = {Equational description of pseudovarieties of homomorphisms},

url = {http://eudml.org/doc/246082},

volume = {37},

year = {2003},

}

TY - JOUR

AU - Kunc, Michal

TI - Equational description of pseudovarieties of homomorphisms

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2003

PB - EDP-Sciences

VL - 37

IS - 3

SP - 243

EP - 254

AB - 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.

LA - eng

KW - pseudovariety; pseudoidentity; implicit operation; variety of regular languages; syntactic homomorphism; pseudovarieties; bases of pseudoidentities; implicit operations; varieties of regular languages; syntactic homomorphisms

UR - http://eudml.org/doc/246082

ER -

## References

top- [1] J. Almeida, Finite Semigroups and Universal Algebra. World Scientific, Singapore (1995). Zbl0844.20039MR1331143
- [2] D. Mix Barrington, K. Compton, H. Straubing and D. Thérien, Regular languages in $N{C}^{1}$. J. Comput. System Sci. 44 (1992) 478–499. Zbl0757.68057
- [3] S. Eilenberg, Automata, Languages and Machines. vol. B, Academic Press, New York (1976). Zbl0359.94067MR530383
- [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. Zbl0484.08007
- [6] M.P. Schützenberger, On finite monoids having only trivial subgroups. Inform. and Control 8 (1965) 190–194. Zbl0131.02001
- [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. Zbl1059.03034

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