Equational description of pseudovarieties of homomorphisms

Michal Kunc

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

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

Abstract

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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 A C 0 is given.

How to cite

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Kunc, 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

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  1. [1] J. Almeida, Finite Semigroups and Universal Algebra. World Scientific, Singapore (1995). Zbl0844.20039MR1331143
  2. [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. [3] S. Eilenberg, Automata, Languages and Machines. vol. B, Academic Press, New York (1976). Zbl0359.94067MR530383
  4. [4] J.E. Pin, A variety theorem without complementation. Russian Math. (Iz. VUZ) 39 (1995) 74–83. 
  5. [5] J. Reiterman, The Birkhoff theorem for finite algebras. Algebra Universalis 14 (1982) 1–10. Zbl0484.08007
  6. [6] M.P. Schützenberger, On finite monoids having only trivial subgroups. Inform. and Control 8 (1965) 190–194. Zbl0131.02001
  7. [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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