Some results on 𝒞 -varieties

Jean-Éric Pin; Howard Straubing

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2005)

  • Volume: 39, Issue: 1, page 239-262
  • ISSN: 0988-3754

Abstract

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In an earlier paper, the second author generalized Eilenberg’s variety theory by establishing a basic correspondence between certain classes of monoid morphisms and families of regular languages. We extend this theory in several directions. First, we prove a version of Reiterman’s theorem concerning the definition of varieties by identities, and illustrate this result by describing the identities associated with languages of the form ( a 1 a 2 ⋯ a k ) + , where a 1 , ... , a k are distinct letters. Next, we generalize the notions of Mal’cev product, positive varieties, and polynomial closure. Our results not only extend those already known, but permit a unified approach of different cases that previously required separate treatment.

How to cite

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Pin, Jean-Éric, and Straubing, Howard. "Some results on $\mathcal {C}$-varieties." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 39.1 (2005): 239-262. <http://eudml.org/doc/244768>.

@article{Pin2005,
abstract = {In an earlier paper, the second author generalized Eilenberg’s variety theory by establishing a basic correspondence between certain classes of monoid morphisms and families of regular languages. We extend this theory in several directions. First, we prove a version of Reiterman’s theorem concerning the definition of varieties by identities, and illustrate this result by describing the identities associated with languages of the form $(a_1a_2\cdots a_k)^+$, where $a_1,\ldots ,a_k$ are distinct letters. Next, we generalize the notions of Mal’cev product, positive varieties, and polynomial closure. Our results not only extend those already known, but permit a unified approach of different cases that previously required separate treatment.},
author = {Pin, Jean-Éric, Straubing, Howard},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {monoid morphisms; varieties; regular languages; finitely generated free monoids; length-preserving morphisms; finite monoids; stamps; identities},
language = {eng},
number = {1},
pages = {239-262},
publisher = {EDP-Sciences},
title = {Some results on $\mathcal \{C\}$-varieties},
url = {http://eudml.org/doc/244768},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Pin, Jean-Éric
AU - Straubing, Howard
TI - Some results on $\mathcal {C}$-varieties
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 1
SP - 239
EP - 262
AB - In an earlier paper, the second author generalized Eilenberg’s variety theory by establishing a basic correspondence between certain classes of monoid morphisms and families of regular languages. We extend this theory in several directions. First, we prove a version of Reiterman’s theorem concerning the definition of varieties by identities, and illustrate this result by describing the identities associated with languages of the form $(a_1a_2\cdots a_k)^+$, where $a_1,\ldots ,a_k$ are distinct letters. Next, we generalize the notions of Mal’cev product, positive varieties, and polynomial closure. Our results not only extend those already known, but permit a unified approach of different cases that previously required separate treatment.
LA - eng
KW - monoid morphisms; varieties; regular languages; finitely generated free monoids; length-preserving morphisms; finite monoids; stamps; identities
UR - http://eudml.org/doc/244768
ER -

References

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  15. [15] I. Simon, Hierarchies of Events with Dot-Depth One. Ph.D. Thesis, University of Waterloo, Waterloo, Ontario, Canada (1972). 
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  18. [18] H. Straubing, On logical descriptions of regular languages, in LATIN 2002. Springer, Berlin, Lect. Notes Comput. Sci. 2286 (2002) 528–538. Zbl1059.03034

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