Commutative images of rational languages and the Abelian kernel of a monoid

Manuel Delgado

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 35, Issue: 5, page 419-435
  • ISSN: 0988-3754

Abstract

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Natural algorithms to compute rational expressions for recognizable languages, even those which work well in practice, may produce very long expressions. So, aiming towards the computation of the commutative image of a recognizable language, one should avoid passing through an expression produced this way. We modify here one of those algorithms in order to compute directly a semilinear expression for the commutative image of a recognizable language. We also give a second modification of the algorithm which allows the direct computation of the closure in the profinite topology of the commutative image. As an application, we give a modification of an algorithm for computing the Abelian kernel of a finite monoid obtained by the author in 1998 which is much more efficient in practice.

How to cite

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Delgado, Manuel. "Commutative images of rational languages and the Abelian kernel of a monoid." RAIRO - Theoretical Informatics and Applications 35.5 (2010): 419-435. <http://eudml.org/doc/222037>.

@article{Delgado2010,
abstract = { Natural algorithms to compute rational expressions for recognizable languages, even those which work well in practice, may produce very long expressions. So, aiming towards the computation of the commutative image of a recognizable language, one should avoid passing through an expression produced this way. We modify here one of those algorithms in order to compute directly a semilinear expression for the commutative image of a recognizable language. We also give a second modification of the algorithm which allows the direct computation of the closure in the profinite topology of the commutative image. As an application, we give a modification of an algorithm for computing the Abelian kernel of a finite monoid obtained by the author in 1998 which is much more efficient in practice. },
author = {Delgado, Manuel},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Rational language; semilinear set; profinite topology; finite monoid.; algorithms; semilinear expressions; commutative images; rational languages; rational expressions; finite monoids},
language = {eng},
month = {3},
number = {5},
pages = {419-435},
publisher = {EDP Sciences},
title = {Commutative images of rational languages and the Abelian kernel of a monoid},
url = {http://eudml.org/doc/222037},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Delgado, Manuel
TI - Commutative images of rational languages and the Abelian kernel of a monoid
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 5
SP - 419
EP - 435
AB - Natural algorithms to compute rational expressions for recognizable languages, even those which work well in practice, may produce very long expressions. So, aiming towards the computation of the commutative image of a recognizable language, one should avoid passing through an expression produced this way. We modify here one of those algorithms in order to compute directly a semilinear expression for the commutative image of a recognizable language. We also give a second modification of the algorithm which allows the direct computation of the closure in the profinite topology of the commutative image. As an application, we give a modification of an algorithm for computing the Abelian kernel of a finite monoid obtained by the author in 1998 which is much more efficient in practice.
LA - eng
KW - Rational language; semilinear set; profinite topology; finite monoid.; algorithms; semilinear expressions; commutative images; rational languages; rational expressions; finite monoids
UR - http://eudml.org/doc/222037
ER -

References

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