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Commutative images ofrational languages and the Abelian kernel of a monoid

Published online by Cambridge University Press:  15 August 2002

Manuel Delgado
Manuel Delgado*
Affiliation:
Centro de Matemática, Universidade do Porto P. Gomes Teixeira, 4099-002 Porto, Portugal; mdelgado@fc.up.pt.
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Abstract

Natural algorithms to compute rational expressions for recognizablelanguages, even those which work well in practice, may produce very longexpressions. So, aiming towards the computation of the commutative image of arecognizable language, one should avoid passing through an expressionproduced this way.We modify here one of those algorithms in order to compute directly a semilinear expression for the commutative imageof a recognizable language. We also give a secondmodification of the algorithm which allows the direct computation of theclosure in the profinite topology of the commutative image. As anapplication, we give a modification of an algorithm for computing the Abelian kernel of a finite monoid obtainedby the author in 1998 which is much more efficient in practice.

Keywords

Rational languagesemilinear setprofinite topologyfinite monoid.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 5 , September 2001 , pp. 419 - 435
Copyright
© EDP Sciences, 2001

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