Commutative images of rational languages and the abelian kernel of a monoid
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 5, pp. 419-435.

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.

Classification : 20M35,  68Q99
Mots clés : rational language, semilinear set, profinite topology, finite monoid
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     author = {Delgado, Manuel},
     title = {Commutative images of rational languages and the abelian kernel of a monoid},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {419--435},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {5},
     year = {2001},
     zbl = {1028.68087},
     mrnumber = {1908864},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2001__35_5_419_0/}
}
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Delgado, Manuel. Commutative images of rational languages and the abelian kernel of a monoid. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 5, pp. 419-435. http://www.numdam.org/item/ITA_2001__35_5_419_0/

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