Locality and Centrality: The Variety ZG
Document type :
Article dans une revue scientifique: Article original
Title :
Locality and Centrality: The Variety ZG
Author(s) :
Amarilli, Antoine [Auteur]
Data, Intelligence and Graphs [DIG]
Département Informatique et Réseaux [INFRES]
Paperman, Charles [Auteur]
Inria Lille - Nord Europe
Linking Dynamic Data [LINKS]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Data, Intelligence and Graphs [DIG]
Département Informatique et Réseaux [INFRES]
Paperman, Charles [Auteur]
Inria Lille - Nord Europe
Linking Dynamic Data [LINKS]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Journal title :
Logical Methods in Computer Science
Publisher :
Logical Methods in Computer Science Association
Publication date :
2023-10-18
HAL domain(s) :
Informatique [cs]/Théorie et langage formel [cs.FL]
English abstract : [en]
We study the variety ZG of monoids where the elements that belong to a group are central, i.e., commute with all other elements. We show that ZG is local, that is, the semidirect product ZG * D of ZG by definite semigroups ...
Show more >We study the variety ZG of monoids where the elements that belong to a group are central, i.e., commute with all other elements. We show that ZG is local, that is, the semidirect product ZG * D of ZG by definite semigroups is equal to LZG, the variety of semigroups where all local monoids are in ZG. Our main result is thus: ZG * D = LZG. We prove this result using Straubing's delay theorem, by considering paths in the category of idempotents. In the process, we obtain the characterization ZG = MNil \vee Com, and also characterize the ZG languages, i.e., the languages whose syntactic monoid is in ZG: they are precisely the languages that are finite unions of disjoint shuffles of singleton languages and regular commutative languages.Show less >
Show more >We study the variety ZG of monoids where the elements that belong to a group are central, i.e., commute with all other elements. We show that ZG is local, that is, the semidirect product ZG * D of ZG by definite semigroups is equal to LZG, the variety of semigroups where all local monoids are in ZG. Our main result is thus: ZG * D = LZG. We prove this result using Straubing's delay theorem, by considering paths in the category of idempotents. In the process, we obtain the characterization ZG = MNil \vee Com, and also characterize the ZG languages, i.e., the languages whose syntactic monoid is in ZG: they are precisely the languages that are finite unions of disjoint shuffles of singleton languages and regular commutative languages.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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