Topological rewriting systems applied to standard bases and syntactic algebras

Chenavier, Cyrille

Type de document :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1016/j.jalgebra.2019.12.007

Titre :

Topological rewriting systems applied to standard bases and syntactic algebras

Auteur(s) :

Chenavier, Cyrille [Auteur]
Finite-time control and estimation for distributed systems [VALSE]

Titre de la revue :

Journal of Algebra

Pagination :

410-431

Éditeur :

Elsevier

Date de publication :

2020

ISSN :

0021-8693

Mot(s)-clé(s) en anglais :

topological confluence
standard bases
series representations and syntactic algebras

Discipline(s) HAL :

Informatique [cs]/Calcul formel [cs.SC]
Mathématiques [math]/Anneaux et algèbres [math.RA]

Résumé en anglais : [en]

We introduce topological rewriting systems as a generalisation of abstract rewriting systems, where we replace the set of terms by a topological space. Abstract rewriting systems correspond to topological rewriting systems ...
Lire la suite >We introduce topological rewriting systems as a generalisation of abstract rewriting systems, where we replace the set of terms by a topological space. Abstract rewriting systems correspond to topological rewriting systems for the discrete topology. We introduce the topological confluence property as an approximation of the confluence property. Using a representation of linear topological rewriting systems with continuous reduction operators, we show that the topological confluence property is characterised by lattice operations. Using this characterisation, we show that standard bases induce topologically confluent rewriting systems on formal power series. Finally, we investigate duality for reduction operators that we relate to series representations and syntactic algebras. In particular, we use duality for proving that an algebra is syntactic or not.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Collections :