Topological rewriting systems applied to standard bases and syntactic algebras

Chenavier, Cyrille

Document type :

Article dans une revue scientifique

DOI :

10.1016/j.jalgebra.2019.12.007

Title :

Topological rewriting systems applied to standard bases and syntactic algebras

Author(s) :

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

Journal title :

Journal of Algebra

Pages :

410-431

Publisher :

Elsevier

Publication date :

2020

ISSN :

0021-8693

English keyword(s) :

topological confluence
standard bases
series representations and syntactic algebras

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL

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http://arxiv.org/pdf/1907.06394
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https://hal.archives-ouvertes.fr/hal-02355020v2/document
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https://hal.archives-ouvertes.fr/hal-02355020v2/document
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