Galois Connections for Patterns: An Algebra of Labelled Graphs - Université Toulouse III - Paul Sabatier - Toulouse INP Accéder directement au contenu
Communication Dans Un Congrès Année : 2021

Galois Connections for Patterns: An Algebra of Labelled Graphs

Résumé

A pattern is a generic instance of a binary constraint satisfaction problem (CSP) in which the compatibility of certain pairs of variable-value assignments may be unspecified. The notion of forbidden pattern has led to the discovery of several novel tractable classes for the CSP. However, for this field to come of age it is time for a theoretical study of the algebra of patterns. We present a Galois connection between lattices composed of sets of forbidden patterns and sets of generic instances, and investigate its consequences. We then extend patterns to augmented patterns and exhibit a similar Galois connection. Augmented patterns are a more powerful language than flat (i.e. nonaugmented) patterns, as we demonstrate by showing that, for any k ≥ 1, instances with tree-width bounded by k cannot be specified by forbidding a finite set of flat patterns but can be specified by a finite set of augmented patterns. A single finite set of augmented patterns can also describe the class of instances such that each instance has a weak nearunanimity polymorphism of arity k (thus covering all tractable language classes).We investigate the power of forbidding augmented patterns and discuss their potential for describing new tractable classes.
Fichier principal
Vignette du fichier
Cohen2021_Chapter_GaloisConnectionsForPatternsAn.pdf (698.94 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03311388 , version 1 (31-07-2021)

Licence

Paternité

Identifiants

Citer

David A Cohen, Martin Cooper, Peter G Jeavons, Stanislav Živný. Galois Connections for Patterns: An Algebra of Labelled Graphs. 6th International Workshop on Graph Structures for Knowledge Representation and Reasoning (GKR 2020), Sep 2020, en ligne, France. pp.125 - 150, ⟨10.1007/978-3-030-72308-8_9⟩. ⟨hal-03311388⟩
31 Consultations
38 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More