Allegories: decidability and graph homomorphisms

Damien Pous (1, 2) , Valeria Vignudelli (1, 2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 PLUME - Preuves et Langages

Allegories were introduced by Freyd and Scedrov; they form a fragment of Tarski's calculus of relations. We show that their equational theory is decidable by characterising it in terms of a specific class of graph homomorphisms. We actually do so for an extension of allegories which we prove to be conservative, namely allegories with top. This generalisation makes it possible to exploit the correspondence between terms and K4-free graphs, for which isomorphism was known to be finitely axiomatisable.

Mots clés: Graphs; Treewidth; Minors; De- cidability; Homomorphisms; Algebra; Allegories

Domaines: Logique en informatique [cs.LO]

Damien Pous, Valeria Vignudelli. Allegories: decidability and graph homomorphisms. Logic in Computer Science, Jul 2018, Oxford, United Kingdom. ⟨10.1145/3209108.3209172⟩. ⟨hal-01703906v2⟩