The Algebra of Languages with Intersection and Converse

Paul Brunet (1)

1 UCL-CS - Department of Computer science [University College of London]

We consider the equational theory generated by all algebras of languages with the regular operations (union, composition and Kleene star), together with the intersection and mirror image. Building on results by Andréka, Mikulás and Németi from 2011, we construct the free model for this algebra. We then adapt the notion of Petri automata, which we introduced with Pous in 2015 to tackle a similar problem for algebras of binary relations, to provide a procedure to decide equations over this signature. This allows us to show that testing the validity of equations in this algebra is ExpSpace-complete.

Mots clés: Kleene algebra; Automata; Petri nets; Decidability; Complexity

Domaines: Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]

Paul Brunet. The Algebra of Languages with Intersection and Converse. 2017. ⟨hal-01474911v1⟩