Reversible Kleene lattices

Paul Brunet (1)

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

We investigate the equational theory of reversible Kleene lattices, that is 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 representation of this algebra. We then provide an automaton model to compare representations. These automata are adapted from Petri automata, which we introduced with Pous in 2015 to tackle a similar problem for algebras of binary relations. This allows us to show that testing the validity of equations in this algebra is decidable, and in fact ExpSpace-complete.

Mots clés: Automata; Kleene algebra; Petri nets; Decidability; Complexity; Formal languages and automata; Lattice Theory

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

Paul Brunet. Reversible Kleene lattices. 42nd International Symposium on Mathematical Foundations of Computer Science, Kim G. Larsen, Aug 2017, Aalborg, Denmark. pp.66:1--66:14, ⟨10.4230/LIPIcs.MFCS.2017.66⟩. ⟨hal-01474911v3⟩