On Decidability of Concurrent Kleene Algebra

Paul Brunet (1, 2) , Damien Pous (1, 2) , Georg Struth (3)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 PLUME - Preuves et Langages
3 Department of Computer Science [Sheffield]

Concurrent Kleene algebras support equational reasoning about computing systems with concurrent behaviours. Their natural semantics is given by series(parallel) rational pomset languages, a standard true concurrency semantics, which is often associated with processes of Petri nets. We use constructions on Petri nets to provide two decision procedures for such pomset languages motivated by the equational and the refinement theory of concurrent Kleene algebra. The contribution to the first problem lies in a much simpler algorithm and an ExpSpace complexity bound. Decidability of the second, more interesting problem is new and, in fact, ExpSpace-complete.

Mots clés: Concurrent Kleene algebra; Series-parallel pomsets; Petri nets

Domaines: Informatique [cs]

Paul Brunet, Damien Pous, Georg Struth. On Decidability of Concurrent Kleene Algebra. CONCUR, Sep 2017, Berlin, Germany. ⟨hal-01558108⟩