Completeness for Identity-free Kleene Lattices

Amina Doumane (1, 2) , Damien Pous (1, 2)

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

We provide a finite set of axioms for identity-free Kleene lattices, which we prove sound and complete for the equational theory of their relational models. Our proof builds on the completeness theorem for Kleene algebra, and on a novel automata construction that makes it possible to extract axiomatic proofs using a Kleene-like algorithm.

Mots clés: Graph languages; Axiomatisation; Kleene theorem; Petri Automata

Domaines: Logique en informatique [cs.LO]

Amina Doumane, Damien Pous. Completeness for Identity-free Kleene Lattices. CONCUR, Sep 2018, Beijing, China. ⟨10.4230/LIPIcs.CONCUR.2018.18⟩. ⟨hal-01780845v2⟩