Completeness for Identity-free Kleene Lattices

Amina Doumane (1) , Damien Pous (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme

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: Axiomatisation; Graph languages; Petri Automata; Kleene theorem

Domaines: Logique en informatique [cs.LO]

Amina Doumane, Damien Pous. Completeness for Identity-free Kleene Lattices. 2018. ⟨hal-01780845v1⟩