A Tactic for Deciding Kleene Algebras

Thomas Braibant (1) , Damien Pous (1)

1 SARDES - System architecture for reflective distributed computing environments

We present a Coq reflexive tactic for deciding equalities or inequalities in Kleene algebras. This tactic is part of a larger pro ject, whose aim is to provide tools for reasoning about binary relations in Coq: binary relations form a Kleene algebra, where the star operation is the reflexive transitive closure. Our tactic relies on an initiality theorem, whose proof goes by replaying finite automata algorithms in an algebraic way, using matrices.

Mots clés: Coq; reflexive tactic; Kleene algebra; finite automata; decision procedure

Domaines: Logiciel mathématique [cs.MS]; Mathématique discrète [cs.DM]

Thomas Braibant, Damien Pous. A Tactic for Deciding Kleene Algebras. 2009. ⟨hal-00383070v2⟩