Kleene algebra with tests: Completeness and decidability [chapter]

Dexter Kozen, Frederick Smith
1997 Lecture Notes in Computer Science  
Kleene algebras with tests provide a rigorous framework for equational speci cation and veri cation. They have been used successfully in basic safety analysis, source-to-source program transformation, and concurrency control. We prove the completeness of the equational theory of Kleene algebra with tests and *-continuous Kleene algebra with tests over language-theoretic and relational models. We also show decidability. Cohen's reduction of Kleene algebra with hypotheses of the form r = 0 to
more » ... ne algebra without hypotheses is simpli ed and extended to handle Kleene algebras with tests. Proof. We rst de ne a congruence on the set T ;B of terms in the language of Kleene algebra with tests. For s; t 2 T ;B , de ne s t def () s + uru = t + uru : The relation is an equivalence relation. We show that it is a *-continuous Kleene algebra congruence.
doi:10.1007/3-540-63172-0_43 fatcat:f2ztqth6angwjisiycrpn5f57u