Abstract

Kleene algebras with tests provide a rigorous framework for equational specification and verification. 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 Kleene algebra without hypotheses is simplified and extended to handle Kleene algebras with tests.

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