Kleene Algebra with Tests: Completeness and Decidability
Kozen, Dexter; Smith, Frederick
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.
computer science; technical report
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