Kleene Algebra with Dynamic Tests: Completeness and Complexity

We study versions of Kleene algebra with dynamic tests, that is, extensions of Kleene algebra with domain and antidomain operators. We show that Kleene algebras with tests and Propositional dynamic logic correspond to special cases of the dynamic test framework. In particular, we establish completeness results with respect to relational models and guarded-language models, and we show that two prominent classes of Kleene algebras with dynamic tests have an EXPTIME-complete equational theory.