Alexandra Silva

"Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs "

( MPI-SWS talk in Kooperation mit dem Fachbereich Informatik)

In Nearly Linear Time Guarded Kleene Algebra with Tests (GKAT) is a variation on Kleene Algebra with Tests (KAT) that arises by restricting the union (+) and iteration (*) operations from KAT to predicate-guarded versions. We develop the (co)algebraic theory of GKAT and show how it can be efficiently used to reason about imperative programs. In contrast to KAT, whose equational theory is PSPACE-complete, we show that the equational theory of GKAT is (almost) linear time. We also provide a full Kleene theorem and prove completeness for an analogue of Salomaa’s axiomatization of Kleene Algebra. We will also discuss how this result has practical implications in the verification of programs, with examples from network and probabilistic programming. If time permits, I will also talk about recent work on extending GKAT with probabilistic constructs.

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