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Guarded Kleene Algebra with Tests (GKAT) is a fragment of Kleene Algebra withTests (KAT) that was recently introduced to reason efficiently about imperativeprograms. In contrast to KAT, GKAT does not have an algebraic axiomatization,but relies on an analogue of Salomaa's axiomatization of Kleene Algebra. Inthis paper, we present an algebraic axiomatization and prove two completenessresults for a large fragment of GKAT consisting of skip-free programs.

A Complete Inference System for Skip-free Guarded Kleene Algebra with Tests