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Kleene algebra (KA) is the algebra of regular events. Familiar examples ofKleene algebras include regular sets, relational algebras, and trace algebras.A Kleene algebra with tests (KAT) is a Kleene algebra with an embedded Booleansubalgebra. The addition of tests allows one to encode {\tt while} programs asKAT terms, thus the equational theory of KAT can express (propositional)program equivalence. More complicated statements about programs can beexpressed in the Hoare theory of KAT, which suffices to encode PropositionalHoare Logic.  That the equational theory of KAT reduces to the equational theory of KA hasbeen shown by Cohen et al. Unfortunately, their reduction involves anexponential blowup in the size of the terms involved. Here we give an alternatefeasible reduction.

Feasibly Reducing KAT Equations to KA Equations