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

翻译：Kleene 代数与 Tests (GKAT) 是 Kleene 代数与 Tests (KAT) 的一块碎片, 最近引入了 Kleene 代数与 Tests (KAT ), 以有效解释紧急程序。 与 KAT 相比, GKAT 没有代数异形化, 而是依赖Salomaa 的同义化Kleene 代数的类比。 在本文中, 我们展示了代数异形化, 并证明以无跳程序形式出现的大型 GKAT 碎片有两种完整性结果 。