Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear Time
Abstract
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 predicateguarded 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 PSPACEcomplete, 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2019
 arXiv:
 arXiv:1907.05920
 Bibcode:
 2019arXiv190705920S
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Programming Languages
 EPrint:
 Extended version with appendix