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Guarded Kleene algebra with tests: verification of uninterpreted programs in nearly linear time

Smolka, S; Foster, N; Hsu, J; Kappé, T; Kozen, D; Silva, A; (2019) Guarded Kleene algebra with tests: verification of uninterpreted programs in nearly linear time. Proceedings of the ACM on Programming Languages , 4 (POPL) , Article 61. 10.1145/3371129. Green open access

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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 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.

Type: Article
Title: Guarded Kleene algebra with tests: verification of uninterpreted programs in nearly linear time
Open access status: An open access version is available from UCL Discovery
DOI: 10.1145/3371129
Publisher version: https://doi.org/10.1145/3371129
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10090950
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