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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.

Wed 22 Jan
Times are displayed in time zone: (GMT-06:00) Saskatchewan, Central America change

15:35 - 16:40: Research Papers - Automatic Differentiation / Kleene Algebra at Ile de France II (IDF II)
Chair(s): Lars BirkedalAarhus University
POPL-2020-Research-Papers15:35 - 15:56
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POPL-2020-Research-Papers15:56 - 16:18
Aloïs BrunelDeepomatic, Damiano MazzaCNRS, Michele PaganiIRIF - Université de Paris
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POPL-2020-Research-Papers16:18 - 16:40
Steffen SmolkaCornell University, Nate FosterCornell University, Justin HsuUniversity of Wisconsin-Madison, USA, Tobias KappéUniversity College London, Dexter KozenCornell University, Alexandra SilvaUniversity College London
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