Write a Blog >>

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.

Conference Day
Wed 22 Jan

Displayed time zone: Saskatchewan, Central America change

15:35 - 16:40
Automatic Differentiation / Kleene AlgebraResearch Papers at Ile de France II (IDF II)
Chair(s): Lars BirkedalAarhus University
15:35
21m
Talk
A Simple Differentiable Programming Language
Research Papers
Link to publication DOI Media Attached
15:56
21m
Talk
Backpropagation in the Simply Typed Lambda-calculus with Linear Negation
Research Papers
Aloïs BrunelDeepomatic, Damiano MazzaCNRS, Michele PaganiIRIF - Université de Paris
Link to publication DOI Media Attached File Attached
16:18
21m
Talk
Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear TimeDistinguished Paper
Research Papers
Steffen SmolkaCornell University, Nate FosterCornell University, Justin HsuUniversity of Wisconsin-Madison, USA, Tobias KappéUniversity College London, Dexter KozenCornell University, Alexandra SilvaUniversity College London
Link to publication DOI Media Attached