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Kleene Algebra with Observations

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arxiv 1811.10401 v4 pith:PDUAGS22 submitted 2018-11-16 cs.LO cs.FL

Tobias Kappé , Paul Brunet , Jurriaan Rot , Alexandra Silva , Jana Wagemaker , Fabio Zanasi This is my paper · ORCID
classification cs.LOcs.FL
keywords algebrakleeneaxiomsconcurrentobservationsprogramsalgebraicalternative
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Kleene algebra with tests (KAT) is an algebraic framework for reasoning about the control flow of sequential programs. Generalising KAT to reason about concurrent programs is not straightforward, because axioms native to KAT in conjunction with expected axioms for concurrency lead to an anomalous equation. In this paper, we propose Kleene algebra with observations (KAO), a variant of KAT, as an alternative foundation for extending KAT to a concurrent setting. We characterise the free model of KAO, and establish a decision procedure w.r.t. its equational theory.

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