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Kleene Algebra with Observations Kappé, Tobias Brunet, Paul Rot, Jurriaan Silva, Alexandra Wagemaker, Jana Zanasi, Fabio Concurrent Kleene algebra Kleene algebra with tests free model axiomatisation decision procedure 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Tobias Kappé and Paul Brunet and Jurriaan Rot and Alexandra Silva and Jana Wagemaker and Fabio Zanasi 2019 Is Part Of LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2019.41 urn:nbn:de:0030-drops-109431 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.41 eng https://creativecommons.org/licenses/by/3.0/legalcode