Kleene Algebra with Observations
conference paper, in CONCUR 2019
Kleene algebra with tests (KAT) gives an algebraic perspective on reasoning about the control flow of sequential programs. However, when generalising KAT to reason about concurrent programs, axioms native to KAT in conjunction with axioms for reasoning about concurrency lead to a bizarre 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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