  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.
