Concurrent Kleene Algebra (CKA) was introduced by Hoare, Moeller, Struth and
Wehrman in 2009 as a framework to reason about concurrent programs. We prove
that the axioms for CKA with bounded parallelism are complete for the semantics
proposed in the original paper; consequently, these semantics are the free
model for this fragment. This result settles a conjecture of Hoare and
collaborators. Moreover, the techniques developed along the way are reusable;
in particular, they allow us to establish pomset automata as an operational
model for CKA.Comment: Version 2 includes an overview section that outlines the completeness
proof, as well as some extra discussion of the interpolation lemma. It also
includes better typography and a number of minor fixes. Version 3
incorporates the changes by comments from the anonymous referees at ESOP.
Among other things, these include a worked example of computing the syntactic
closure by han
