Concurrent Kleene Algebra of Partial Strings

Concurrent Kleene Algebra (CKA) by Tony Hoare et al. is an algebraic structure that unifies the laws of concurrent programming. The unifying power of CKA rests largely on the so called exchange law that describes how concurrent and sequential composition operators can be interchanged. This paper extends Gischer's pomsets model with least fixed point operators thereby constructing a partial order model of CKA including its exchange law. The existence of such a model is particularly relevant when we want to disprove properties about concurrent programs with loops thereby possibly facilitating the analysis of real world bugs.