Combinatorics and geometry of consistent cuts : Application to concurrency theory

We define a concurrency measure of a distributed computation which is based on the number μ of its consistent cuts. We prove that counting consistent cuts takes into account the non-transitivity of the concurrency relation. Besides this combinatorial study, we give a geometric interpretation of μ using the clock designed by Fidge and Mattern for characterizing concurrency between two events. This geometric approach shows how much this clock is also a powerful tool for assessing the global concurrency. Moreover it provides a geometric picture of the concurrency phenomena in a distributed computation.