An efficient algorithm for time separation of events in concurrent systems

The time separation of events (TSE) problem is that of finding the maximum and minimum separation between the times of occurrence of two events in a concurrent system. It has applications in the performance analysis, optimization and verification of concurrent digital systems. This paper introduces an efficient polynomial-time algorithm to give exact bounds on TSE's for choice-free concurrent systems, whose operational semantics obey the max-causality rule. A choice-free concurrent system is modeled as a strongly-connected marked graph, where delays on operations are modeled as bounded intervals with unspecified distributions. While previous approaches handle acyclic systems only, or else require graph unfolding until a steady-state behavior is reached, the proposed approach directly identifies and evaluates the asymptotic steady-state behavior of a cyclic system via a graph-theoretical approach. As a result, the method has significantly lower computational complexity than previously-proposed solutions. A prototype CAD tool has been developed to demonstrate the feasibility and efficacy of our method. A set of experiments have been performed on the tool as well as two existing tools, with noticeable improvement on runtime and accuracy for several examples.