An Algorithm for Exact Bounds on the Time Separation of Events in Concurrent Systems 1

Determining the time separation of events is a fundamental problem in the analysis, synthesis, andoptimization of concurrent systems. Applications range from logic optimization of asynchronousdigital circuits to evaluation of execution times of programs for real-time systems. We present ane cient algorithm to nd exact (tight) bounds on the separation time of events in an arbitrary pro-cess graph without conditional behavior. This result is more general than the methods presented inseveral previously published papers as it handles cyclic graphs and yields the tightest possible boundson event separations. The algorithm is based on a functional decomposition technique that permitsthe implicit evaluation of an in nitely unfolded process graph. Examples are presented that demon-strate the utility and e ciency of the solution. The algorithm will form a basis for exploration oftiming-constrained synthesis techniques.