Comparative analysis of the notions of equivalence for process specifications

Several notions for semantic equivalence of process specifications have been developed. It has widespread applicability in verification and testing. Each notion has its criteria for checking equivalence. We develop a comparative analysis of these notions where we investigate their limitations and their adequacies to meet the requirements of conformance testing and verification. Then, we order the various notions according to their distinguishing powers. We also develop generalizations of failure weak observation, and strong observation notions to ratify shortcomings.