On "Axiomatising Finite Concurrent Processes"

In his pioneering paper [Axiomatising finite concurrent processes, SIAM J. Comput., 17 (1988), pp. 997--1017], Hennessy gave complete axiomatizations of Milner's observational congruence and of t-observational congruence which made use of an auxiliary operation to axiomatize parallel composition. Unfortunately, those axiomatizations turn out to be flawed due to the subtle interplay between Hennessy's auxiliary parallel operator and synchronization. The aim of this paper is to present correct versions of the equational characterizations given in Hennessy's paper. Some of the problems which arise in giving operational semantics to the auxiliary operators used by Bergstra and Klop and Hennessy in the theory of congruences like Milner's observational congruence are also discussed.