ACM Transactions on Computational Logic (TOCL)
The theory of interactive generalized semi-Markov processes
Theoretical Computer Science
Discrete time generative-reactive probabilistic processes with different advancing speeds
Theoretical Computer Science
Mathematical Structures in Computer Science
CCS with Hennessy's merge has no finite-equational axiomatization
Theoretical Computer Science - Expressiveness in concurrency
The saga of the axiomatization of parallel composition
CONCUR'07 Proceedings of the 18th international conference on Concurrency Theory
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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.