Process algebra needs proof methodology

This note contains the contribution to the Concurrency Column of the EATCS Bulletin of February, 2004. It indicates on the one hand what the strengths of process algebras are, and on the other hand mentions a major shortcoming. Using elementary process algebra it is hard to prove correctness of complex distributed algorithms, protocols and systems. We encountered this when providing a process algebraic proof that the sliding window protocol of buffer size n is behaviourally equivalent to a bounded queue of size 2n. We used and developed notions such as invariants, cones and foci and coordinate transformations together providing the means to give a precise and insightful proof of the correctness of the sliding window protocol. These and other techniques are all shortly addressed in this note. The main message however is that in order to make process algebra the universal tool for the study of correct system behaviour (for which we believe it is one of the best candidates) much more of effective proof techniques need to be developed. Why is process algebra exciting? An early paper by Milner in 1973 [41] gave a clear motivation for process algebra. He gave three reasons to design a process algebra. • All (computer) systems interact with their environment. For most of these, this is their primary ‘raison d’être’. So, within computer science, we need a formalism in which interaction is a primary citizen. • Nondeterminism is important. The actual behaviour of a computer system is influenced by factors that we do not understand or are too complex to include in a comprehensive description. For instance the exact moments at which interrupts