The parallel composition of processes

We have been arguing for some years (really since the appearance of our paper on Span(Graph) in AMAST 97) that the usual operation in process algebras called parallel is a wrong direction, not describing explicitly the media of communication. I talked about this in Calais at CT 2008, saying on the first slide that our work "hasn’t as yet been used by the concurrency community but it should be".

Well it seems that at last someone from that community is listening.

After the talk Pawel Sobocinski came up to me saying he had an idea of a process algebra like Span(Graph). We had actually produced such a thing, but rather half-heartedly, to try to communicate with process algebra people. But Pawel is now developing a full-blown process algebra with communication like Span(Graph).

It is interesting that Pawel, in his second year at University in Sydney, did a vacation project with me on Span(Graph) and attended the 1997 AMAST meeting.

His process algebra does not incorporate the full sequential operations of Cospan which we introduced in the paper "P. Katis, N. Sabadini, R.F.C. Walters, A formalisation of the IWIM Model. in: Proc. COORDINATION 2000,(Eds.) Porto A., Roman G.-C., LNCS 1906:267-283, Springer Verlag, 2000".

We became involved in thinking about Coordination through visits to Como by Farhad Arbab. Our paper showed how to give an abstraction of his IWIM model in CospanSpan(Graph) which had however the advantage of a compositional theory of connectors, not a feature of Manifold. We criticized Manifold for this defect to Farhad and I think this had an influence on his new coordination language Reo.