A metric characterization of fair computations in CCS

Abstract

We address the problem of characterizing fair (infinite) behaviours of concurrent systems as limits of finite approximations. The framework chosen is Milner's Calculus of Communicating Systems. The results can be summarized as follows. On the set FD of all finite derivations in the calculus we define three distances: da, dw, ds. Then the metric completion of (FD,da) yields the space of all derivations, while the completion of (FD,dw), resp. (FD,ds), yields the space of all finite derivations together with all — and only — the weakly, resp. strongly, fair computations (i.e. non-extendable derivations). The results concerning da and dw are a reformulation of previously known ones, while that concerning ds is — we believe — new.