On the expressiveness of infinite behavior and name scoping in process calculi

In the literature there arc several CCS-like process calculi differing in the constructs for the specification of infinite behavior and in the scoping rules for channel names. In this paper we study various representatives of these calculi based upon both their relative expressiveness and the decidability of divergence. We regard any two calculi as being equally expressive iff for every process in each calculus, there exists a weakly bisimilar process in the other. By providing weak bisimilarity preserving mappings among the various variants, we show that in the context of relabeling-free and finite summation calculi: (1) CCS with parameterless (or constant) definitions is equally expressive to the variant with parametric definitions. (2) The CCS variant with replication is equally expressive to that with recursive expressions and static scoping. We also state that the divergence problem is undecidable for the calculi in (1) but decidable for those in (2). We obtain this from (un)decidability results by Busi, Gabbrielli and Zavattaro, and by showing the relevant mappings to be computable and to preserve divergence and its negation. From (1) and the well-known fact that parametric definitions can replace injective relabelings, we show that injective relabelings are redundant (i.e., derived) in CCS (which has constant definitions only).