  In the standard testing theory of DeNicola-Hennessy one process is considered
to be a refinement of another if every test guaranteed by the former is also
guaranteed by the latter. In the domain of web services this has been recast,
with processes viewed as servers and tests as clients. In this way the standard
refinement preorder between servers is determined by their ability to satisfy
clients. But in this setting there is also a natural refinement preorder
between clients, determined by their ability to be satisfied by servers. In
more general settings where there is no distinction between clients and
servers, but all processes are peers, there is a further refinement preorder
based on the mutual satisfaction of peers. We give a uniform account of these
three preorders. In particular we give two characterisations. The first is
behavioural, in terms of traces and ready sets. The second, for finite
processes, is equational.
