We are aiming at a classification of semantical models for Communicating Processes that will enable us to recommend certain models which are just detailed enough for particular applications. But before such an aim can be fully realised, more sophisticated models of processes should be studied.
For example, we have not considered the notion of state so far. This would allow to add assignment and explicit value passing between processes, thus combining sequential programs with Communicating Processes.
It is also important to ensure that the operators satisfy the usual algebraic laws, for example parallel composition should be associative. And the relationship between specification-oriented denotational semantics used here and the operational semantics used in [12,13,16] should be studied. This requires an explicit concept of divergence. In particular, it is interesting to investigate how the criterion P sat S can be derived systematically from the operational semantics. A significant step in this direction has already been made in .
Finally, an explicit syntax for specifications and proof systems for the relation P sat S should be developed. First proposals for such proof systems can be found in [5,9].