Two implementation relations and the correctness of communicating replicated processes

This paper studies the correctness of distributed systems made up of replicated processes that communicate by message passing. Processes are described within the divergence model of CSP. The notion of correctness introduced is based on a relation that formally expresses the conformance of an implementation process with the target process it is intended to implement. A weak and a strong version of the relation are introduced, aimed at treating acyclic and cyclic process networks respectively. Both allow the study of (total) correctness and may cope with non-deterministic targets and implementations.We then show how a target process may be implemented (in the formal sense introduced) by replicating it in a set of copies, a majority of which is non-faulty.