Modelling and Verification of Communicating Processes in the Event of Interface Difference

We extend our investigation of the notion that a system built of communicating processes is an acceptable implementation of another base or target system, in the case that respective specification and implementation processes have different interfaces and we combine into a single scheme implementation relations previously presented. We also relax significantly the restrictions placed upon target processes. Using this implementation relation scheme, two basic kinds of results are obtained: realisability and compositionality. The former ensures that implementations may be put to good use; in practice, this means that plugging an implementation into an appropriate environment should yield a conventional implementation of the target. The latter requires that a target composed of several connected systems may be implemented by connecting their respective implementations. We then give graph-based representations of the formal structures which we use, develop graph theoretic statements of the implementation relations and finally present algorithms for their automatic verification.