Specification of Required Non-determinism

We present an approach to the speci cation of required external non-determinism: the willingness of a component to respond to a number of external action requests, using a language, COMMUNITY, which provides both permission and willingness guards on actions. This enables a program-like declaration of required non-determinism, in contrast to the use of a branching-time temporal logic. We give a de nition of parallel composition for this language, and show that re nement is compositional with respect to parallel composition. We use the concepts developed for COMMUNITY to identify extensions to the B and VDM model-based speci cation languages to incorporate speci cation of required non-determinism. In particular, we show that preconditions may be considered as a form of willingness guard, separating concerns of acceptance and termination, once module contracts are re-interpreted in a way suitable for a concurrent environment.