Equational reasoning about nondeterministic processes

A deterministic message-communicating process can be characterised by a “continuous” functionf which describes the relationship between the inputs and the outputs of the process. The operational behaviour of a network of deterministic processes can be deduced from the least fixpoint of a functiong, whereg is obtained from the functions that characterise the component processes of the network. We show in this paper that a nondeter-ministic process can be characterised by a “description” consisting of a pair of functions. The behaviour of a network consisting of such processes can be obtained from the “smooth” solutions of the descriptions characterising its component processes. The notion of smooth solution is a generalisation of least fixpoint. Descriptions enjoy the crucial property that a variable may be replaced by its definition.