A Kahn Principle for Networks of Nonmonotonic Real-time Processes

We show that the input-output function computed by a network of asynchronous real-time processes is denoted by the unique xed point of a Scott continuous functional even though the network or its components may compute a discontinuous function. This extends a well-known principle of Kahn [Kahn, 1974] to an important class of parallel systems that has resisted the traditional xed point approach. We present a fully abstract order-theoretic denotational semantics for networks of asynchronous real-time processes. The time-sensitive nature of the component processes allows them to compute functions which are not Scott continuous, nor even monotonic, on the domain of timed message streams ordered by the usual pre x relation. Because of the discontinuous behavior of the components, the characterization of networks with nonmonotonic processes as xed points of continuous functionals (the standard approach of denotational semantics, applied to untimed networks of monotonic processes by Kahn in 1974) has been a much-sought but unattained goal. We show that the function computed by any real-time network, even those containing nonmonotonic processes, is identical to the unique xed point of a continuous network functional whose construction is original.