Denotational semantics of nets with nondeterminism

Abstract

We define a topological framework for streams of traces. With this approach Kahn's method generalizes to nets with bounded nondeterminism. We consider fixpoints of multivalued functions. We have a standard fixed point theorem, which can be used to model feed back loops. These fixed points can also be obtained by iteration. We give a general syntax of nets and see how we can analyze them in our streamframework. We show how to avoid the Brock-Ackerman and Keller anomalies. We are able to model the fair merge, which is a continuous function in our framework, and delay along lines. We prove a lemma that says that the order in which we connect nodes in our networks does not matter. If we have nets with nodes with unbounded nondeterminism, we can still use these fixpoints, but we do lose in our topological framework our iteration theorem.

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