A fixpoint semantics for nondeterministic data flow

Abstract

Criteria for adequacy of a data flow semantics are discussed and Kahn's successful semantics for functional (deterministic) data flow is reviewed. Problems arising from nondeterminism are introduced and the paper's approach to overcoming them is introduced. The approach is based on generalizing the notion of input-output relation, essentially to a partially ordered multiset of input-output histories. The Brock-Ackerman anomalies concerning the input-output relation model of nondeterministic data flow are reviewed, and it is indicated how the proposed approach avoids them. A new anomaly is introduced to motivate the use of multisets. A formal theory of asynchronous processes is then developed. The main result is that the operation of forming a process from a network of component processes is associative. This result shows that the approach is not subject to anomalies such as that of Brock and Ackerman.