Parallel Program Schemata and Maximal Parallelism I. Fundamental Results

Abstract

The phenomenon of maximal parallelism is investigated in the framework of a class of parallel program schemata. Part I presents the basic properties of this model. Two types of equivalence relation on computations are presented, to each of which there corresponds a concept of determinacy and equivalence for schemata. The correspondence between these relations is shown and related to other properties of schemata. Then the concept of maximal parallelism using one of the relations as a basis is investigated. A partial order on schemata is defined which relates their inherent parallelism. The results presented are especially concerned with schemata which are maximal with respect to this order, i.e. maximally parallel schemata. Several other properties are presented and shown to be equivalent to the property of maximal parallelism. It is then shown that for any schema of a certain class, there exists a unique equivalent schema which is maximally parallel. We call such a schema the “closure” of the original schema.