Application of Church-Rosser properties to increase the parallelism and efficiency of algorithms

Abstract

Besides the Church-Rosser property (here called full), three other commutativity properties of transformations (the mutual, inner and strong Church-Rosser property) are also defined, which are less restrictive than the first. These properties are used to decide:1)when and how the rules belonging to the same loop can be applied in parallel2)when a rule can be eliminated3)when a rule can be removed from a loop. The transformations of algorithms our methods yield are particularly significant in that they depend only on the semantics of the original algorithm, i.e., the input-output relations. To perform the parallelization (point 1), a new model of structured programming language is used, sufficiently general to ensure that every program can be automatically translated into a structured one.