Duality: an Architecture Independent Design Model for Parallel Systems Based on Partial Order Semantics

This paper introduces DUALITY, a design model that provides a more structured style of parallel programming and reenes causal-ity from concurrency. We investigate semantic and syntactic transformations that support identifying the structure of a parallel program, as the basis for reducing the design complexity. The initial focus is on specii-cation and correctness, then gradually adding architectural details and nally addressing eeciency. A parallel program is viewed as a Meta-Program-the result of causally composing an architecture-independent algorithm-the speciication, with an architecture-dependent program-the mapping. This approach supports the derivation of eecient parallel implementations from program speciications. Consequently, transparent and architecture-independent speciications can be transformed into forms that match particular target architectures. Correctness of the implementation is inferred from correctness of the speciication, by gradually imposing temporal and causal order and by transforming any property of the speciication into a property of the parallel program. DUALITY relates data and process parallelism and aims to reuse design knowledge from sequential patterns. DUALITY is developed in the context of the UNITY formalism and the principle and algebraic laws of Communication Closed Layers (CCL), and illustrated through the algorithm of all-points shortest path.