Derivation of Systolic Convolution Arrays

Abstract

We show how the refinement calculus, combined with the action system formalism gives a stepwise refinement method for deriving parallel convolution algorithms that model systolic computation. We inspect how different architectural designs influence the derivation process. The action systems framework allows us to reuse the derivation to a large extent. We start from the definition of convolution and give an initial action system. Through a series of refinement steps we derive a parallel version of this system. The other designs are derived by merely reorganizing the variables of the system. Every transformation step is verified within the refinement calculus. 1 Introduction The paper presents an outline of a method for formal derivations of parallel convolution. The work has been carried out within the refinement calculus and the action system framework. An action system is a parallel or distributed program where parallel activity is described in terms of events, so called actions. Se..