An Algebraic Approach to Systolic Circuits

Abstract:
The goal of deductive design is the systematic construction of a system implementation starting from its behavioural specification according to formal, provably correct rules. We use Gofer/Haskell to formulate a functional model of directional, synchronous and deterministic systems with discrete time. We develop an algebra of slowdown. The associated laws are then employed in deductive hardware design of two systolic circuits, a convolver and a recogniser for regular expressions. The strategy used is applicable to the derivation of other systolic circuits as well.