Verification of systolic arrays: a stream functional approach

We illustrate that the verification of systolic architectures can be carried out using techniques developed in the context of verification of programs. This is achieved by a decomposition of the original problem into separately proving the correctness of the data representation and of the individual processing elements in the systolic architecture. By expressing a processing element as a function on a stream of data we are able to utilize standard proof techniques from programming language theory. This decomposition leads to relatively straightforward proofs of the properties of the systolic architecture. We illustrate the techniques via a substantial example, the proof of the correctness of a linear-time systolic architecture for computing the gcd of polynomials. Although this architecture has been designed a few years ago, a formal proof of correctness has not hitherto appeared in the literature.