Towards a Formal Treatment of VLSI Arrays

Abstract

This paper presents a formalism for describing the behavior of computational networks at the algorithmic level. It establishes a direct correspondence between the mathematical expressions defining a function and the computational networks which compute that function. By formally manipulating the symbolic expressions that define a function, it is possible to obtain different networks that compute the function. From this mathematical description of a network, one can directly determine certain important characteristics of computational networks, such as computational rate, performance and communication requirements. The use of this formalism for design and verification is demonstrated on computational networks for Finite Impulse Response (FIR) filters, matrix operations, and the Discrete Fourier Transform (DFT). The progression of computations can often be modeled by wave fronts in an illuminating way. The formalism supports this model. A computational network can be viewed in an abstract form that can be represented as a graph. The duality between the graph representation and the mathematical expressions is briefly introduced.