Equational Realizations of Switching Functions

Equational logic is an approach to combinational synthesis based on the equation f(x) = 1 rather than on the function f(x). The central problem of equational logic is to find a system of equations gi(x) = hi(x) (i = 1,2,...,k), of the simplest possible form, that has the same solutions as f(x) = 1. Given such a k-equation system, f(x) may be realized as the output of a k-wide digital comparator whose inputs are the 2k g's and h's constituting the system.