Comments on "The Application of the Rademacher-Walsh Transform to Boolean Function Classification and Threshold Logic Synthesis"

In the above paper¹Edwards shows the implementation of several Boolean functions using a threshold gate and XOR gates. An unstated, but implicit, result is that any given Boolean function can be synthesized in this way. This result is of some historical interest. We wish to relate it to a previous paper by Kaplan and Winder [1], which in effect derived the result, and then to a mathematical study of Lawson [2], [3], which yields a synthesis procedure with very general applicability.