System for evaluating boolean expressions using total differential generating tree structured processing elements controlled by partial subfunction differentials

摘要

Arbitrary and complex Boolean functions can be evaluated at high speed and with a minimal amount of memory by evaluating the total derivatives of the subfunctions out of which any given Boolean function is built. The Boolean function is then generated from its total derivative. The total derivative of any binary or two input Boolean function is defined by a method dependent only on the inputs and the partial derivatives of the subfunction. By combining the subfunctions in a binary tree, a Boolean function of any complexity can be built up. By using a binary tree structure in a processing circuit or memory organization, the method is generalized to accommodate all possible Boolean functions. A processing element may be devised to generate the total derivative of each subfunction in a tree circuit of such processing elements, or arrays may be defined in a general purpose computer and elements in the array generated according to a processing methodology which assumes a tree relationship between elements in the array.