Realization of Logical Functions by a Network of Threshold Components with Specified Sensitivity

In the realization of a logical function by a network of threshold components, one important engineering parameter is the tolerances which must be placed on the coefficients and threshold of the individual components. For threshold gates in which the logical ``zero´´ corresponds to a constant signal of zero value and in which the coefficients are all positive or all negative, these tolerances are functions only of the gap boundaries of the map realized by the component. A set of theorems is presented that define ``algebraic-like´´ operations which provide a means for performing a sequence of symbolic operations on the desired logical function whereby the latter is transformed into a description of a network of threshold components which is its realization. Using these theorems a procedure is given for realizing an arbitrary logical function as a network of threshold components with specified sensitivity.