An Approach for the Synthesis of Multithreshold Threshold Elements

A new approach for the realization of multithreshold threshold elements is presented. The procedure is based on the fact that the excitations at contradictory vertices of the switching function must be unequal. The weights of the multithreshold element, in general, satisfy simple relations of the form U·W = 0, where U=(u1, u2, ... , un) and W=(w1, w2, ... , wn) such that ui ¿{1,0, ¿1,}, i=1,2, ... n, and W¿Iⁿ. Comparison of the excitations E(Xi) = W·Xi and E(Xj) = W·XjM at TRUE, and FALSE vertices Xi and Xj, respectively, for all specified vertices reusult in some inequalities of the form U·W¿0. Subsets of the remaining set of weight expressions U·W that are compatible are then determined, i.e., no linear combination of some or all of these expressions results in an expression Ui·W such that Ui·W¿0 and independent of each other. Each expression of each of these subsets is then equated to zero, and simple relations between weights are established. These are then used to find the weights vectors W´s. The threshold vector T for each W is next established. From the set of weight-threshold vectors (W, T) the desired solution is determined by some minimality criterion. An example has been worked out by hand and an algorithm is given for systematic synthesis procedure.