Synthesis of Switching Functions by Threshold Elements

In this paper, two general methods of determining a separating surface f(x)= Σ
^n-1
_i=0
αiøi(x) = 0 will be developed for any switching problem in terms of threshold elements ø
_i
(x). First, a polynomial decision function f(x) is synthesized so that it has no more than N terms in it where N is the total number of pattern vectors of the switching problem. This decision function is easily amenable for mechanization since it needs the solution of a triangular system of N equations in N unknowns. In addition, a method of deriving aminimal polynomial solution f(x) will also be given. Second, a decision function f(x) involving general threshold elements ø
_i
(x) is derived from the polynomial solution so that it has fewer terms than the polynomial solution. Examples will be given to illustrate the methods and compare these results with those obtained by the traditional method of prime implicants.