ABSTRACT

In this paper we shall study the problem of nonlinear separation. As usual, a Boolean function F of n binary variables, x<inf>l</inf>,..., x<inf>n</inf>, x<inf>i</inf>S{1,0}, i=1,..., n, will be represented by a set of vertices C in the n-dimensional Euclidean space E<sup>n</sup>where each vertex has n binary-valued components, {1,0}.

INDEX TERMS

Contradiction equation, discriminate function, echolon matrix, high-order threshold function, homogeneous equation, miniimum degree ? function, orthogonal function, positivization, statistical recognition, successive higher ordering method, ? function of degree r, variable weight, vertex weight method, vertex weight.

CITATION

C. Sheng and H. Hwa, "An Approach for the Realization of Threshold Functions of Order r," in

*IEEE Transactions on Computers*, vol. 18, no. , pp. 923-939, 1969.

doi:10.1109/T-C.1969.222548

CITATIONS