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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}.
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.

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.
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