A shortcut hand-reduction method known as the Karnaugh map (K map) is an efficient way of reducing Boolean functions to a minimum form for the purpose of minimizing hardware requirements. In this paper, by applying the prime group and the essential prime group concepts of the K maps to pattern classification problems, the K1-map reduction method is proposed. The K1-map reduction method can be used to design restricted Coulomb energy networks and to determine the number of hidden units problems in a systematic manner.

In this article we present a k-winners-take-all (k-WTA) neural net that is established based on the concept of the constant time sorting machine by Hsu and Wang. It fits some specific applications, such as real-time processing, since its Theta(1) time complexity is independent to the problem size. The proposed k-WTA neural net produces the solution in constant time while the Hopfield network requires a relatively long transient to converge to the solution from some initial states.