The computing capacity of three-input multiple-valued one-threshold perceptrons

Abstract

In this paper, an exact and general formula is derived for the number of linear partitions of a given point set V in three-dimensional space, depending on the configuration formed by the points of V. The set V can be a multi-set, that is it may contain points that coincide. Based on the formula, we obtain an efficient algorithm for counting the number of k-valued logic functions simulated by a three-input k-valued one-threshold perceptron.