Classification capability of the two-layer perceptron

This paper treats the classification capability of a two-layer perceptron [1]. The discussion is confined to the problem to separate two classes of objects. The aim of the study has been to investigate what shapes the decision regions of a two-layer perceptron can have. Two theorems are established for this purpose. One which can be used to decide whether a given partition of the input space is realizable or not and one that states that a general property of a non-realizable partition of the input space leads to a number of inconsistent inequalities. Three corollaries treating a few special geometrical shapes are also presented.