Hyperplane arrangements separating arbitrary vertex classes in n-cubes

Strictly layered feedforward networks with binary neurons are viewed as map s from the vertex set of an n-cube to the vertex set of an l-cube. With onl y one output neuron, they can in principle realize any Boolean function on n inputs. We address the problem of determining the necessary and sufficien t numbers of hidden units for this task by using separability properties of affine oriented hyperplane arrangements. (C) 2000 Academic Press.