On Linear Separability of Random Subsets of Hypercube Vertices

The classical Cover results on linear separability of points in R^d are a milestone in neural network theory. Nevertheless they are not valid for digital input networks because in this case the points are not in general position being vertices of a d-dimensional hypercube. I show here that for large d all Cover findings can be extended to this case. It is also shown that for n < O((d + 1)^(3/2)) the number of linear separations of n random hypercube vertices tends to that of n points in general position.