Boundary Points of Threshold Functions

Boundary points of a threshold function fare those vertices of the n-cube that produce a minimal irredundant set of inequalities for the realization of f. In this paper they are shown to be those vertices that can be contained in separating hyperplanes. With this theorem it is shown that knowledge of canonical boundary points of self-dual canonical threshold functions allows complete determination of boundary points of equivalent functions. This provides a compact and geometrically interesting characterization of threshold functions.