Geometric methods of convex polytopes are applied to demonstrate a
new connection between convexity and threshold logic. A
cutcomplex is a cubical complex whose vertices are strictly
separable from rest of the vertices of the ncube by a
hyperplane of R^{n}. Cutcomplexes are geometric presentations for
threshold Boolean functions and thus are thus are related to
threshold logic. For an old classical theorem of threshold logic a
shorter but geometric proof is given. The dimension of the cube
hull of a cutcomplex is shown to be the same as the maximum
degree of the vertices in the complex. A consequence of the latter
result indicates that any two isomorphic cutcomplexes are
isometric.
Download TeX format
