A New Connection Between Convex Geometry and Threshold Logic

• M. R. Emamy-K.
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 329)

Abstract

A threshold Boolean function is a Boolean function defined on {0, l}n whose On-vertices and Off-vertices are strictly separable by a hyperplane in Rn. Threshold logic is the main source for study of threshold Boolean functions, while Boolean algebraic methods have been the classical tools to study these objects.

Recently, we have claimed there exists a purely geometric approach to these linearly separable Boolean functions. The principal motivation to this claim is the fact that these functions are just linearly separable cubical complexes and their place is convex geometry and polytopes. Here, we present a brief overview of a few results justifying this new connection.

Keywords

Boolean Function Convex Polytope Boolean Expression Convex Geometry Cubical Complex
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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