Graphs of Threshold Functions of up to Five Variables

Abstract

Threshold functions are Boolean functions that model neurons, processing units of an artificial neural network. These functions can be represented geometrically as a unit hypercube in which each vertex is labeled either by 1 or 0. The geometrical representations can be simplified into graphs without losing the relationship between minterms and vertices. A graph labeling is used to store threshold functions as well as to keep the relation between the minterms and the vertices. There are 119 different graphs that represent all 94.572 threshold functions of five variables. This paper presents graphs of threshold functions for small number of variables and some patterns followed by these graphs.