Graphs of Threshold Functions of up to Five Variables
Kasiyah Machmudin kasiyah@makara.cso.ui.ac.id
Mathematics Dept. of. Math., The Univ of Indonesia Indonesia
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.
