  Mathematical definitions of polyhedrons and perceptron networks are
discussed. The formalization of polyhedrons is done in a rather traditional
way. For networks, previously proposed systems are developed. Perceptron
networks in disjunctive normal form (DNF) and conjunctive normal forms (CNF)
are introduced. The main theme is that single output perceptron neural networks
and characteristic functions of polyhedrons are one and the same class of
functions. A rigorous formulation and proof that three layers suffice is
obtained. The various constructions and results are among several steps
required for algorithms that replace incremental and statistical learning with
more efficient, direct and exact geometric methods for calculation of
perceptron architecture and weights.
