On the Computability of Primitive Recursive Functions by Feedforward Artificial Neural Networks

Abstract

We show that, for a primitive recursive function (Formula presented.), where (Formula presented.) is a n-tuple of natural numbers and t is a natural number, there exists a feedforward artificial neural network (Formula presented.), such that for any n-tuple of natural numbers (Formula presented.) and a positive natural number m, the first (Formula presented.) terms of the sequence (Formula presented.) are the same as the terms of the tuple (Formula presented.) (Formula presented.).