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

We show that, for a primitive recursive function h(x, t), where x is a n-tuple of natural numbers and t is a natural number, there exists a feedforward artificial neural network (x, t), such that for any n-tuple of natural numbers z and a positive natural number m, the first m + 1 terms of the sequence {h(z, t)} are the same as the terms of the tuple ((z, 0), ... ,(z, m))