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

Abstract

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 N(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 (N(z,0),…,N(z,m)).

Keywords

• computability theory
• theory of recursive functions
• artificial neural networks