On the computational power of neural nets

Abstract

This paper deals with finite size networks which consist of interconnections of synchronously evolving processors. Each processor updates its state by applying a "sigmoidal" function to a linear combination of the previous states of all units. We prove that one may simulate all Turing machines by such nets. In particular, one can simulate any multi-stack Turing machine in real time, and there is a net made up of 886 processors which computes a universal partial-recursive function. Products (high order nets) are not required, contrary to what had been stated in the literature. Non-deterministic Turing machines can be simulated by non-deterministic rational nets, also in real time. The simulation result has many consequences regarding the decidability, or more generally the complexity, of questions about recursive nets. © 1995 by Academic Press, Inc.