Computational Power of Neuroidal Nets

Abstract

Neuroid as a kind of a programmable neuron has been introduced by L. G. Valiant in 1988. Essentially it is a combination of a standard threshold element with a mechanism that allows for modification of neuroid’s computational behaviour. This is done by changing the settings of its weights and of its threshold in the course of computation. It is shown that the computational power of neuroidal nets crucially depends on the size of allowable weights. For bounded weights their power equals to that of that of finite automata, whereas for unbounded weights finite neuroidal nets posses the computational power of Turing machines. It follows that the former neuroidal nets are computationally equivalent to standard, non-programmable discrete neural nets, while, quite surprisingly, the latter nets are computationally equivalent to a certain kind of analog neural nets.

This research was supported by GA ČR Grant No. 201/98/0717.