New Normal Forms for Spiking Neural P Systems

Abstract

We consider a natural restriction in the architecture of a spiking neural P system, namely, to have neurons of a small number of types (i.e., using a small number of sets of rules), and we prove that three types of neurons are su±cient in order to generate each recursively enumerable set of numbers as the distance between the first two spikes emitted by the system or as the number of spikes in a specified neuron, in the halting configuration. The case we investigate is that of spiking neural P systems with standard rules, with delays, but without using forgetting rules; similar normal forms remain to be found for other types of systems.