Simplified and yet Turing universal spiking neural P systems with polarizations optimized by anti-spikes

Abstract

Spiking neural P systems with polarizations (PSN P systems) are a class of neural-inspired computation models, where the firing condition of rules is the neuron-associated polarization. It has previously been shown that PSN P systems are Turing universal by using tree types of polarizations, and 164 neurons are needed for constructing a Turing universal PSN P system as a function computing device. In this work, in order to answer the open problem whether this determination mechanism of polarizations can be simplified without the loss of computation power, one more type of object for information encoding, i.e., the anti-spike, is introduced into PSN P systems, thus, PSN P systems with anti-spikes are proposed, abbreviated as PASN P systems. It is proved that two types of polarizations are enough to guarantee the Turing universality of PASN P systems both as number generators and number acceptors. Furthermore, it is demonstrated that 121 neurons are sufficient for a PASN P system with two types of polarizations to achieve universality as a function computing device. These results manifest that anti-spikes are a powerful ingredient of PASN P systems to yield the improvement in computation performance and the reduction in the description complexity necessary to achieve Turing universality.