On the Computational Power of Spiking Neural P Systems with Self-Organization.

Xun Wang,Tao Song,Faming Gong,Pan Zheng

doi:10.1038/srep27624

Abstract

Neural-like computing models are versatile computing mechanisms in the field of artificial intelligence. Spiking neural P systems (SN P systems for short) are one of the recently developed spiking neural network models inspired by the way neurons communicate. The communications among neurons are essentially achieved by spikes, i. e. short electrical pulses. In terms of motivation, SN P systems fall into the third generation of neural network models. In this study, a novel variant of SN P systems, namely SN P systems with self-organization, is introduced, and the computational power of the system is investigated and evaluated. It is proved that SN P systems with self-organization are capable of computing and accept the family of sets of Turing computable natural numbers. Moreover, with 87 neurons the system can compute any Turing computable recursive function, thus achieves Turing universality. These results demonstrate promising initiatives to solve an open problem arisen by Gh Păun.

Highlights

In the central nervous system, there are abundant amount of computational intelligence precipitated throughout millions of years of evolution
The computational power of the system is investigated as well. It demonstrates that SN P systems with self-organization can compute and accept any set of Turing computable natural numbers
There is a universal SN P system with self-organization having 87 neurons for computing functions. These results show that SN P systems with self-organization are powerful computing models, i.e., they are capable of doing what Turing machine can do

Summary

Introduction

In the central nervous system, there are abundant amount of computational intelligence precipitated throughout millions of years of evolution. Neural-like computing models are a class of powerful models inspired by the way how neurons communicate. Using different mathematic approaches to describe neural spiking behaviours, various neural-like computing models have been proposed, such as artificial neural networks[5] and spiking neural networks[6]. In the field of membrane computing, a kind of distributed and parallel neural-like computation model, named spiking neural P systems (SN P systems), were proposed in 20067. SN P systems are known as a class of neural-like computing models under the framework of membrane computing[36]. Models[37], which incorporates the concept of time into their operating model, besides neuronal and synaptic state in general artificial neural networks, The neuron in SNN cannot fire at each propagation cycle, but only when a membrane potential reaches a specific value. In terms of motivation of models, SN P systems fall into the spiking neural network models, i.e., the third generation of neural network models

Methods

Results

Conclusion