Asynchronous spiking neural P systems with rules on synapses and coupled neurons

The asynchronous spiking neural P system with rules on synapses (ASNPR system) is a type of distributive and non-deterministic computing model inspired by neural activities in biology. In this work, the synchronous excitation/inhibition phenomenon of coupled neurons is abstracted as the all-or-none behavior of coupled neurons: spikes in the coupled neurons are supplemented/consumed if and only if all the coupled neurons in the same set synchronously receive/consume spikes. Based on all-or-none behaviors, the ASNPR system with coupled neurons (ASNPRC system) is introduced, where coupled neurons are grouped into several sets, and the changes in the content of coupled neurons in the same set are positively correlated. The computational power of the ASNPRC systems is investigated. It has been proven that ASNPRC systems using standard rules are Turing universal function-computing devices. Moreover, a universal ASNPRC system consisting of four neurons is constructed to compute functions. The results show that “coupled neurons” is an efficient ingredient for the computation power of ASNPR systems in the sense that ASNPR systems using relatively few neurons achieve their universality with the help of “couple neurons”.