Sequential SNP systems based on min/max spike number

Abstract

We consider the properties of spiking neural P (SNP) systems that work in a sequential manner. These SNP systems are a class of computing devices recently introduced as a bridge between spiking neural nets and membrane computing. The general sequentiality of these systems was considered previously; now we focus on the sequentiality induced by the spike number: at each step, the neuron with the maximum (or minimum) number of spikes among the neurons that are active (can spike) will fire. This strategy corresponds to a global view of the whole network that makes the system sequential. We study the properties of this type of a restriction (i.e. considering the case of sequentiality induced by the function maximum defined on numbers of spikes as well as the case of the sequentiality induced by the function minimum similarly defined on numbers of spikes). Several universality results are obtained for the cases of maximum and minimum induced sequentiality.