A return to stochasticity and probability in spiking neural P systems

Abstract

This work continues the investigations of introducing probabilities to spiking neural P systems, SN P systems in short—membrane computing models inspired from biological spiking neurons. A particular interest for SN P systems in this work is the nondeterministic selection of applicable firing rules. Rules represent the possible reactions of a neuron to the number of electrical impulses, or spikes, present. Intuitively, having nondeterministic selection can be interpreted as having a random choice with equal probabilities for all options. This seems unnatural in some biological sense, since some reactions are more active than others in general as emphasized in Obtulowicz and Păun, BioSystems 70(2):107–121, 2003. Results found that the stochastic process introduced to the nondeterministic selection of firing rules also applies to application of rules in general whether the rule is for firing or forgetting and whether a single rule is applicable or multiple. This work proposes SN P systems with stochastic application of rules, $$\star $$ SN P systems in short. $$\star $$ SN P systems are variants which introduce a stochastic process a priori to the application of rules in SN P systems.