Universality of spiking neural P systems with polarizations working in sequential mode induced by maximum spike number

Based on the inspiration that the communication signal between neurons in biology is composed of short electrical pulses, we investigate a new variant of spiking neural P systems, i.e., spiking neural P systems with polarizations (PSN P systems), which have a rule-triggering condition associated with polarization. In this work, we focus on the computational power of sequential PSN P systems with delay based on the maximum number of spikes, i.e., the ability to preferentially fire the neuron with the maximum number of spikes among the active neurons at each step (except for the neurons in the refractory period) of the computation. Thus, two strategies are considered, i.e., the max-sequentiality strategy and the max-pseudo-sequentiality strategy, and we prove that PSN P systems with delay adopting the max-sequentiality strategy or the max-pseudo-sequentiality strategy are Turing universal as number generating devices. The results give positive answers to the open problem formulated in [Tingfang Wu et al. (2020), Neurocomputing, 401, 392-404].

Automated summary

This study investigates a new variant of spiking neural P systems with polarizations, focusing on their computational power in sequential systems with delay. The results show that PSN P systems with delay adopting certain strategies are Turing universal as number generating devices, providing positive answers to an open problem in the field.