Spiking neural P systems with anti-spikes working in sequential mode induced by maximum spike number

Abstract

Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired by spiking neurons. SN P systems with anti-spikes (ASN P systems) are a variant of SN P systems, which were inspired by inhibitory impulses/spikes or inhibitory synapses. In this work, we consider ASN P systems with the restrictions: (1) systems are simple in the sense that each neuron has only one rule; (2) at each step the neuron(s) with the maximum number of spikes among the neurons that are active (can spike) will fire; (3) the feature of delays and forgetting rules are not used. These restrictions make the systems working in a sequential way. We investigate the computational power of ASN P systems under these restrictions. Specifically, we prove that such systems with spiking rules of categories (a,a) and (a,a¯) are universal as both number generating and accepting devices. We also prove that ASN P systems with inhibitory synapses using spiking rules of category (a,a) are universal as both generating and accepting devices. These results show that ASN P systems are still powerful working with these restrictions.