Computational completeness of sequential spiking neural P systems with inhibitory rules

Abstract

Spiking neural P systems with inhibitory rules (in short, IR-SN P systems) are a kind of bio-inspired computing systems, which are abstracted by the inhibitory synaptic mechanism of biological neurons. IR-SN P systems work in synchronous mode. This paper investigates their sequential version, sequential IR-SN P systems (in short, IR-SSN P systems). In sequential mode, not only the rules in each neuron are applied sequentially, but also the neurons fire in a sequential manner. The maximum-spike-number strategy is considered in sequential mode, and two sub-modes are further distinguished: max-sequentiality strategy and max-pseudo-sequentiality strategy. Computational completeness of IR-SSN P systems as number generating/accepting devices and function computing devices are discussed. It is proven that IR-SSN P systems are Turing universal number generating/accepting devices. Moreover, a small universal IR-SSN P system for computing functions is established in max-sequential strategy.