Homogenous Spiking Neural P Systems with Inhibitory Synapses

Abstract

Spiking neural P systems with inhibitory synapses (ISN P systems, for short) are a class of discrete neural-like computing models, which are inspired by the way of biological neurons storing and processing information and communication by means of excited and inhibitory impulses. In this work, we prove that ISN P systems can compute and accept any set of Turing computable numbers by using one type of neurons, thus can achieve Turing universality. Such systems are called homogenous ISN P systems. The results give a positive answer to an open problem left in (Pan and Pă?un, Int J Comput Commun 4(3):273---282, 2009) that "whether the number of types of neurons in universal SN P systems can be decreased by using inhibitory synapses". The obtained result is optimal in the sense of having minimal number of types of neurons in Turing universal SN P systems.