Spiking neural P systems with autapses

Abstract

• Present SN P systems with autapses as a new variant of SN P systems by introducing autapses. • Prove SN P systems with autapses are Turing universal as natural number generators . • Construct an SN P systems with autapses with 53 neurons for computing functions. • A simulator is developed and used to check the correctness of universal SNP-AU systems. Inspired by the structure and communication method of neural systems, a parallel computing model, spiking neural P systems (SN P systems, for short), was proposed in 2006. A new class of SN P systems, SN P systems with autapses (SNP-AU systems), is presented in this work. Autapses are a special kind of synapses, connecting the axon of a neuron onto itself. We prove that SNP-AU systems can generate Turing-computable numbers, through the simulation of the modules of universal register machines. This result improves significantly the results given by classical SN P systems in terms of the number of neurons and rules, while preserving simplicity and power to a reasonable extent. Moreover, we construct an SNP-AU system using 53 neurons, proving its universality for computing functions. Finally, going beyond the design of the building blocks of register machines, a whole universal machine is provided. Thus, a simulator is developed and used to check the correctness of two universal SNP-AU systems proposed in this paper, complementing the theoretical proof with the experimental validation of our systems with respect to the reference example appearing in the foundational paper of small register machines.