Modelling and Simulation of SN P Systems using Petri Nets

Abstract

Natural computing deals with the extraction of mathematical models of computation from nature, investigating their theoretical properties, and identifying the extent of their real-world applications. P systems (also called membrane systems) were introduced as parallel computationalmodels inspired by the hierarchical structure ofmembranes in living organisms and the biological processes which take place in and between cells. Spiking neural P systems (for short, SN P systems) are a class of P systems inspired by the spiking activity of neurons in the brain. An SN P system is represented as a directed graph where nodes correspond to the neurons having spiking and forgetting rules. The rules involve the spikes present in the neuron in the form of occurrences of a symbol a. It is a versatile formal model of computation that can be used for designing efficient parallel algorithms for solving known computer science problems. SN P systems are used as a computing device in various ways - generators, acceptors, and transducers. SN P system with anti-spikes (for short, SN PA systems) is a variant of SN P systemcontaining two types of objects, spikes (denoted by a) and anti-spikes (denoted by a), corresponding somewhat to inhibitory impulses from neurobiology. Because of the use of two types of objects, the system can encode the binary digits in a natural way and hence can represent the formalmodelsmore efficiently and naturally than the SN P systems. The thesis investigates the computing power of spiking neural P system with anti-spikes as language generators and transducers. We show that SN PA systems as generators can generate languages that cannot be generated by the standard SN P systems. It is demonstrated that, as transducers, spiking neural P systems with anti-spikes can simulate any Boolean circuit and computing devices such as finite automata and finite transducers.