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. We also investigate how the use of anti-spikes in spiking neural P systems affect the capability to solve the satisfiability problem in a non-deterministic way. For efficient formalization and to dealwith the implementation and formal correctness of SN P systems, this thesis also shows the structural link between SN P systems and Petri nets. A major strength of Petri nets is their support for analysis of many properties and problems associated with parallel systems. Petri nets working in sequential or parallelmode are also used as language generators. The SN P system works in a locally sequential and globally maximal way. That is, each neuron, at each step, if more than one rule is enabled, then only one of them can fire. But still, all neurons fire in parallel at the system level. This makes it suitable for a natural translation to Petri net with parallel semantics. In general for arbitrary classes of P systems using maximal parallelism, translations to Petri nets are only possible through special semantics associated with them. In this thesis we are interested in those interactions investigating the role of Petri nets as a tool to express behavioural semantics for SN P systems. The thesis proposes a direct translation of standard SN P systems, SNP systems with anti-spikes and extended SNP systems into Petri netmodels that exactlymimic the working of the systems on simulation. The Petri netmodels obtained after translation are considered for simulation using PNetLab. PNetLab is a Java based Petri net tool which supports the parallel execution of transitions. It also allows to write user defined guard functions in C/C++, which makes it possible to represent the regular expressions associated with spiking/forgetting rules. It also provides step-by-step system watching for collecting simulation reports. We relate the languages generated by the SN P systems with the step languages generated by the corresponding Petri nets. We emphasize the relationship between spiking neural P systems and Petri nets by constructing SN P systems for simplex stop-and-wait protocol and producer/consumer paradigm. They are translated into equivalent Petri netmodels, which are observed as standard solutions based on Petri nets already present in the literature. It is attractive to adopt Petri nets to model SN P systems so the rich theoretical concepts and practical tools from well-developed Petri nets could be introduced in the current research of SN P systems.