Research On Modeling And Computational Power Of Non-traditional Spiking Neural P Systems

Biological computing is a highly inter-discipline filed ranging from computer science to biotechnology and it focuses on the development of novel computation models and algorithms.As a hot branch of biological computing,membrane computing aims to abstract computation models from the structure and the functioning of the living cell.The abstracted computation models in the filed of membrane computation are called membrane systems or P systems.Spiking neural P systems are known as a class of neural-like computation models,which are inspired by the way in which neurons communicated with each other by means of spikes,and they have been a hot research in the filed of membrane computing.The present work mainly focuses on the research of the essential ingredients of spiking neural P systems,including the topology structure,the form of rules,the application condition of rules,the communication pattern between neurons.The main contents of this dissertation are as follows.Spiking neural P systems have a network structure,while the basic models of membrane computing(cell-like P systems)start from the hierarchy structure.With mathematical motivation,a combination of the hierarchy structure of cell-like P systems with only one kind of object and evolution rules as those in spiking neural P systems is considered,thus a type of spiking neural P system with a hierarchical arrangement of membranes is constructed,namely cell-like spiking neural P systems.Firstly,the computation power of cell-like spiking neural P systems is investigated as number generators,and the universality of these systems is proved.In addition,the computation power of cell-like spiking neural P systems is also investigated as language generators,and the hierarchy of the languages generated by cell-like spiking neural P systems is constructed.Spiking neural P systems are hardly able to handle some numerical problems,where multisets are used as data structure,and rules in form of formal grammar production are used as data operation;moreover,due to the discontinuous nature of integrate-and-fire behavior of neurons,developing learning algorithms is challenging for spiking neural P systems.To avoid these problems,rules in a numerical form is introduced into spiking neural P systems,and numerical spiking neural P systems are proposed.In this kind of spiking neural P system,each neuron substitutes numerical variables and mathematical functions for spikes and evolution rules,which makes numerical spiking neural P systems are more suitable for some real-world problems that are amenable to formal quantitative modeling and to numerical computation techniques;and the rules in the form of mathematical function makes it possible to develop a learning algorithm for numerical spiking neural P systems,thus enhancing the application potential of the systems.The computation power of numerical spiking neural P systems is investigated.Specifically,it is proved that such systems are universal as both number generating and number accepting devices.In the classical spiking neural P systems,it is NP-hard to decide whether a rule associated with a regular expression can be applied.This determination method will consume a mass of computation overheads.In order to identify an easy way to determine the applicability of rules,inspired by a biological phenomenon that the cell membrane of a neuron is polarized,a new determination mechanism by introducing polarizations instead of regular expressions is proposed,and spiking neural P systems with polarizations are investigated.Such systems are proved to be universal.This result has an important sense: the computation overheads can be greatly saved without the loss of computation power of spiking neural P systems.On this basis of the aforementioned result,by analyzing and optimizing the instructions in the simulated small universal register machine,universal spiking neural P system with polarizations is constructed as a function computing device.This work investigates the computation power of spiking neural P systems with communication on request in the case of using one type of spikes.It is proved that one type of spike suffices for spiking neural P systems with communication on request achieving Turing universality.This result answers the corresponding open problem formulated by Zhang et al: whether the universality of spiking neural P systems with communication on request can be obtained by using only one type of spikes.The significance of this conclusion is as follows: the reduction to only one type of spike reduces the descriptional complexity of spiking neural P systems with communication on request,and leads to computationally cheaper integration-fire conditions,but without a deterioration of the computation power.Moreover,a parameter,namely the number of unbounded neurons,is proposed for estimating the computation power of various types of spiking neural P systems,and the relationship between this parameter and the complexity of a spiking neural P systems with communication on request is investigated.The software implementation for membrane computing can not only contribute to a better understanding of computation properties of various P systems,but also assist in the design and formal verification of complex P systems,thus saving the researchers heavy hand-made calculations.The framework given by P-Lingua and Me Co Sim provides a common infrastructure with facilities to deal with different types of models based on P systems in terms of design,simulation,analysis,verification.In this work,a simulation application for cell-like spiking neural P systems within the framework of P-Lingua and Me Co Sim is developed,and it is used to simulate different examples of cell-like spiking neural P systems.The simulation results demonstrate that this simulation application can play an important role assisting in tasks related with the simulation and experimental validation of the cell-like spiking neural P systems.