Research On Property And Application Of Spiking Neural P Systems

Abstract:Membrane computing is a new branch of natural computing, and this cross-disciplinary research involved in computer science, mathematics and biology aims to abstract computing ideas and models from the structure and the functioning of living cells, as well as from the way the cells are organized in tissues or higher order structure, which are called membrane systems, or P systems.Spiking neural P systems are a class of neural-like P systems, and are a class of distributed and parallel computing models inspired from the way neurons communicate with each other by means of electrical impulses, which incorporate the ideas of spiking neural networks into P systems.In this dissertation, from the three aspects of theory of computation, application, and software simulation research, the computational power, small universality, logic and arithmetic operations and formal verification of several Spiking neural P systems are investigated. The detailed contents are as follows:The small universality of homogeneous spiking neural P systems is studied. As devices computing functions, we construct a small universal homogeneous spiking neural P system with standard rules and weight having53neurons. As devices generating of sets of numbers, a small universal homogeneous spiking neural P system with standard rules and weight having52neurons is found. For spiking neural P systems, besides in computer science, small universality is also interesting in biology:a measure method of small universal "brain" is given.The universality of two kinds of homogeneous standard spiking neural P systems without delays is investigated, including systems with weighted synapses and without weight on synapses. We prove that these two kinds of homogeneous standard spiking neural P systems are universal both in the generating mode and in the accepting mode. This dissertation provides an answer to an open problem about whether there is a universal homogeneous spiking neural P system without delays formulated by Zeng Xiang-xiang et al. In addition, the universality of two kinds of homogeneous extended spiking neural P systems without delays is investigated and proved, including homogeneous extended spiking neural P systems with weighted synapses and without weight on synapses.The universality of homogeneous spiking neural P systems with anti-spikes without delays and weighted synapses is investigated. We prove that such homogeneous P systems are universal both in the generating mode and in the accepting mode. This dissertation provides answers to two open problems about whether there is a universal homogeneous spiking neural P system without delays and how to eliminate weights on synapses formulated by Zeng Xiang-xiang et al.We consider spiking neural P systems as devices which can be used to perform some basic arithmetic operations, namely two’s complement, addition/subtraction on signed integers, and multiplication on two arbitrary natural numbers. The inputs and outputs of those systems are indicated by binary form and encoded as corresponding spike trains. This dissertation provides an answer to an open problem about multiplication operation of two arbitrary natural numbers formulated by Gutierrez-Naranjo MA. and Leporati A. The present work maybe considered as the basis for more complex applications, and maybe for designing of a CPU based on spiking neural P systems.Spiking neural P system with anti-spikes are a variant of spiking neural P systems consisting of two types of objects called spikes and anti-spikes, and can encode the balanced ternary digits in a natural way. In this dissertation, we use spiking neural P system with anti-spikes to simulate universal balanced ternary logic gates including AND, OR and NOT, also use these systems to perform balanced ternary arithmetic operations like addition and subtraction on balanced ternary integers. The present work may be considered as a first step in theoretics towards the design of a balanced ternary CPU based on spiking neural P systems with anti-spikes. This dissertation provides the first applicational answer to an open problem formulated by Pan LQ and Paun G.In this dissertation, we illustrate and analyse two transition diagrams associated with two SN P Systems generated by SnpsGUI software simulator by means of two examples and deduce three general conclusions between spiking neural P systems and transition diagrams. This allows us to verify the correctness and completeness of SN P Systems models aided by computers. Conclusions show the transition diagram is an efficient methodology to realize the formal verification of a spiking neural P system. Meanwhile, prospect of other more effective formal verification methods of spiking neural P systems and improvement direction of SnpsGUI was proposed.