Research On The Computational Power Of Spiking Neural Membrane Systems Inspired By Neural Systems

After decades of development, people wish the fourth generation computer, namely, massive scale integrated circuit computer would possess more intelligence that resembles human intelligence. Thus they commence seeking to replace them with the fifth generation computers, namely, biological computers and quantum computers. As for biological com-puters, membrane computing is one of the important branches in the field of bio-computing. It constructs paralleled computation models of distribution structure by simulating the struc-tures and functions of cells and their tissues. Our research has explored one type of the membrane systems, namely spiking neural membrane systems. These systems are inspired by the biological mechanism, with which the neurons in the brain cooperate through pro-cessing impulses in the complex net established by synapses. This dissertation has investi-gated a number of different variants of the spiking neural membrane systems in the aspect of language generating power, commotional university and efficiency and number recognizing power. The main research work are as follows:This dissertation created a new variant of spiking neural membrane systems with astro-cyte, inspired by the biological phenomenon that the astrocyte around neurons have signif-icant impact on the communication between neurons. Through simulating Turing machine, it is proved that these systems are Turing universal in synchronous working mode. The sys-tems could generate semi-linear set of natural numbers if we restrict the number of spikes in each neuron. Moreover, these new systems combined by neurons and astrocytes are also Turing universal when they work in asynchronous mode. All those research results demon-strate that the network constructed by the simple neurons has great computational power.Furthermore, in this dissertation we create the time bounded asynchronous model to solve the open problem introduced by Ibarra, that whether the spiking neural membrane systems with standard rules are Turing complete. In this model, all the spiking rules have the same bounded time. By simulating register machine, we proved that using the model we created, spiking neural systems could calculate any set of Turing computable numbers as the number generators.In standard spiking neural membrane systems, there is a potential NP-complete prob-lem to determine whether a spiking rule can be applied or not. It is also not in accordance with biological facts in biological neural networks. This dissertation established a new de-termine method by introducing membrane potential to replace spikes, and real number to replace natural number, into the systems. It saves large amount of computing time, enables the system to handle problems related to rational numbers, improves the system functions and computing power, and extends scope of problems that it could solve. By simulating register machine, we proved that spiking neural membrane systems are computationally completed and solve computing difficulty problems. In these systems, if we use natural numbers instead of integers, the systems can only characterize semi-linear set of numbers.We construct another two new systems respectively using the features of budding rules and neuron division, to generate the needed computational space, subsequently transform the space in to time, solving the problem of low computational efficiency of spiking neural membrane systems. This dissertation proved that these two systems can solve all instances of NP-complete problem in a polynomial time.