Research On The Computational Power Of Spiking Neural P Systems With Differential Biological Backgrounds

With the rapid development of computer technology, looking for a computing device dealing with large-scale information more quickly and effectively has became one of the serious problems to be solved. Inspired by the structure and functioning of biological cells, a non-conventional model-P system is proposed by Gh. Paun to provide a new research direction for the development of Computer Science.As distributed parallel computing model, P systems mainly include cell-like P systems, tissue-like P systems and neural-like P systems. The computational power of spiking neural P systems are improved by astrocytes. Moreover, inspired by different biological Back-grounds, several new variants of spiking neural P systems are presented, and the work deals with the computational power of spiking neural P systems. The details about this work are as follows:Based on the computational power of spiking neural P systems with astrocytes as num-ber generating devices, we investigate the computational power of such systems as language generators in synchronized and non-synchronized modes, respectively. In the synchronized manner, the power of spiking neural P systems as language generators is improved because of the astrocytes. The finite language of form {0,1} can be generated by spiking neural P systems with astrocytes, but cannot by spiking neural P systems without astrocytes. In the case of no forgetting rule or the delay feature of firing rules, spiking neural P systems remain equivalent with Turing machines because of the astrocytes. In the non-synchronized manner, we not only construct a class of spiking neural P systems which can characterize recursively enumerable languages, but also construct a class of Petri nets equivalent to such systems.From the universality and reversibility aspects, the further studies on the power of spiking neural P systems with astrocytes are shown. Aiming to optimize the computing re-sources and keep the computational completeness, a small universal spiking neural P system with astrocytes is constructed. By reducing the number of additional neurons and sharing neurons between instructions, we effectively reduce the computing resources of such sys-tems, obtaining the following results:there is a universal spiking neural P system having57neurons and19astrocytes for Turing computing functions; there is a universal spiking neural P system having54neurons and17astrocytes for Turing computing numbers. In order to research the computational efficiency, the reversible spiking neural P systems with astrocytes are considered. When the number of spikes contained in neurons is unbounded, such systems can do what Turing machines can do. When the number of spikes contained in neurons is bounded, such systems can generate finite sets of numbers.In human brain, the synapses between neurons not only transmit spikes, but also deal with the information; the spikes transfer is affected by the strength of synapses connec-tions between neurons. Inspired by such biological feature, spiking neural P systems with rules and weights on synapses are considered. In such systems, the neurons contain spikes, the rules are moved on the synapses and each synapse is assigned with weight. If sever-al synapses starting from the same neuron are fired at the same time, then the number of consumed spikes by them should be less than or equal to the number of spikes contained in the neuron. Otherwise, a subset of these synapses is chosen to fire, and the number of consumed spikes by the subset should be maximal but not larger than the number of spikes contained in the neuron. When the number of spikes consumed by synapses is unbounded, such systems as generating devices are Turing universal, which can generate any recursively enumerable set and k-dimensional vectors of positive integers. If the consumed spikes by synapses is bounded, the semi-linear sets can be characterized, and the systems can simulate the sequential strictly monotonic k-output register machine。In biological systems, the communication between different cells is affected by pro-tein channel state. According to the biological background, spiking neural P systems with synapses states are presented. In such systems, each synapse has a given state; the form of firing rule is E/αc→(α,s);d, indicating that the produced spike should pass along the synapses with states s, otherwise it is removed and cannot reach its destination neurons. The computational power of such systems as generating and accepting devices is studied, respec-tively. And we try to simulate the basic statements and constructors of parallel programming language Occam by spiking neural P systems with synapse states. Inspired by the energy change in the process of neural activity, a class of spiking neural P systems with energy is introduced. In such systems, the neurons contain the objects, energy and evolution rules as well as the spikes, the firing rules and forgetting rules. The objects in a neuron can be evolved by evolution rules with producing or consuming some quantity of energies. The application of firing rules and forgetting rules should consume some quantity of energies. The computational power of such systems is discussed, and the obtained results indicate that such systems are Turing universal in generative mode. And there is a universal spiking neural P system with energy having5neurons for Turing computing.