Research On Spiking Neural P Systems With A Minimal Parallelism Of Using Of Rule

Membrane computing is a branch of natural computing which was abstracted from the structure and the functioning of biological cells. In the basic model, the membrane systems (P systems, for short) are distributed parallel computing devices in the compartments delimited by the mosaic model of the membrane structure. However, neurons are a kind of special cells which connect to each other and form a network; the P systems are not suitable for the modeling of spiking neural nets directly. Recently, a new model called spiking neural P systems (SN P systems, for short) is introduced in this field in order to propose a computational concept which mimics the way that neurons communicate with each other by means of short electrical impulses. It is known that SN P systems are computational universality. Since its first publication, SN P systems have already attracted a lot of attention of researchers. In this dissertation, the main contributions of the aspect are outlined as follows:1. In SN P systems, the neurons can contain several rules which can be used simultaneously. This leads to a non-deterministic way of using the rules. Therefore, non-deterministic systems need lots of rules in the neurons. How to decrease the number of rules? In order to solve the problem, we consider SN P systems with a new type of rule application: whenever a rule (spiking and forgetting rules are written in the same way) is enabled in a neuron, it is used in a minimal parallel manner, i.e., if a rule associated with a neuron can be used many times, then the rule must be used at least one time. Thus, the number of the times of spiking in a step in that neuron can be arbitrarily; all produced spikes are transmitted to neighboring neurons through synapses. In this way, just one rule in the neuron can leads to a non-deterministic systems. Also, in this framework, we prove the computational completeness of our systems.2. There are several kinds of rules in the SN P systems; however, the rules are not necessary all the times. Eliminating both the delay and forgetting rules made the systems easier. Then, we continue the study of SN P systems with a minimal parallel using of rule and in this case pass to focusing on normal forms of the systems ( SN mnoirn P systems , for short) while preserving their computational power. We demonstrate that the new models are also universal when eliminating both delays and forgetting rules at the same time. Finally, we get a characterization of finite sets of numbers and semilinear sets of numbers.