形式化多维结构膜计算模型研究与应用

项目名称： 形式化多维结构膜计算模型研究与应用

项目编号： No.61472231

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 计算机科学学科

项目作者： 刘希玉

作者单位： 山东师范大学

项目金额： 80万元

中文摘要： 膜计算是近年来提出的基于细胞结构的新型计算模型，是生物计算中新的和快速发展的分支，也是继DNA计算后最重要的生物计算模型。目前为止常见的膜计算模型大致有三类：类细胞P系统、类组织P系统、类神经P系统，这些膜计算模型的共同特点是其形式化拓扑结构（链接结构）为图类结构，其链接关系为一维。本研究的目的是研究提出一种多维结构形式化膜计算模型，其链接结构建立在单纯复合型之上，这种结构的一维情形即为图。多维结构期望可更好的描述生物细胞的立体结构和复杂多向信息交互关系，在形式化意义上也将拓扑结构从一位拓展到了高维。项目将研究单纯复合型P系统的模型构造和规则设计，证明代表其计算能力的计算完备性，并与其它膜系统进行一定对比。我们还将研究一种符合膜计算模型，即基于链式结构的抽象膜模型。项目还将研究膜计算在聚类分析中的应用，描述可用于聚类分析这种优化问题的P系统模型，设计仿真实验并进行时间和空间复杂度分析。

中文关键词： 膜计算；计算智能；数据挖掘

英文摘要： Membrane computing is a new computing model based on cell structures. It is a new and fast evolving branch of biological computing while it is the most important biological computing model since the founding and development of DNA computing. Up to now there are three categories of membrane computing models, that is, the cell-like P systems, the tissue-like P systems, and the neural-like P systems. The common feature of these P systems is that the formal topological structure, or its information exchange structure, is a one dimensional data structure. This data structure is mainly a tree, or a graph. The purpose of this research is to propose a multi-dimensional formal membrane computing model based on simplex. The topological structure, or data structure, of this model is a simplex, or simplicial complex. In the one-dimensional case, this structure coincides with the traditional model, i.e., the graph model. With the help of this new model it is expected to better describe the spatial structure of cells and complicated multi-modal information exchange therein. In the sense of topological structure we extend the one dimensional data structure of traditional P systems to multi-dimensional structures. In this project we will propose new membrane models with rules. Computation completeness will be proved. We will also propose a hybrid abstract chain membrane model with chain rules. Comparison with traditional P systems will be made. Research on cluster analysis of membrane computing will also be a focus of this research. Specific membrane models for cluster analysis as well as other optimization problems will be designated. Experimental simulation and complex analysis will be performed to show the effects of the new algorithms.

英文关键词： membrane computing;computational intelligence;data mining