【作者】 张弘；

【导师】 郭平；

【作者基本信息】 重庆大学 ， 计算机应用技术， 2014， 硕士

【摘要】 膜计算是自然计算的一个新分支，它是根据对生物体内活细胞功能和结构的研究抽象出来的一种新的计算模型。膜计算的一个最大优点就是其能够以最大的并行度实现相应的计算。已经证明，膜计算与图灵机有等价的计算能力，其强大的并行计算能力可以有效解决目前电子计算机所面临的瓶颈。本文通过对基于膜计算的算术运算系统研究，包括基于多重集的混合编码、分式约简和素因素分解问题，为生物计算机的实现奠定坚实的基础。由于目前膜计算中的算术运算还有待研究，所以本论文通过对基于多重集的混合编码、分式约简和素因素分解的研究，用于验证求解复杂算术问题的可行性。本论文所完成的研究工作如下：1)现有的大部分算术P系统的操作数采用位置编码或者非位置编码的多重集来表示。根据这些编码方式存在的不足之处，设计了基于混合编码的基本算术运算P系统，以实现大操作数在P系统中的算术运算。与此同时，举出例子详细阐述规则的执行流程，并利用电子计算机实现了基于混合编码的基本算术运算P系统的仿真实验，对所构造的P系统分别进行验证。2)提出并证明了适用于类细胞P系统的分式约简求解方法，根据提出的分式约简算法设计了基于规则优先级的分式约简P系统，结合例子详细阐述了规则的执行流程，并利用电子计算机实现了基于规则优先级的分式约简P系统的仿真实验，对所构造的P系统进行验证。3)讨论了素数分解的相关理论基础和类细胞P系统中素因素分解方法，根据提出的素数分解算法设计了基于混合编码的素因素分解P系统，并结合例子详细阐述了规则的执行流程。本文的研究成果更加丰富了膜计算中算术运算的理论，研究了基于多重集的混合编码、以分式约简和素数分解作为研究实例，扩大了算术P系统的使用范围，可作为今后研究相关问题的参考资料。更多还原

【Abstract】 Membrane computing is a new branch of natural computing and abstracts computingmodels from the architecture and the functioning of living cells. One of the biggestadvantages of membrane computing is that it can achieve calculations in maximumdegree of parallelism. It was proved that the computing power of membrane computingis equivalent to that of Turning machine, and membrane computing’s powerful parallelcomputing ability can effectively solve the bottleneck that current computer faced. Inthis paper, our study direction is arithmetic operation systems in membrane computing,which includes hybrid encoding over multisets, fraction reduction and primedecomposition, and then lays a solid foundation for the realization of the biologicalcomputer.Because of the arithmetic operation remains to be studied, by studying hybridencoding over multisets, fraction reduction and prime decomposition, this paper able toverify the feasibility of solving complex arithmetic problems. The following is anintroduction to the work of completed studied in this paper:1) Most of existing P systems are proposed to perform arithmetic operations withthe operands encoded by positional or non-positional encodings over multisets.According to the shortcoming of these encodings, this paper presents a family ofcell-like P systems for primary arithmetic operations based on hybrid encoding,implementing arithmetic operations for large numbers by P systems. At the same time,we give examples to describe the implementation process of the rules in detail, andachieve to simulation of the P system respectively for hybrid encoding over multisets byusing computer, which is used to virify the constructed P systems.2) Propose and prove a method of fraction reduction and discuss how to carry it outin cell-like P systems with the membrane structure and the rules with priority designedaccording to the proposed algorithm. Then we give example to describe theimplementation process of the rules in detail, and achieve to simulation of the P systemfor fraction reduction by using computer, which is used to virify the constructed Psystems.3) Discuss the theoretical basis of prime decomposition and the method of primedecomposition which is suitable in cell-like P systems. Then design the primedecomposition P system based on hybrid encoding and give example to describe the implementation process of the rules in detail.Results of this paper is to further enrich the theory of arithmetic operations in the membranecomputing, and it extends application of arithmetic P systems through studying hybridencoding over multisets, fraction reduction and prime decomposition, so it is able tobecome the references that improve the other problems.更多还原