有理数域中膜计算的表达式求值

发布时间：2018-01-05 15:08

本文关键词：有理数域中膜计算的表达式求值　出处：《重庆大学》2012年硕士论文　论文类型：学位论文

【摘要】：根据摩尔定律的表述，集成电路上可容纳的晶体管数目，约每隔18个月便会增加一倍。但是，晶体管数目不可能无限制的增加，它总会达到一个极限。另外由于电子计算机自身计算性能存在局限性（因为从本质上讲电子计算机是串行工作的），所以选择一种新型的计算模型代替电子计算机已经成为当下需要研究解决的问题。而其中选择生物计算机作为替代模型拥有为数众多的支持者，之所以选择生物计算机是基于其两点明显的优势：极低的能量消耗、极高的并行特性。膜计算是生物计算的一个新分支，它是通过研究生物体内细胞膜的生命进化过程，从而抽象出来的计算模型。膜计算也可以被称为P系统，该研究方向由罗马尼亚科学家Gheorghe.P un创立于1998年，并已迅速发展为拥有很大潜力的科学领域，，它的出现为许多领域的重难点问题带来了新的求解思路。本文研究的是膜计算领域中的一个方向，即有理数域中的算术运算和表达式求值。通过对有理数域中膜计算的算术运算以及表达式求值的研究，为以后实现生物计算机奠定坚实的基础。由于目前膜计算算术运算的研究停留在整数域内，所以本论文通过对有理数域中算术运算P系统的研究，来扩展算术P系统的使用范围，使之进一步提高生物计算机的计算能力。下面就简单介绍一下本论文所完成的研究工作： 1)根据膜计算的基础思想及执行特点，设计了基于规则优先级的有理数算术运算P系统，为有理数膜计算表达式求值的实现奠定基础。 2)通过利用有理数域中算术运算P系统，设计了基于有理数域表达式膜结构的构造算法以及膜计算执行算法。 3)利用电子计算机实现了有理数表达式求值的仿真，对有理数算术P系统以及表达式膜结构构造算法进行了验证。 4)通过对约分规则的研究，实现了对最终结果形式的简化。本文的研究成果进一步丰富了膜计算中算术运算及表达式求值的理论，扩大了算术运算P系统的应用范围，可以作为今后完善其他问题的参考资料。
[Abstract]:According to the description of Moore's law, the number of transistors on an integrated circuit can accommodate, about every 18 months will be doubled. However, can not be increased without limit the number of transistors, it will reach a limit. In addition to the computer itself computing performance limitations (because that computer is essentially a serial work), so the choice of a new computing model to replace the electronic computer has become the current need to study and solve the problem. Which chooses biologicalcomputer as an alternative model has a large number of supporters, so choose biological computer is based on two obvious advantages: low energy consumption, high parallelism.
Membrane computing is a new branch of biological computing, it is through the life evolution of organism cell membrane process, which is abstracted. The calculation model of membrane computing can also be called the P system, the research direction was founded in 1998 by Romania scientist Gheorghe.P UN, and has rapidly developed into a field of science with great potential bring a new way of solution, it appears as a problem in many fields. This paper is a direction in the field of membrane computing, which is the field of rational numbers in arithmetic and arithmetic expression evaluation. Through the calculation of rational number field in the film and expression evaluation, to lay a solid foundation for the future implementation of biological computer.
Due to the current calculation of the arithmetic for membrane in the integer domain, so the study of arithmetic P system rational number field in this paper, to expand the range of application of arithmetic P system, to further improve the computing ability of biological computer. Following a brief introduction about the research work completed in this thesis:
1) according to the basic idea and implementation characteristics of membrane computing, a P system based on rule priority is designed, which lays the foundation for the realization of rational number membrane computing expression evaluation.
2) by using the arithmetic operation P system in rational number domain, a structure algorithm based on rational domain expression membrane structure and a membrane computing execution algorithm are designed.
3) the simulation of rational number expression evaluation is realized by electronic computer, and the rational number arithmetic P system and the construction algorithm of the expression membrane structure are verified.
4) through the research on the reduction rules, the final results form simplified.
The research results of this paper further enrich the theory of arithmetic operation and expression evaluation in membrane computing, expand the application scope of arithmetic operation P system, and serve as references for other problems in the future.

【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TP38;O156

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