本文關(guān)鍵詞：有理數(shù)域中膜計(jì)算的表達(dá)式求值　出處：《重慶大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： P系統(tǒng) 膜計(jì)算 有理數(shù)算術(shù)運(yùn)算 有理數(shù)表達(dá)式求值

【摘要】：根據(jù)摩爾定律的表述，集成電路上可容納的晶體管數(shù)目，約每隔18個(gè)月便會(huì)增加一倍。但是，晶體管數(shù)目不可能無(wú)限制的增加，它總會(huì)達(dá)到一個(gè)極限。另外由于電子計(jì)算機(jī)自身計(jì)算性能存在局限性（因?yàn)閺谋举|(zhì)上講電子計(jì)算機(jī)是串行工作的），所以選擇一種新型的計(jì)算模型代替電子計(jì)算機(jī)已經(jīng)成為當(dāng)下需要研究解決的問(wèn)題。而其中選擇生物計(jì)算機(jī)作為替代模型擁有為數(shù)眾多的支持者，之所以選擇生物計(jì)算機(jī)是基于其兩點(diǎn)明顯的優(yōu)勢(shì)：極低的能量消耗、極高的并行特性。 膜計(jì)算是生物計(jì)算的一個(gè)新分支，它是通過(guò)研究生物體內(nèi)細(xì)胞膜的生命進(jìn)化過(guò)程，從而抽象出來(lái)的計(jì)算模型。膜計(jì)算也可以被稱為P系統(tǒng)，該研究方向由羅馬尼亞科學(xué)家Gheorghe.P un創(chuàng)立于1998年，并已迅速發(fā)展為擁有很大潛力的科學(xué)領(lǐng)域，，它的出現(xiàn)為許多領(lǐng)域的重難點(diǎn)問(wèn)題帶來(lái)了新的求解思路。本文研究的是膜計(jì)算領(lǐng)域中的一個(gè)方向，即有理數(shù)域中的算術(shù)運(yùn)算和表達(dá)式求值。通過(guò)對(duì)有理數(shù)域中膜計(jì)算的算術(shù)運(yùn)算以及表達(dá)式求值的研究，為以后實(shí)現(xiàn)生物計(jì)算機(jī)奠定堅(jiān)實(shí)的基礎(chǔ)。 由于目前膜計(jì)算算術(shù)運(yùn)算的研究停留在整數(shù)域內(nèi)，所以本論文通過(guò)對(duì)有理數(shù)域中算術(shù)運(yùn)算P系統(tǒng)的研究，來(lái)擴(kuò)展算術(shù)P系統(tǒng)的使用范圍，使之進(jìn)一步提高生物計(jì)算機(jī)的計(jì)算能力。下面就簡(jiǎn)單介紹一下本論文所完成的研究工作： 1)根據(jù)膜計(jì)算的基礎(chǔ)思想及執(zhí)行特點(diǎn)，設(shè)計(jì)了基于規(guī)則優(yōu)先級(jí)的有理數(shù)算術(shù)運(yùn)算P系統(tǒng)，為有理數(shù)膜計(jì)算表達(dá)式求值的實(shí)現(xiàn)奠定基礎(chǔ)。 2)通過(guò)利用有理數(shù)域中算術(shù)運(yùn)算P系統(tǒng)，設(shè)計(jì)了基于有理數(shù)域表達(dá)式膜結(jié)構(gòu)的構(gòu)造算法以及膜計(jì)算執(zhí)行算法。 3)利用電子計(jì)算機(jī)實(shí)現(xiàn)了有理數(shù)表達(dá)式求值的仿真，對(duì)有理數(shù)算術(shù)P系統(tǒng)以及表達(dá)式膜結(jié)構(gòu)構(gòu)造算法進(jìn)行了驗(yàn)證。 4)通過(guò)對(duì)約分規(guī)則的研究，實(shí)現(xiàn)了對(duì)最終結(jié)果形式的簡(jiǎn)化。 本文的研究成果進(jìn)一步豐富了膜計(jì)算中算術(shù)運(yùn)算及表達(dá)式求值的理論，擴(kuò)大了算術(shù)運(yùn)算P系統(tǒng)的應(yīng)用范圍，可以作為今后完善其他問(wèn)題的參考資料。
[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.

【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：TP38;O156

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本文編號(hào)：1383639