【摘要】：經(jīng)過近幾十年的發(fā)展,人們希望第四代計(jì)算機(jī)(即超大規(guī)模集成電路計(jì)算機(jī))具有更多的類似人的智能,于是開始尋找第五代的計(jì)算機(jī)來取代它們,例如：生物計(jì)算機(jī),量子計(jì)算機(jī)等。其中膜計(jì)算是生物計(jì)算的重要分支,它通過模擬細(xì)胞及其組織的結(jié)構(gòu)與功能,構(gòu)造出具有分布式結(jié)構(gòu)的并行計(jì)算模型。我們研究的是其中一種網(wǎng)狀膜系統(tǒng),即脈沖神經(jīng)膜系統(tǒng)。這種膜計(jì)算模型源自于生物神經(jīng)系統(tǒng)中神經(jīng)元通過突觸傳遞脈沖交換信息的機(jī)制。本文通過結(jié)合形式語言和自動(dòng)機(jī)理論,從語言的產(chǎn)生能力、計(jì)算通用性和有效性以及數(shù)的識(shí)別能力幾方面,對多種具有其它生物特性的脈沖神經(jīng)膜系統(tǒng)進(jìn)行了研究,主要工作如下： 針對神經(jīng)元周圍的星狀神經(jīng)膠質(zhì)細(xì)胞可以對神經(jīng)元間的相互左右產(chǎn)生重要影響的現(xiàn)象,本文建立了一種具有星細(xì)胞的脈沖神經(jīng)膜系統(tǒng)。通過模擬注冊機(jī),證明了在同步模式下,該系統(tǒng)可實(shí)現(xiàn)計(jì)算通用性。如果我們限制系統(tǒng)中每個(gè)神經(jīng)元中的脈沖數(shù)目,那么該系統(tǒng)可以刻畫自然數(shù)的半線性集合。另外在異步工作模式下,這種神經(jīng)元和星細(xì)胞結(jié)合起來的新系統(tǒng)也是等價(jià)于圖靈機(jī)的。這些結(jié)果表明,盡管神經(jīng)元很簡單,但是它組成的網(wǎng)絡(luò)卻可以具有很強(qiáng)的計(jì)算能力。 針對Ibarra等人提出的,使用標(biāo)準(zhǔn)規(guī)則的異步脈沖神經(jīng)膜系統(tǒng)是否具有通用性的公開問題,本文提出了一種具有激發(fā)時(shí)限的異步模式,在此模式下,所有的激發(fā)規(guī)則都具有同一個(gè)激發(fā)時(shí)限,我們通過模擬注冊機(jī),證明了使用標(biāo)準(zhǔn)規(guī)則的脈沖神經(jīng)膜系統(tǒng)可以達(dá)到計(jì)算通用性,解決了公開問題。 在經(jīng)典的脈沖神經(jīng)膜系統(tǒng)中,判斷一條激發(fā)規(guī)則的使用與否,有時(shí)可能是NP困難的,這在某種程度上也不符合生物神經(jīng)系統(tǒng)的現(xiàn)實(shí)。本文引入細(xì)胞膜電勢來代替脈沖值,建立了一種新的規(guī)則判斷方式,避免了大量的計(jì)算損耗。另外用有理數(shù)取代自然數(shù)來表示各種參數(shù),使系統(tǒng)可以處理跟有理數(shù)有關(guān)的問題,提升了系統(tǒng)的功能與計(jì)算能力,擴(kuò)大了解決問題的范圍。通過模擬注冊機(jī),我們證明了這種帶權(quán)值的脈沖神經(jīng)膜系統(tǒng)可以實(shí)現(xiàn)計(jì)算通用性,并能求解計(jì)算困難問題。該系統(tǒng)使用自然數(shù)來表示各種參數(shù)時(shí),只能刻畫數(shù)字的半線性集合。 針對脈沖神經(jīng)膜系統(tǒng)的計(jì)算效率問題,我們分別使用生物里面神經(jīng)元分裂和芽殖的特性創(chuàng)建了兩種新的系統(tǒng),來生成所需的計(jì)算空間,從而實(shí)現(xiàn)空間換時(shí)間。本文證明這兩種系統(tǒng)可求解著名的NP完全問題,可以在多項(xiàng)式時(shí)間內(nèi)求解給定規(guī)模的NP完全問題的所有算例。
[Abstract]:After decades of development, people wanted the fourth-generation computers (that is, VLSI computers) to have more human-like intelligence, so they began to look for fifth-generation computers to replace them, such as biological computers. Quantum computers, etc. Membrane computing is an important branch of biological computing. By simulating the structure and function of cells and their tissues, a parallel computing model with distributed structure is constructed. We study one of the reticular membrane systems, the impulsive membrane system. The membrane computing model is derived from the mechanism of the transmission of information by synaptic pulses in the biological nervous system. In this paper, by combining formal language and automata theory, a variety of impulsive neural membrane systems with other biological characteristics are studied from the aspects of language generation ability, computational generality and validity, and recognition ability of numbers. The main work is as follows: aiming at the phenomenon that astroglial cells around neurons can exert important influence on the left and right of neurons, a pulsed neuromembrane system with star cells is established in this paper. By simulating the registration machine, it is proved that the system can be used to calculate generality in synchronous mode. If we limit the number of impulses in each neuron in the system, the system can characterize the semilinear set of natural numbers. In asynchronous mode, the new system, which combines neurons with star cells, is also equivalent to Turing machine. These results show that although the neuron is simple, the network can have strong computational power. In order to solve the open question whether the asynchronous pulse membrane system using standard rules is universal, an asynchronous mode with excitation time limit is proposed in this paper. All the excitation rules have the same excitation time limit. By simulating the registration machine, we prove that the pulse nerve-membrane system using the standard rules can achieve the universal calculation and solve the open problem. In the classical impulsive membrane system, it may be difficult for NP to judge the use of an excitation rule, which to some extent does not accord with the reality of the biological nervous system. In this paper, the cell membrane potential is introduced to replace the pulse value, and a new regular judgment method is established to avoid a large amount of computational losses. In addition, rational numbers are used to represent various parameters instead of natural numbers, so that the system can deal with problems related to rational numbers, enhance the system's function and computational power, and expand the scope of solving problems. By simulating the registration machine, we prove that the weighted impulsive neural membrane system can be used to calculate generality and solve the difficult problems. When the system uses natural numbers to represent all kinds of parameters, it can only depict the semilinear set of numbers. To solve the problem of computational efficiency of impulsive membrane system, we have created two new systems using the characteristics of neuron division and bud colonization in biology to generate the necessary computing space and realize space exchange time. In this paper, it is proved that these two systems can solve famous NP complete problems, and can solve all examples of NP complete problems of a given size in polynomial time.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：TP387

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