【摘要】：摘要：膜計算是自然計算的新分支,是計算機科學、數(shù)學、生物學等眾多學科交叉的研究領域,旨在從細胞的結構和功能,以及從組織和器官等細胞群相互協(xié)作處理信息的方式中,抽象出新的計算模型,也稱為膜系統(tǒng)或P系統(tǒng)。 脈沖神經膜系統(tǒng)是膜計算中的一種神經型P系統(tǒng),是源于大腦神經元之間通過電脈沖進行信息傳遞的生物現(xiàn)象,并吸收脈沖神經網絡的特點而提出的一種新型的分布式、并行計算模型。 本文從計算理論、應用和軟件仿真研究三個方面分別對幾類脈沖神經膜系統(tǒng)的計算能力、小通用性、邏輯與算術運算實現(xiàn)方法以及模型的形式化驗證等內容進行了研究,主要工作如下： 研究了同質脈沖神經膜系統(tǒng)的小通用性：在使用標準規(guī)則和權值情況下,作為計算函數(shù)的裝置,需要53個神經元可以構造一個通用同質脈沖神經膜系統(tǒng)；作為產生數(shù)的裝置,則需要52個神經元。研究脈沖神經膜系統(tǒng)的小通用性問題既具有計算機科學上的意義,也具有生物學上的用義：尋找小通用“腦”。 研究了突觸上帶權值和突觸上不帶權值的兩種同質脈沖神經膜系統(tǒng)在不使用具有延遲的激發(fā)規(guī)則情況下的計算通用性問題,并證明了這兩種不帶延遲的同質脈沖神經膜系統(tǒng)無論是工作在產生模式下,還是工作在接收模式下都是計算通用的。解決了曾湘祥等人提出的關于不帶延遲的同質脈沖神經膜系統(tǒng)是否具有計算通用性的公開問題。同時,也構造了不使用延遲激發(fā)規(guī)則的突觸上帶權值和不帶權值的兩類同質延展脈沖神經膜系統(tǒng),并證明了它們的計算通用性。 研究了無延遲規(guī)則和突觸權值情況下的帶反脈沖同質脈沖神經膜系統(tǒng)的計算通用性問題,證明了這種膜系統(tǒng)無論是工作在產生模式,還是接收模式下都是計算通用的。研究結果能同時解決了曾湘祥等人提出的關于是否存在無延遲規(guī)則的同質脈沖神經膜系統(tǒng)和如何有效移除突觸權值的兩個公開問題。 考慮在脈沖神經膜系統(tǒng)這種裝置上處理一些簡單的邏輯與算術運算問題,構建了包括實現(xiàn)二進制補碼轉換、實現(xiàn)有符號整數(shù)的加、減法運算和實現(xiàn)任意兩個自然數(shù)的乘法運算的多族脈沖神經膜系統(tǒng),這些系統(tǒng)的輸入、輸出數(shù)均采用二進制方式,編碼采用合適的脈沖序列。較好地解決了Gutierrez-Naranjo MA.和Leporati A.提出的關于如何實現(xiàn)兩個任意自然數(shù)乘法運算的公開問題。當前工作可以作為解決更加復雜問題的基礎,也有助于設計基于脈沖神經膜系統(tǒng)的生物型“CPU”。 使用帶反脈沖的脈沖神經膜系統(tǒng)分別構建了能實現(xiàn)對稱三值的通用與、或、非邏輯門功能和實現(xiàn)對稱三值的整數(shù)加、減算術運算功能的多族脈沖神經膜系統(tǒng)。目前的工作是基于帶反脈沖的脈沖神經膜系統(tǒng)的三值型“CPU”設計在理論上的首次嘗試,也為潘林強和Paun G提出的一個公開問題提供了首個實用案例。 基于SnpsGUI仿真軟件,例證了兩個脈沖神經膜系統(tǒng)的形式化驗證過程,重點分析并揭示了格局轉移圖和脈沖神經膜系統(tǒng)之間的內在聯(lián)系,并總結出了三個一般性結論,達到了通過計算機輔助驗證脈沖神經膜系統(tǒng)正確性與完整性的目的。同時,對基于脈沖神經膜系統(tǒng)更有效的形式化驗證方法提出了展望,對SnpsGUI軟件進行了評述,提出了改進方向。
[Abstract]:Abstract: Membrane calculation is a new branch of natural calculation. It is the research field of computer science, mathematics, biology and so on. It aims to abstract a new computing model from the structure and function of cells and the way of processing information from cell groups such as tissues and organs. also known as membrane systems or p systems. The pulse nerve membrane system is a kind of nerve type P system in the calculation of membrane, which is a new kind of distributed and parallel computing based on the biological phenomenon of information transmission between nerve cells and the characteristics of pulse neural network. In this paper, three aspects, such as computing power, small universality, logic and arithmetic operation, and formal verification of models, are studied from three aspects: computing theory, application and software simulation. To work as follows: To study the small versatility of a homogeneous pulsed neural membrane system: in the case of using standard rules and weight values, 53 neurons may be required to construct a universal homogeneous pulse neural membrane system; as a means of generating numbers, then 52 neurons are required. The study of the small versatility of the pulsed neural membrane system has both the meaning of computer science and biology. a sense of righteousness: In this paper, we study the general problem of the two homogeneous pulse neural membrane systems with the right value on the synapse and the non-band right in the synapse without using the delayed excitation rule, and prove the two non-delayed homogeneous pulse neural membrane systems. Whether it's working in the production mode, it's still working. The invention solves the problem of whether or not the homogeneous pulse nerve membrane system with delay, which has been proposed by Xiang Xiang, et al. At the same time, there are two kinds of homogeneous extended pulse neural membrane systems which do not use delayed excitation rules, and the two kinds of homogeneous extended pulse neural membrane systems with no right value are also constructed. In this paper, the computational versatility of an anti-pulse homogeneous pulse neural membrane system with non-delay rule and synapse weight is studied. It is proved that this kind of membrane system works in the generating mode. It is also common in the receiving mode. The results of this study can solve the problem of whether there is a homogeneous pulse nerve membrane system with no delay rule and how to have the same In order to solve the problem of simple logic and arithmetic operation on the device of pulse neural membrane system, we construct a method which includes realizing twos complement conversion, realizing adding and subtracting operation with sign integer and realizing any two self-functions. The multi-family pulse neural membrane system based on the multiplication of numbers, the input and output of these systems are all adopted. Binary mode, coding adopts a suitable pulse sequence. Better solve Gu tierrez-Naranjo MA. and Leephii A. How to real The present invention can be used as a basis for solving more complex problems, Type 鈥淐PU鈥，

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