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研究生: 吳樹恆
Shu-Han Wu
論文名稱: 由網路觀點看布林函數在 Von Neumann 域之動態行為
Network perspective of the dynamics of Boolean mappings in Von Neumann neigjborhood
指導教授: 施茂祥
Shih, Mau-Hsiang
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2005
畢業學年度: 93
語文別: 英文
論文頁數: 17
中文關鍵詞: 布林函數有向圖固定點迭代圖離散微分影響矩陣
英文關鍵詞: Boolean mapping, Digraph, Fixed point, Iteration graph, Discrete derivative, Incidence matrix
論文種類: 學術論文
相關次數: 點閱:229下載:7
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  • 給定一個布林函數F由{0,1}^n送到{0,1}^n,我們可以得到F的迭代圖,更進一步的說,我們可以考慮F的影響矩陣B(F)以及F在x點的離散微分F'(x),離散微分F'(x)是一個布林矩陣可以對應到一個n個點的有向圖Γ(F'(x)),也就是說,我們可以藉由F的迭代圖與有向圖Γ(F'(x))來觀察F的行為,在這篇文章裡面我們將由網路觀點來研究布林函數F在 Von Neumann 域之動態行為。

    Give a Boolean mapping F from {0,1}^n
    to {0,1}^n, we get a iteration graph for F.
    Furthermore, we may consider the incidence matrix B(F) and the discrete derivative
    F'(x) of F at x in {0,1}^n. In fact,
    B(F)=sup_{x in {0,1}^n}{F'(x)}.
    The discrete derivative F'(x), which is a Boolean matrix, can correspond to a
    direct graph Γ(F'(x))
    with n nodes. That is to say, we can estimate the function F from the iteration
    graph of F and the direct graph Gamma(F'(x)). In this paper, we search for the dynamics of
    the Boolean mapping F in von Neumann
    neighborhood from network structure.

    1. Induction........................1 2. Definition and notations.........2 3. Some useful properties...........7 4. The main problem.................10 5. Conclusion.......................17

    [1] E. Goles and S. Martinez, "Neural and Automata Networks, Dynamical Behavior and Applications," Kluwer Academic, Dordrecht-Boston-London, 1991.
    [2] F. Robert, "Discrete Iteration, A Metric Study,"
    Springer Series in Computational Mathematics, Springer-Verlag, Berlin-Heidelberg-New York, 1986.
    [3] M.-H. Shih and J.-L. Dong, A combinatorial
    analogue of the Jacobian problem in automata networks,
    Advances in Applied Mathematics, 34 (2005), 30-46.
    [4] M.-H. Shih and J.-L. Ho, Solution of the Boolean Markus-Yamabe Problem, Advances in Applied Mathematics, 22 (1999), 60-102.

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