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:205 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] 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.