布尔网络
吸引子
数学
布尔函数
逻辑矩阵
基质(化学分析)
状态转移矩阵
离散数学
张量积
产品(数学)
矩阵乘法
线性系统
纯数学
对称矩阵
数学分析
群(周期表)
材料科学
几何学
化学
有机化学
复合材料
特征向量
物理
量子
量子力学
作者
Daizhan Cheng,Hongsheng Qi
出处
期刊:IEEE Transactions on Automatic Control
[Institute of Electrical and Electronics Engineers]
日期:2010-10-01
卷期号:55 (10): 2251-2258
被引量:589
标识
DOI:10.1109/tac.2010.2043294
摘要
A new matrix product, called semi-tensor product of matrices, is reviewed. Using it, a matrix expression of logic is proposed, where a logical variable is expressed as a vector, a logical function is expressed as a multiple linear mapping. Under this framework, a Boolean network equation is converted into an equivalent algebraic form as a conventional discrete-time linear system. Analyzing the transition matrix of the linear system, formulas are obtained to show a) the number of fixed points; b) the numbers of cycles of different lengths; c) transient period, for all points to enter the set of attractors; and d) basin of each attractor. The corresponding algorithms are developed and used to some examples.
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