Dynamics of linear systems over finite commutative rings

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• 作者：Yangjiang Wei ; Guangwu Xu ; Yi Ming Zou
• 关键词：Finite ring ; Module ; Linear system ; Cycle length
• 刊名：Applicable Algebra in Engineering, Communication and Computing
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：27
• 期：6
• 页码：469-479
• 全文大小：401 KB
• 刊物类别：Computer Science
• 刊物主题：Symbolic and Algebraic Manipulation
  Computer Hardware
  Theory of Computation
  Artificial Intelligence and Robotics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0622
• 卷排序：27

文摘

The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous publication, the last two authors developed an efficient algorithm to determine whether a linear dynamical system over a finite commutative ring is a fixed point system or not. The algorithm can also be used to reduce the problem of finding the cycles of such a system to the case where the system is given by an automorphism. Here, we further analyze the cycle structure of such a system and develop a method to determine its cycles.