Limit Set Problem of Multi-Agent Systems with Finite States: An Eigenvalue-Based Approach

作     者：WANG Lin WANG Xiaofan WANG Jinhuan 

作者机构：Department of Automation Shanghai Jiao Tong University and Key Laboratory of System Control and Information Processing Ministry of Education School of Sciences Hebei University of Technology 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2015年第28卷第3期

页      面：570-579页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.61473189,61374176,61203142 and 61203073 a Doctoral Program of High Education of China under Grant No.20110073120027 partly by the Excellent Young Technology Innovation Foundation of Hebei University of Technology under Grant No.2012005 

主　　题：Cellular automata eigenvalue finite states limit set multi-agent system nilpotent. 

摘      要：This paper studies the limit set of multi-agent system with finite states, in which the system is converted into a linear system through an expansion of space. Then, the structure properties of the system matrix are investigated, and the relationships between the eigenvalues and the limit set are developed. As an application, the nilpotent problem of elementary cellular automata(ECA) known as algorithmically undecidable is considered, and all the nilpotent ECA are found out which consists of rules 0, 8, 64, 239, 253, 255.