Eigenvalue-based investigation of multi-agent system with logical dynamics
Lin Wang, Xiaofan Wang, Jinhuan Wang · 2011
In this paper, we study the limit set of multi-agent logical system via an algebraic method. We first show that such system can be converted into a linear system through an expansion of space. Then, we discuss the structure properties of system matrix and investigate the relationship between the eigenvalues and the limit set. 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.