2021/12/28 by Prashant Kumar, Puneet Sharma, Kumar, Prashant +1
Computer Science · Mathematics · #Cellular Automata and Applications #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2112.14079
\beginabstract In this paper, we investigate a shift arising from graph G. We prove that any k-dimensional shift of finite type can be generated through a k-dimensional graph. We investigate the structure of the shift space using the generating matrices for the shift space. We prove that a two dimensional shift space has a horizontally (vertically) periodic point if and only if it possesses a (m,n)-periodic point (for some m,n∈ ℤ∖ \0\). We prove that a shift space is finite if and only if it can be generated by permutation matrices. We study the non-emptiness problem and existence of periodic points in terms of the generating matrices.