Multidimensional Shifts And Finite Matrices

Abstract

Let $X$ be a $2$-dimensional subshift of finite type generated by a finite set of forbidden blocks (of finite size). We give an algorithm for generating the elements of the shift space using sequence of finite matrices (of increasing size). We prove that the sequence generated yields precisely the elements of the shift space $X$ and hence characterizes the elements of the shift space $X$. We extend our investigations to a general $d$-dimensional shift of finite type. In the process, we prove that that elements of $d$-dimensional shift of finite type can be characterized by a sequence of finite matrices (of increasing size).