MUTIDIMENSIONAL SHIFTS AND FINITE MATRICES

Let X be a multi-dimensional subshift of finite type generated by a finite set of finite forbidden blocks. We give an algorithm for generating the elements of the shift space using a sequence of finite matrices (of increasing order). 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. In the process, we prove that elements of d-dimensional shift of finite type can be characterized by a sequence of finite matrices.