Two-Dimensional Sofic Systems and Shift of Finite Type using Allowable Block

A two-dimensional sofic system has been defined by using the notion of allowable block. This definition is an extension of the original definition in the one-dimensional case. It is shown that the present definition is equivalent to using the notion of symbolic factors of subshift of finite types and to point out some of the phenomena which arise in the transition from classical shift of finite type to two-dimensional shift of finite type where, A is the finite alphabet. The rigidity properties of certain two dimensional shift of finite type and two dimensional sofic system has been discussed. Some examples are presented to illustrate this notation.