Verification of mixing properties in two-dimensional shifts of finite type

This work introduces constructive and systematic methods for verifying the topological mixing strong specification (or irreducibility) of two-dimensional shifts finite type. First, we define transition matrices on infinite strips width n all ≥ 2. To determine primitivity matrices, introduce connecting operators that reduce high-order to lower-order matrices. Then, two sufficient conditions are provided; they invariant diagonal cycles primitive commutative operators. primitivity, corner-extendability, crisscross-extendability used demonstrate mixing. Finally, show hole-filling condition yields property. The application above-mentioned can be verified in a number steps.