A sufficient condition for non-soficness of higher-dimensional subshifts
Steve Kass, Kathleen Madden · Proceedings of the American Mathematical Society · 2013
A shift space is said to be sofic if it is the factor of a shift of finite type. In one dimension, there are complete characterizations of soficness. There are no characterizations in higher dimensions, and there are few examples of non-sofic $\mathbb {Z}^d$ shifts for $d>1$. In this work we give a condition that implies non-soficness in higher-dimensional shift spaces, and we apply it to a variety of examples.