Shift of finite type; sofic; multidimensional
In one dimension, sofic shifts are fairly well-understood and special examples of shift spaces which must satisfy very restrictive properties. However, in multiple dimensions there are very few known conditions which guarantee nonsoficity of a shift space. In this paper, we show that for any Z d sofic shift X which satisfies a uniform mixing condition called block gluing in all directions ~e2, . . . , ~ed, the set of legal rows of X in the ~e1-direction has a synchronizing word. This allows us to define a (new) large class of nonsofic Z d shift spaces
Povlov, Ronnie, "A Class of Nonsofic Multidimensional Shift Spaces" (2012). Mathematics Preprint Series. 33.