A Class of Nonsofic Multidimensional Shift Spaces
نویسنده
چکیده
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 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 shift spaces.
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