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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


First published in Proc. Amer. Math. Soc. 141 (July 2012), published by the American Mathematical Society. © 2012 American Mathematical Society.

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