"A Class of Nonsofic Multidimensional Shift Spaces" by Ronnie Pavlov
 

Publication Date

2012

Document Type

Article

Keywords

Shift of finite type, Sofic, Multidimensional

Abstract

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

Comments

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



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