A class of nonsofic multidimensional shift spaces

Author:
Ronnie Pavlov

Journal:
Proc. Amer. Math. Soc. **141** (2013), 987-996

MSC (2010):
Primary 37B50; Secondary 37B10, 37A15

DOI:
https://doi.org/10.1090/S0002-9939-2012-11382-6

Published electronically:
July 31, 2012

MathSciNet review:
3003690

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Abstract | References | Similar Articles | Additional Information

Abstract: In one dimension, sofic shifts are fairly well understood and are 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 sofic shift which satisfies a uniform mixing condition called block gluing in all directions , the set of legal rows of in the -direction has a synchronizing word. This allows us to define a (new) large class of nonsofic shift spaces.

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Additional Information

**Ronnie Pavlov**

Affiliation:
Department of Mathematics, University of Denver, 2360 S. Gaylord Street, Denver, Colorado 80208

Email:
rpavlov@du.edu

DOI:
https://doi.org/10.1090/S0002-9939-2012-11382-6

Keywords:
$\mathbb{Z}^{d}$,
shift of finite type,
sofic,
multidimensional

Received by editor(s):
March 25, 2011

Received by editor(s) in revised form:
August 2, 2011

Published electronically:
July 31, 2012

Communicated by:
Bryna Kra

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.