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A sufficient condition for non-soficness of higher-dimensional subshifts


Authors: Steve Kass and Kathleen Madden
Journal: Proc. Amer. Math. Soc. 141 (2013), 3803-3816
MSC (2010): Primary 37B50; Secondary 37B10
DOI: https://doi.org/10.1090/S0002-9939-2013-11646-1
Published electronically: July 10, 2013
MathSciNet review: 3091770
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Abstract: A shift space is said to be sofic if it is the factor of a shift of
finite type. In one dimension, there are complete characterizations of soficness. There are no characterizations in higher dimensions, and there are few examples of non-sofic $ \mathbb{Z}^d$ shifts for $ d>1$. In this work we give a condition that implies non-soficness in higher-dimensional shift spaces, and we apply it to a variety of examples.


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Additional Information

Steve Kass
Affiliation: Department of Mathematics and Computer Science, Drew University, Madison, New Jersey 07940

Kathleen Madden
Affiliation: Department of Mathematics and Computer Science, Drew University, Madison, New Jersey 07940

DOI: https://doi.org/10.1090/S0002-9939-2013-11646-1
Received by editor(s): June 9, 2011
Received by editor(s) in revised form: October 26, 2011, and January 9, 2012
Published electronically: July 10, 2013
Communicated by: Bryna Kra
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.