A sufficient condition for non-soficness of higher-dimensional subshifts
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- by Steve Kass and Kathleen Madden PDF
- Proc. Amer. Math. Soc. 141 (2013), 3803-3816 Request permission
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.References
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Additional Information
- Steve Kass
- Affiliation: Department of Mathematics and Computer Science, Drew University, Madison, New Jersey 07940
- MR Author ID: 246105
- Kathleen Madden
- Affiliation: Department of Mathematics and Computer Science, Drew University, Madison, New Jersey 07940
- MR Author ID: 350229
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3091770