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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 | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [C] Cassaigne, J., Le Shift Impair Bidimensionnel est Sofique, Seminar Talk on September 30, 2010, http://www.lif.univ-mrs.fr/Sycomore/Julien-Cassaigne.html, accessed May 30, 2011.
  • [H] Hochman, M., private communication.
  • [HQ] Hoffman, C. and Quas, A., private communication.
  • [JKM] Johnson, A., Kass, S., and Madden, K., Projectional Entropy in Higher Dimensional Shifts of Finite Type, Complex Systems, 17 (2007), 243-257. MR 2373706 (2008m:37028)
  • [LM] Lind, D. and Marcus, B., An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, 1995. MR 1369092 (97a:58050)
  • [LMN] Lindgren, K., Moore, C., Nordahl, M., Complexity of Two-Dimensional Patterns, Journal of Statistical Physics, 91 (1998), 909-951. MR 1637266 (2000d:68104)
  • [KM] Kass, S., and Madden, K., A Note on the Uniform Filling Property and Strong Irreducibility, Acta Applicandae Math. DOI 10.1007/s10440-013-9816-5
  • [P] Pavlov, R., A Class of Nonsofic $ \mathbb{Z}^d$ Shift Spaces, Proceedings of the American Mathematical Society, 141 (2013), 987-996. MR 3003690
  • [P2] Pavlov, R., private communication.
  • [PS] Pavlov, R. and Schraudner, M., Projectional Subdynamics of $ \mathbb{Z}^d$ Shifts of Finite Type (submitted).
  • [S] Schraudner, M., Projectional Entropy and the Electrical Wire Shift, Discrete and Continuous Dynamical Systems, 26 (2010), no. 1, 333-346. MR 2552791 (2010k:37027)

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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.

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