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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the existence of open and bi-continuing codes


Author: Uijin Jung
Journal: Trans. Amer. Math. Soc. 363 (2011), 1399-1417
MSC (2010): Primary 37B10; Secondary 37B40, 54H20
Published electronically: October 20, 2010
MathSciNet review: 2737270
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Abstract: Given an irreducible sofic shift $ X$, we show that an irreducible shift of finite type $ Y$ of lower entropy is a factor of $ X$ if and only if it is a factor of $ X$ by an open bi-continuing code. If these equivalent conditions hold and $ Y$ is mixing, then any code from a proper subshift of $ X$ to $ Y$ can be extended to an open bi-continuing code on $ X$. These results are still valid when $ X$ is assumed to be only an almost specified shift, i.e., a subshift satisfying an irreducible version of the specification property.


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Additional Information

Uijin Jung
Affiliation: Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea
Address at time of publication: School of Mathematics, Korea Institute for Advanced Study, Hoegiro 87, Dongdaemun-Gu, Seoul 130-722, Korea
Email: uijin@kaist.ac.kr, uijin@kias.re.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05035-4
PII: S 0002-9947(2010)05035-4
Keywords: Open, continuing, sofic shift, shift of finite type, almost specified, specification property
Received by editor(s): November 7, 2008
Received by editor(s) in revised form: February 26, 2009
Published electronically: October 20, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.