On the existence of open and bi-continuing codes

Jung, Uijin

doi:10.1090/S0002-9947-2010-05035-4

On the existence of open and bi-continuing codes
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Trans. Amer. Math. Soc. 363 (2011), 1399-1417 Request permission

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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