ON THE EXISTENCE OF OPEN AND BI-CONTINUING CODES

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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.
Publisher
AMER MATHEMATICAL SOC
Issue Date
2011
Language
English
Article Type
Article
Keywords

FINITE-TYPE; MAPS; SYSTEMS; SHIFTS

Citation

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.363, no.3, pp.1399 - 1417

ISSN
0002-9947
URI
http://hdl.handle.net/10203/100239
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