A characterization of the entropies of multidimensional shifts of finite type

Michael Hochman*, Tom Meyerovitch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

87 Scopus citations

Abstract

We show that the values of entropies of multidimensional shifts of finite type (SFTs) are characterized by a certain computation-theoretic property: a real number h ≥ 0 is the entropy of such an SFT if and only if it is right recursively enumerable, i.e. there is a computable sequence of rational numbers converging to h from above. The same characterization holds for the entropies of sofic shifts. On the other hand, the entropy of strongly irreducible SFTs is computable.

Original languageAmerican English
Pages (from-to)2011-2038
Number of pages28
JournalAnnals of Mathematics
Volume171
Issue number3
DOIs
StatePublished - 2010
Externally publishedYes

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