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 language | English |
|---|---|
| Pages (from-to) | 2011-2038 |
| Number of pages | 28 |
| Journal | Annals of Mathematics |
| Volume | 171 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 Jan 2010 |
| Externally published | Yes |
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty