A characterization of the entropies of multidimensional shifts of finite type

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 $h\geq0$ 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.