  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 $h\geq 0$ 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 an irreducible SFT is
computable.
