Shifts with decidable language and non-computable entropy

Abstract : We consider subshifts of the full shift of all binary bi-infinite sequences. On the one hand, the topological entropy of any subshift with computably co-enumerable language is a right-computable real number between 0 and 1. We show that, on the other hand, any right-computable real number between 0 and 1, whether computable or not, is the entropy of some subshift with even polynomial time decidable language. In addition, we show that computability of the entropy of a subshift does not imply any kind of computability of the language of the subshift
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Peter Hertling, Christoph Spandl. Shifts with decidable language and non-computable entropy. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2008, 10 (3), pp.75--93. ⟨hal-00972331⟩

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