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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2008

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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Dates and versions

hal-00972331 , version 1 (03-04-2014)

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Peter Hertling, Christoph Spandl. Shifts with decidable language and non-computable entropy. Discrete Mathematics and Theoretical Computer Science, 2008, Vol. 10 no. 3 (3), pp.75--93. ⟨10.46298/dmtcs.425⟩. ⟨hal-00972331⟩

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