Hertling, Peter and Spandl, Christoph - Shifts with decidable language and non-computable entropy

dmtcs:425 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, Vol. 10 no. 3
Shifts with decidable language and non-computable entropy

Authors: Hertling, Peter and Spandl, Christoph

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


Source : oai:HAL:hal-00972331v1
Volume: Vol. 10 no. 3
Section: Automata, Logic and Semantics
Published on: January 1, 2008
Submitted on: March 26, 2015
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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