Simonsen, Jakob Grue - On the computability of the topological entropy of subshifts

dmtcs:365 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, Vol. 8
On the computability of the topological entropy of subshifts

Authors: Simonsen, Jakob Grue

We prove that the topological entropy of subshifts having decidable language is uncomputable in the following sense: For no error bound less than 1/4 does there exists a program that, given a decision procedure for the language of a subshift as input, will approximate the entropy of the subshift within the error bound. In addition, we prove that not only is the topological entropy of sofic shifts computable to arbitary precision (a well-known fact), but all standard comparisons of the topological entropy with rational numbers are decidable.


Volume: Vol. 8
Published on: January 1, 2006
Submitted on: March 26, 2015
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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