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Computability of the entropy of one-tape Turing Machines (1302.1170v1)

Published 5 Feb 2013 in cs.FL, cs.CC, cs.IT, math.DS, and math.IT

Abstract: We prove that the maximum speed and the entropy of a one-tape Turing machine are computable, in the sense that we can approximate them to any given precision $\epsilon$. This is contrary to popular belief, as all dynamical properties are usually undecidable for Turing machines. The result is quite specific to one-tape Turing machines, as it is not true anymore for two-tape Turing machines by the results of Blondel et al., and uses the approach of crossing sequences introduced by Hennie.

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