Computability of the entropy of one-tape Turing machines
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 . This is counterintuitive, 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.
Turing Machines
Dynamical Systems
Entropy
Crossing Sequences
Automata
421-432
Regular Paper
Emmanuel
Jeandel
Emmanuel Jeandel
10.4230/LIPIcs.STACS.2014.421
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode