eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2014-03-05
421
432
10.4230/LIPIcs.STACS.2014.421
article
Computability of the entropy of one-tape Turing machines
Jeandel, Emmanuel
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol025-stacs2014/LIPIcs.STACS.2014.421/LIPIcs.STACS.2014.421.pdf
Turing Machines
Dynamical Systems
Entropy
Crossing Sequences
Automata