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Computability of the entropy of one-tape Turing machines

Author Emmanuel Jeandel



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LIPIcs.STACS.2014.421.pdf
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Emmanuel Jeandel

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Emmanuel Jeandel. Computability of the entropy of one-tape Turing machines. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 421-432, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.STACS.2014.421

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 . 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.
Keywords
  • Turing Machines
  • Dynamical Systems
  • Entropy
  • Crossing Sequences
  • Automata

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