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URN: urn:nbn:de:0030-drops-44767
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Computability of the entropy of one-tape Turing machines

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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.

BibTeX - Entry

@InProceedings{jeandel:LIPIcs:2014:4476,
  author =	{Emmanuel Jeandel},
  title =	{{Computability of the entropy of one-tape Turing machines}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{421--432},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Ernst W. Mayr and Natacha Portier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4476},
  URN =		{urn:nbn:de:0030-drops-44767},
  doi =		{10.4230/LIPIcs.STACS.2014.421},
  annote =	{Keywords: Turing Machines, Dynamical Systems, Entropy, Crossing Sequences, Automata}
}

Keywords: Turing Machines, Dynamical Systems, Entropy, Crossing Sequences, Automata
Seminar: 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)
Issue date: 2014
Date of publication: 2014


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