Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Hoyrup, Mathieu; Rojas, Cristóbal http://www.dagstuhl.de/lipics License
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URN: urn:nbn:de:0030-drops-49337
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On the Information Carried by Programs about the Objects They Compute

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Abstract

In computability theory and computable analysis, finite programs can compute infinite objects. Presenting a computable object via any program for it, provides at least as much information as presenting the object itself, written on an infinite tape. What additional information do programs provide? We characterize this additional information to be any upper bound on the Kolmogorov complexity of the object. Hence we identify the exact relationship between Markov-computability and Type-2-computability. We then use this relationship to obtain several results characterizing the computational and topological structure of Markov-semidecidable sets.

BibTeX - Entry

@InProceedings{hoyrup_et_al:LIPIcs:2015:4933,
  author =	{Mathieu Hoyrup and Crist{\'o}bal Rojas},
  title =	{{On the Information Carried by Programs about the Objects They Compute}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{447--459},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Ernst W. Mayr and Nicolas Ollinger},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/4933},
  URN =		{urn:nbn:de:0030-drops-49337},
  doi =		{10.4230/LIPIcs.STACS.2015.447},
  annote =	{Keywords: Markov-computable, representation, Kolmogorov complexity, Ershov topology}
}

Keywords: Markov-computable, representation, Kolmogorov complexity, Ershov topology
Seminar: 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)
Issue date: 2015
Date of publication: 2015


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