2 Search Results for "Rojas, Cristobal"

Document
DOI: 10.4230/LIPIcs.STACS.2015.447
On the Information Carried by Programs about the Objects They Compute

Authors: Mathieu Hoyrup and Cristóbal Rojas

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

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.
Cite as

Mathieu Hoyrup and Cristóbal Rojas. On the Information Carried by Programs about the Objects They Compute. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 447-459, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{hoyrup_et_al:LIPIcs.STACS.2015.447,
  author =	{Hoyrup, Mathieu and Rojas, Crist\'{o}bal},
  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 =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.447},
  URN =		{urn:nbn:de:0030-drops-49337},
  doi =		{10.4230/LIPIcs.STACS.2015.447},
  annote =	{Keywords: Markov-computable, representation, Kolmogorov complexity, Ershov topology}
}
Document
DOI: 10.4230/LIPIcs.STACS.2009.1828
Randomness on Computable Probability Spaces - A Dynamical Point of View

Authors: Peter Gacs, Mathieu Hoyrup, and Cristobal Rojas

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

Abstract
We extend the notion of randomness (in the version introduced by Schnorr) to computable Probability Spaces and compare it to a \emph{dynamical} notion of randomness: typicality. Roughly, a point is \emph{typical} for some dynamic, if it follows the statistical behavior of the system (Birkhoff's pointwise ergodic theorem). We prove that a point is Schnorr random if and only if it is typical for every \emph{mixing} computable dynamics. To prove the result we develop some tools for the theory of computable probability spaces (for example, morphisms) that are expected to have other applications.
Cite as

Peter Gacs, Mathieu Hoyrup, and Cristobal Rojas. Randomness on Computable Probability Spaces - A Dynamical Point of View. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 469-480, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

Copy BibTex To Clipboard

@InProceedings{gacs_et_al:LIPIcs.STACS.2009.1828,
  author =	{Gacs, Peter and Hoyrup, Mathieu and Rojas, Cristobal},
  title =	{{Randomness on Computable Probability Spaces - A Dynamical Point of View}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{469--480},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1828},
  URN =		{urn:nbn:de:0030-drops-18280},
  doi =		{10.4230/LIPIcs.STACS.2009.1828},
  annote =	{Keywords: Schnorr randomness, Birkhoff's ergodic theorem, Computable measures}
}
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