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License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2016.86
URN: urn:nbn:de:0030-drops-64943
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6494/
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Huang, Xiang ; Stull, Donald M.

Polynomial Space Randomness in Analysis

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LIPIcs-MFCS-2016-86.pdf (0.4 MB)

Abstract

We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko's framework for polynomial space computability in R^n to define weakly pspace-random points, a new variant of polynomial space randomness. We show that the Lebesgue differentiation theorem characterizes weakly pspace random points. That is, a point x is weakly pspace random if and only if the Lebesgue differentiation theorem holds for a point x for every pspace L_1-computable function.

BibTeX - Entry

@InProceedings{huang_et_al:LIPIcs:2016:6494,
  author =	{Xiang Huang and Donald M. Stull},
  title =	{{Polynomial Space Randomness in Analysis}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{86:1--86:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6494},
  URN =		{urn:nbn:de:0030-drops-64943},
  doi =		{10.4230/LIPIcs.MFCS.2016.86},
  annote =	{Keywords: algorithmic randomness, computable analysis, resource-bounded randomness, complexity theory}
}

Keywords: algorithmic randomness, computable analysis, resource-bounded randomness, complexity theory
Collection: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
Issue Date: 2016
Date of publication: 19.08.2016

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