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The PCP theorem for NP over the reals

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Abstract

In this paper we show that the PCP theorem holds as well in the real number computational model introduced by Blum, Shub, and Smale. More precisely, the real number counterpart NP_R of the classical Turing model class NP can be characterized as NP_R = PCP_R(O(log n), O(1)). Our proof structurally follows the one by Dinur for classical NP. However, a lot of minor and major changes are necessary due to the real numbers as underlying computational structure. The analogue result holds for the complex numbers and NP_C.

BibTeX - Entry

@InProceedings{baartse_et_al:LIPIcs:2013:3926,
  author =	{Martijn Baartse and Klaus Meer},
  title =	{{The PCP theorem for NP over the reals}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{104--115},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Natacha Portier and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/3926},
  URN =		{urn:nbn:de:0030-drops-39262},
  doi =		{10.4230/LIPIcs.STACS.2013.104},
  annote =	{Keywords: PCP, real number computation, systems of polynomials}
}

Keywords: PCP, real number computation, systems of polynomials
Seminar: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue date: 2013
Date of publication: 2013


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