The PCP theorem for NP over the reals

Baartse, Martijn; Meer, Klaus

doi:10.4230/LIPIcs.STACS.2013.104

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The PCP theorem for NP over the reals

Authors Martijn Baartse, Klaus Meer

Part of: Volume: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
License: Creative Commons Attribution-NoDerivs 3.0 Unported license
Publication Date: 2013-02-26

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Document Identifiers

DOI: 10.4230/LIPIcs.STACS.2013.104
URN: urn:nbn:de:0030-drops-39262

Subject Classification

Keywords

PCP
real number computation
systems of polynomials

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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.

Cite As Get BibTex

Martijn Baartse and Klaus Meer. The PCP theorem for NP over the reals. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 104-115, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013) https://doi.org/10.4230/LIPIcs.STACS.2013.104

Author Details

Martijn Baartse

Klaus Meer

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