LIPIcs.STACS.2013.104.pdf
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The PCP theorem for NP over the reals
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30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
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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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
https://doi.org/10.4230/LIPIcs.STACS.2013.104
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.
Keywords
- PCP
- real number computation
- systems of polynomials
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