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The PCP theorem for NP over the reals Baartse, Martijn Meer, Klaus PCP real number computation systems of polynomials 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Martijn Baartse and Klaus Meer 2013 Is Part Of LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2013.104 urn:nbn:de:0030-drops-39262 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.104 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode