## AbstractWe introduce and study the notion of probabilistically checkable proofs for real number algorithms. Our starting point is the computational model of Blum, Shub, and Smale and the real analogue $\npr$ of $\mbox{NP}$ in that model. Our main result is, to the best of our knowledge, the first PCP theorem for $\npr.$ It states $\npr \subseteq \mbox{PCP}_{\R}(poly,O(1)).$ The techniques used extend ideas from Rubinfeld and Sudan for self-testing and -correcting certain functions over so-called rational domains to more general domains over the real numbers. Thus, independently from real number complexity theory, the paper can be seen as a contribution to constructing self testers and correctors for linear functions over real domains.
## Available Versions of this Item- Transparent long proofs: A first PCP theorem for $\mbox{NP}_{\R}$ (deposited 04 June 2004)
- Transparent long proofs: A first PCP theorem for $\mbox{NP}_{\R}$ (deposited 11 December 2004)
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- Transparent long proofs: A first PCP theorem for $\mbox{NP}_{\R}$ (deposited 11 December 2004)
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