NDLI: The PCP Theorem for NP Over the Reals

Content Provider	Springer Nature Link
Author	Meer, Klaus Baartse, Martijn
Copyright Year	2014
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 $$\mathrm{NP}_{{\mathbb {R}}}$$ of the classical Turing model class NP can be characterized as $$\mathrm{NP}_{{\mathbb {R}}}= \mathrm{PCP}_{{\mathbb {R}}}(O(\log {n}), O(1))$$ . 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 $$\mathrm{NP}_{{\mathbb {C}}}$$ .
Ending Page	680
Page Count	30
Starting Page	651
File Format	PDF
ISSN	16153375
e-ISSN	16153383
Journal	Foundations of Computational Mathematics
Issue Number	3
Volume Number	15
Language	English
Publisher	Springer US
Publisher Date	2014-03-28
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Complexity classes (hierarchies, relations among complexity classes, etc.) Economics general Linear and Multilinear Algebras, Matrix Theory Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) Numerical Analysis Computer Science Probabilistically checkable proofs Real and complex number computations Hilbert Nullstellensatz decision problem Computation over the reals Applications of Mathematics Math Applications in Computer Science PCP theorem
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis Computational Theory and Mathematics Computational Mathematics

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