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A Hypergraph Dictatorship Test with Perfect Completeness

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Book cover Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2009, RANDOM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5687))

Abstract

A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based PCP construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are o(1). Their test makes q ≥ 3 queries, has amortized query complexity \(1+O\left(\frac{\log q}{q}\right)\), but has an inherent loss of perfect completeness. In this paper we give an (adaptive) hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity \(1+O\left(\frac{\log q}{q}\right)\).

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Author information

Authors and Affiliations

  1. Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, USA

    Victor Chen

Authors
  1. Victor Chen
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Editor information

Editors and Affiliations

  1. Dept. of Applied Math and Computer Science, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Irit Dinur

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Technion, Computer Science Department, 32000, Haifa, Israel

    Joseph Naor

  4. University of Geneva, Centre Universitaire d’Informatique, Battelle Bat. A, 7 rte de Drize, 1227, Carouge, Switzerland

    José Rolim

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© 2009 Springer-Verlag Berlin Heidelberg

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Chen, V. (2009). A Hypergraph Dictatorship Test with Perfect Completeness. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_34

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  • DOI: https://doi.org/10.1007/978-3-642-03685-9_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03684-2

  • Online ISBN: 978-3-642-03685-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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