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Proclaiming Dictators and Juntas or Testing Boolean Formulae

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Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques (RANDOM 2001, APPROX 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2129))

Abstract

We consider the problem of determining whether a given function f: {0, 1n} → {0, 1} belongs to a certain class of Boolean functions \( \mathcal{F} \) or whether it is far from the class. More precisely, given query access to the function f and given a distance parameter ε, we would like to decide whether f ∈ \( \mathcal{F} \) or whether it differs from every g ∈ \( \mathcal{F} \) on more than an ε-fraction of the domain elements. The classes of functions we consider are singleton (“dictatorship”) functions, monomials, and monotone DNF functions with a bounded number of terms. In all cases we provide algorithms whose query complexity is independent of n (the number of function variables), and polynomial in the other relevant parameters.

Supported by the Israel Science Foundation (grant number 32/00-1).

Supported by the NSF (grant number CCR-9987845)

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Author information

Authors and Affiliations

  1. The Academic College of Tel-Aviv-Yaffo, Israel

    Michal Parnas

  2. Department of EE - Systems, Tel-Aviv University, Israel

    Dana Ron

  3. Institute for Advanced Study, Princeton

    Alex Samorodnitsky

Authors
  1. Michal Parnas
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  2. Dana Ron
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  3. Alex Samorodnitsky
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, MIT, Cambridge, MA, 02139, USA

    Michel Goemans

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

    Klaus Jansen

  3. Centre Universitaire d’Informatique, Université de Genéve, 24, Rue General Dufour, 1211, Genéve 4, Switzerland

    José D. P. Rolim

  4. Computer Science Division, University of California at Berkeley, 615 Soda Hall, Berkeley, CA, 94720-1776, USA

    Luca Trevisan

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© 2001 Springer-Verlag Berlin Heidelberg

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Parnas, M., Ron, D., Samorodnitsky, A. (2001). Proclaiming Dictators and Juntas or Testing Boolean Formulae. In: Goemans, M., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques. RANDOM APPROX 2001 2001. Lecture Notes in Computer Science, vol 2129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44666-4_30

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  • DOI: https://doi.org/10.1007/3-540-44666-4_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42470-3

  • Online ISBN: 978-3-540-44666-8

  • eBook Packages: Springer Book Archive

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