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We construct pseudorandom generators that fool functions of halfspaces (threshold functions) under a very broad class of product distributions.
The elementary statistics of majority voting
L.S. Penrose · 1946
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Threshold logic: a synthesis approach
M. Dertouzos · 1965
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Threshold Logic
S.T. Hu · 1965
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Threshold Logic
P.M. Lewis and C.L. Coates · 1967
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A Counterexample in Weighted Majority Games
J.R. Isbell · 1969
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Threshold Logic
Q. Sheng · 1969
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Threshold logic and its applications
S. Muroga · 1971
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Mathematical properties of the banzhaf power index
P. Dubey and L.S. Shapley · 1979
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Hypercontraction principle and random multilinear forms
Wiesław Krakowiak and Jerzy Szulga · 1988
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A note on hypercontractivity of stable random variables
Jerzy Szulga · 1990
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Geometric arguments yield better bounds for threshold circuits and distributed computing
M. Krause · 1991
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Variation ranks of communication matrices and lower bounds for depth two circuits having symmetric gates with unbounded fanin
M. Krause and S. Waack · 1991
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Pseudorandom generators for space-bounded computation
Noam Nisan · 1992
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A Characterization of Weighted Voting
A. Taylor and W. Zwicker · 1992
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Threshold circuits of bounded depth
A. Hajnal, W. Maass, P. Pudlak, M. Szegedy, and G. Turan · 1993
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Pseudorandomness for network algorithms
Russell Impagliazzo, Noam Nisan, and Avi Wigderson · 1994
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Randomness is linear in space
Noam Nisan and David Zuckerman · 1996
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Relations between communication complexity, linear arrangements, and computational complexity
J. Forster, M. Krause, S.V. Lokam, R. Mubarakzjanov, N. Schmitt, and H.-U. Simon · 2001
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The Chow Parameters Problem
R. O’Donnell and R. Servedio · 2008
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Explicit construction of a small epsilon-net for linear threshold functions
Y. Rabani and A. Shpilka · 2008
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Polylogarithmic independence can fool DNF formulas
L. Bazzi · 2009
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Polynomial threshold functions: Structure, approximation and pseudorandomness
Ido Ben-Eliezer, Shachar Lovett, and Ariel Yadin · 2009
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Bounded independence fools halfspaces
Ilias Diakonikolas, Parikshit Gopalan, Ragesh Jaiswal, Rocco A. Servedio, and Emanuele Viola · 2009
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Bounded independence fools degree-2 threshold functions
I. Diakonikolas, D. Kane, and J. Nelson · 2009
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Vidmantas Bentkus · 2004
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Hypercontractivity of random variables and geometry of linear normed spaces, 2006
Paweł Wolff · 2006
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Hypercontractivity of simple random variables
Paweł Wolff · 2006
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Every linear threshold function has a low-weight approximator
R. Servedio · 2007
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On hardness of learning intersection of two halfspaces
S. Khot and R. Saket · 2008
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Gaussian bounds for noise correlation of functions and tight analysis of long codes
Elchanan Mossel · 2008
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Agnostic learning of monomials by halfspaces is hard
V. Feldman, V. Guruswami, P. Raghavendra, and Y. Wu · 2009
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Finding duplicates in a data stream
P. Gopalan and J. Radhakrishnan · 2009
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An invariance principle for polytopes
Prahladh Harsha, Adam Klivans, and Raghu Meka · 2009
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Pseudorandom generators for polynomial threshold functions, 2009
Raghu Meka and David Zuckerman · 2009
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Noise stability of functions with low influences: invariance and optimality
Elchanan Mossel, Ryan O’Donnell, and Krzysztof Oleszkiewicz · 2010
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