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[کتاب][B] Analysis of boolean functions
R O'Donnell - 2014 - books.google.com
Boolean functions are perhaps the most basic objects of study in theoretical computer
science. They also arise in other areas of mathematics, including combinatorics, statistical …
science. They also arise in other areas of mathematics, including combinatorics, statistical …
Pseudorandomness
SP Vadhan - … and Trends® in Theoretical Computer Science, 2012 - nowpublishers.com
This is a survey of pseudorandomness, the theory of efficiently generating objects that" look
random" despite being constructed using little or no randomness. This theory has …
random" despite being constructed using little or no randomness. This theory has …
Average-case complexity
A Bogdanov, L Trevisan - Foundations and Trends® in …, 2006 - nowpublishers.com
We survey the average-case complexity of problems in NP. We discuss various notions of
good-on-average algorithms, and present completeness results due to Impagliazzo and …
good-on-average algorithms, and present completeness results due to Impagliazzo and …
Learning intersections and thresholds of halfspaces
AR Klivans, R O'Donnell, RA Servedio - Journal of Computer and System …, 2004 - Elsevier
We give the first polynomial time algorithm to learn any function of a constant number of
halfspaces under the uniform distribution on the Boolean hypercube to within any constant …
halfspaces under the uniform distribution on the Boolean hypercube to within any constant …
On worst-case to average-case reductions for NP problems
A Bogdanov, L Trevisan - SIAM Journal on Computing, 2006 - SIAM
We show that if an NP-complete problem has a nonadaptive self-corrector with respect to
any samplable distribution, then coNP is contained in NP/poly and the polynomial hierarchy …
any samplable distribution, then coNP is contained in NP/poly and the polynomial hierarchy …
Learning algorithms from natural proofs
ML Carmosino, R Impagliazzo… - 31st Conference on …, 2016 - drops.dagstuhl.de
Abstract Based on Hastad's (1986) circuit lower bounds, Linial, Mansour, and Nisan (1993)
gave a quasipolytime learning algorithm for AC^ 0 (constant-depth circuits with AND, OR …
gave a quasipolytime learning algorithm for AC^ 0 (constant-depth circuits with AND, OR …
Gaussian bounds for noise correlation of functions
E Mossel - Geometric and Functional Analysis, 2010 - Springer
In this paper we derive tight bounds on the expected value of products of low influence
functions defined on correlated probability spaces. The proofs are based on extending …
functions defined on correlated probability spaces. The proofs are based on extending …
Non-interactive correlation distillation, inhomogeneous Markov chains, and the reverse Bonami-Beckner inequality
E Mossel, R O'Donnell, O Regev, JE Steif… - Israel Journal of …, 2006 - Springer
In this paper we study non-interactive correlation distillation (NICD), a generalization of
noise sensitivity previously considered in [5, 31, 39]. We extend the model to NICD on trees …
noise sensitivity previously considered in [5, 31, 39]. We extend the model to NICD on trees …
Better pseudorandom generators from milder pseudorandom restrictions
P Gopalan, R Meka, O Reingold… - 2012 IEEE 53rd …, 2012 - ieeexplore.ieee.org
We present an iterative approach to constructing pseudorandom generators, based on the
repeated application of mild pseudorandom restrictions. We use this template to construct …
repeated application of mild pseudorandom restrictions. We use this template to construct …
Hardness amplification proofs require majority
R Shaltiel, E Viola - Proceedings of the fortieth annual ACM symposium …, 2008 - dl.acm.org
Hardness amplification is the fundamental task of converting a δ-hard function f:(0, 1) n->(0,
1) into a (1/2-ε)-hard function Amp (f), where f is γ-hard if small circuits fail to compute f on at …
1) into a (1/2-ε)-hard function Amp (f), where f is γ-hard if small circuits fail to compute f on at …