On the power of two-point based sampling
Benny Chor,Oded Goldreich +1 more
TLDR
A new sampling technique is presented that consists of picking two elements at random, and deterministically generating a long sequence of pairwise-independent elements that is guaranteed to intersect, with high probability, any set of non-negligible density.About:
This article is published in Journal of Complexity.The article was published on 1989-04-03 and is currently open access. It has received 217 citations till now. The article focuses on the topics: Sampling (statistics) & Simple random sample.read more
Citations
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Probabilistic checking of proofs: a new characterization of NP
Sanjeev Arora,Shmuel Safra +1 more
TL;DR: It is shown that approximating Clique and Independent Set, even in a very weak sense, is NP-hard, and the class NP contains exactly those languages for which membership proofs can be verified probabilistically in polynomial time.
Proceedings ArticleDOI
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
TL;DR: A pseudo-random generator which produces n instances of a problem for which the analog of the XOR lemma holds is given, and it is shown that if any problem in E = DTIAl E(2°t”j) has circuit complexity 2Q(”), then P = BPP.
Journal ArticleDOI
Randomness is Linear in Space
Noam Nisan,David Zuckerman +1 more
TL;DR: In this article, it was shown that any randomized algorithm that runs in spaceSand timeT and uses poly(S) random bits can be simulated using only O(S ) random bits in space Sand timeT+poly(S).
Journal ArticleDOI
The Dense k -Subgraph Problem
TL;DR: An approximation algorithm is developed for the problem of computing the dense k -vertex subgraph of a given graph, namely, the subgraph with the most edges, with approximation ratio O(nδ) , for some δ < 1/3 .
Journal ArticleDOI
Simple Constructions of Almost k-wise Independent Random Variables
TL;DR: This work presents three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent and their simplicity is their simplicity.
References
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Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
Journal ArticleDOI
How to share a secret
TL;DR: This technique enables the construction of robust key management schemes for cryptographic systems that can function securely and reliably even when misfortunes destroy half the pieces and security breaches expose all but one of the remaining pieces.
Journal ArticleDOI
An Introduction to Probability Theory and Its Applications.
Book
An introduction to probability theory
TL;DR: The authors introduce probability theory for both advanced undergraduate students of statistics and scientists in related fields, drawing on real applications in the physical and biological sciences, and make probability exciting." -Journal of the American Statistical Association
Related Papers (5)
How to generate cryptographically strong sequences of pseudo-random bits
Manuel Blum,Silvio Micali +1 more