Efficiency considerations in using semi-random sources
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Combinatorica - Theory of Computing
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Journal of Computer and System Sciences
Handbook of combinatorics (vol. 2)
On extracting randomness from weak random sources (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Randomness-optimal oblivious sampling
Proceedings of the workshop on Randomized algorithms and computation
Extracting randomness: a survey and new constructions
Journal of Computer and System Sciences
Randomness Extractors and their Many Guises
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Error Reduction for Extractors
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Extracting randomness from samplable distributions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Extracting Randomness Using Few Independent Sources
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Extractors for a constant number of polynomially small min-entropy independent sources
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Deterministic extractors for small-space sources
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
An Improved Analysis of Linear Mergers
Computational Complexity
Random Structures & Algorithms
Increasing the Output Length of Zero-Error Dispersers
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
A 2-Source Almost-Extractor for Linear Entropy
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Extractors for Three Uneven-Length Sources
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Extracting Computational Entropy and Learning Noisy Linear Functions
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
On Generating Independent Random Strings
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Improved Polynomial Identity Testing for Read-Once Formulas
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Simulating independence: New constructions of condensers, ramsey graphs, dispersers, and extractors
Journal of the ACM (JACM)
Counting dependent and independent strings
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Impossibility of independence amplification in Kolmogorov complexity theory
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Two-source extractors secure against quantum adversaries
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Multilinear formulas, maximal-partition discrepancy and mixed-sources extractors
Journal of Computer and System Sciences
Deterministic extractors for small-space sources
Journal of Computer and System Sciences
SIGACT news complexity theory column 68
ACM SIGACT News
Deterministic extractors for independent-symbol sources
IEEE Transactions on Information Theory
Extracting Kolmogorov complexity with applications to dimension zero-one laws
Information and Computation
From affine to two-source extractors via approximate duality
Proceedings of the forty-third annual ACM symposium on Theory of computing
An introduction to randomness extractors
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Extractors and lower bounds for locally samplable sources
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
An improved analysis of mergers
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
On the error parameter of dispersers
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Deterministic extractors for independent-symbol sources
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Extracting kolmogorov complexity with applications to dimension zero-one laws
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Extractors and Lower Bounds for Locally Samplable Sources
ACM Transactions on Computation Theory (TOCT)
Distributed computing with imperfect randomness
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Generalized strong extractors and deterministic privacy amplification
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Design extractors, non-malleable condensers and privacy amplification
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Improving the Hadamard extractor
Theoretical Computer Science
New independent source extractors with exponential improvement
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We show how to extract random bits from two or more independent weak random sources in cases where only one source is of linear min-entropy and all other sources are of logarithmic min-entropy. Our main results are as follows: A long line of research, starting by Nisan and Zuckerman[14], gives explicit constructions of seeded-extractors, that is, extractors that use a short seed of truly random bits to extract randomness from a weak random source. For every such extractor E, with seed of length d, we construct an extractor E′, with seed of length d′=O(d), that achieves the same parameters as E but only requires the seed to be of min-entropy larger than (1⁄2+δ) •d′ (rather than fully random), where δ is an arbitrary small constant. Fundamental results of Chor and Goldreich and Vazirani [6,21] show how to extract Ω(n) random bits from two (independent) sources of length n and min-entropy larger than (1⁄2δ) • n, where δ is an arbitrary small constant. We show how to extract Ω(n) random bits (with optimal probability of error) when only one source is of min-entropy (1⁄2+δ) •n and the other source is of logarithmic min entropy.3 A recent breakthrough of Barak, Impagliazzo and Wigderson[4] shows how to extract Ω(n) random bits from a constant number of (independent) sources of length n and min-entropy larger than δ n, where δ is an arbitrary small constant. We show how to extract Ω (n) random bits (with optimal probability of error) when only one source is of min-entropy δ n and all other (constant number of) sources are of logarithmic min-entropy.A very recent result of Barak, Kindler, Shaltiel, Sudakov and Wigderson[5] shows how to extract a constant number of random bits from three (independent) sources of length n and min-entropy larger than δn, where δ is an arbitrary small constant. We show how to extract Ω(n)/ random bits, with sub-constant probability of error, from one source of min-entropy δ n and two sources of logarithmic min-entropy.In the same paper, Barak, Kindler, Shaltiel, Sudakov and Wigderson[5] give an explicit coloring of the complete bipartite graph of size 2n x 2n with two colors, such that there is no monochromatic subgraph of size larger than 2δn x 2 2δn, where δ is an arbitrary small constant. We give an explicit coloring of the complete bipartite graph of size 2n x 2n with a constant number of colors, such that there is no monochromatic subgraph of size larger than 2δn x n5.We also give improved constructions of mergers and condensers. In particular, We show that using a constant number of truly random bits, one can condense a source of length n and min-entropy rate δ into a source of length Ω (n) and min-entropy rate 1-δ, where δ is an arbitrary small constant.We show that using a constant number of truly random bits, one can merge a constant number of sources of length n, such that at least one of them is of min-entropy rate 1-δ, into one source of length Ω(n) and min-entropy rate slightly less than 1-δ, where δ is any small constant.