Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Extractors with weak random seeds
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Deterministic Extractors for Affine Sources over Large Fields
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Addressing the shortcomings of one-way chains
ASIACCS '06 Proceedings of the 2006 ACM Symposium on Information, computer and communications security
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
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
Affine dispersers from subspace polynomials
Proceedings of the forty-first annual ACM symposium on Theory of computing
Extracting Computational Entropy and Learning Noisy Linear Functions
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Simpler constant-seed condensers
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Two sources are better than one for increasing the Kolmogorov complexity of infinite sequences
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
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
Multilinear formulas, maximal-partition discrepancy and mixed-sources extractors
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
On the impossibility of extracting classical randomness using a quantum computer
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
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
Computational complexity since 1980
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
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
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
New independent source extractors with exponential improvement
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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In this work we give the first deterministic extractors from a constant number of weak sources whose entropy rate is less than 1/2. Specifically, for every 驴 0 we give an explicit construction for extracting randomness from a constant (depending polynomially on 1/驴) number of distributions over {0, 1}^n, each having min-entropy 驴n. These extractors output n bits, which are 2^{- n} close to uniform. This construction uses several results from additive number theory, and in particular a recent one by Bourgain, Katz and Tao [BKT03] and of Konyagin [Kon03]. We also consider the related problem of constructing randomness dispersers. For any constant output length m, our dispersers use a constant number of identical distributions, each with min-entropy 驴(log n) and outputs every possible m-bit string with positive probability. The main tool we use is a variant of the "stepping-up lemma" used in establishing lower bound on the Ramsey number for hypergraphs (Erdos and Hajnal, [GRS80]).