Almost Euclidean subspaces of ℓN1 via expander codes
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete 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
Simulating independence: New constructions of condensers, ramsey graphs, dispersers, and extractors
Journal of the ACM (JACM)
Deterministic extractors for small-space sources
Journal of Computer and System Sciences
From affine to two-source extractors via approximate duality
Proceedings of the forty-third annual ACM symposium on Theory of computing
Proceedings of the forty-third annual ACM symposium on Theory of computing
Accelerometers and randomness: perfect together
Proceedings of the fourth ACM conference on Wireless network security
Kolmogorov Complexity in Randomness Extraction
ACM Transactions on Computation Theory (TOCT)
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
Extractors and Lower Bounds for Locally Samplable Sources
ACM Transactions on Computation Theory (TOCT)
Improving the Hadamard extractor
Theoretical Computer Science
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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 $\delta 0$ we give an explicit construction for extracting randomness from a constant (depending polynomially on $1/\delta$) number of distributions over $\bits^n$, each having min-entropy $\delta n$. These extractors output $n$ bits that are $2^{-n}$ close to uniform. This construction uses several results from additive number theory, and in particular a recent result of Bourgain et al. 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 requires min-entropy $\Omega(\log n)$, and outputs every possible $m$-bit string with positive probability. The main tool we use is a variant of the “stepping-up lemma” of Erdo˝s and Hajnal used in establishing a lower bound on the Ramsey number for hypergraphs.