On extracting randomness from weak random sources (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth 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 small-space sources
Journal of Computer and System Sciences
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Mergers are functions that transform k (possibly dependent) random sources (distributions) into a single random source, in a way that ensures that if one of the input sources has min-entropy rate δ then the output has min-entropy rate close to δ. Mergers have proven to be a very useful tool in explicit constructions of extractors and condensers, and are also interesting objects in their own right. In this work we give a refined analysis of the merger constructed by [Raz, STOC'05] (based on [Lu, Reingold, Vadhan, and Wigderson, STOC'03 pp. 602–611, 2003]). Our analysis uses min-entropy instead of Shannon's entropy to derive tighter results than the ones obtained in [Raz STOC'05]. We show that for every constant r and k it is possible to construct a merger that takes as input k strings of length n bits each, and outputs a string of length n-r bits, such that if one of the input sources has min-entropy b, the output will be close to having min-entropy b-(r + 1). This merger uses a constant number of additional uniform bits. One advantage of our analysis is that b (the min-entropy of the “good” source) can be as small as a constant (this constant depends on r and k), while in the analysis given in [Raz STOC'05], b is required to be linear in n. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008