### Abstract

Mergers are functions that transform k (possibly dependent) random sources 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 present a new analysis of the merger construction of [6]. Our analysis shows that the min-entropy rate of this merger's output is actually 0.52 · δ instead of 0.5·δ, where δ is the min-entropy rate of one of the inputs. To obtain this result we deviate from the usual linear algebra methods that were used by [6] and introduce a new technique that involves results from additive number theory.

Original language | English (US) |
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Pages (from-to) | 270-281 |

Number of pages | 12 |

Journal | LECTURE NOTES IN COMPUTER SCIENCE |

Volume | 3624 |

DOIs | |

State | Published - Jan 1 2005 |

Externally published | Yes |

Event | 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th International Workshop on Randomization and Computation, RANDOM 2005 - Berkeley, CA, United States Duration: Aug 22 2005 → Aug 24 2005 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*LECTURE NOTES IN COMPUTER SCIENCE*,

*3624*, 270-281. https://doi.org/10.1007/11538462_23