Disperser

A disperser is a one-sided extractor.[1] Where an extractor requires that every event gets the same probability under the uniform distribution and the extracted distribution, only the latter is required for a disperser. So for a disperser, an event A \subseteq \{0,1\}^{m} we have: Pr_{U_{m}}[A] > 1 - \epsilon

Definition (Disperser): A (k, \epsilon)-disperser is a function

Dis: \{0,1\}^{n}\times \{0,1\}^{d}\rightarrow \{0,1\}^{m}

such that for every distribution X on \{0,1\}^{n} with H_{\infty}(X) \geq k the support of the distribution Dis(X,U_{d}) is of size at least (1-\epsilon)2^{m}.

Graph theory

An (N, M, D, K, e)-disperser is a bipartite graph with N vertices on the left side, each with degree D, and M vertices on the right side, such that every subset of K vertices on the left side is connected to more than (1 − e)M vertices on the right.

An extractor is a related type of graph that guarantees an even stronger property; every (N, M, D, K, e)-extractor is also an (N, M, D, K, e)-disperser.

Other meanings

A disperser is a high-speed mixing device used to disperse or dissolve pigments and other solids into a liquid.

See also

References

  1. ↑ Ronen Shaltiel. Recent developments in explicit construction of extractors. P. 7.
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