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### Paper:

TR12-047 | 24th April 2012 21:58

#### Extractors for Turing-machine sources

TR12-047
Authors: Emanuele Viola
Publication: 24th April 2012 21:58
Keywords:

Abstract:

We obtain the first deterministic randomness extractors
for $n$-bit sources with min-entropy $\ge n^{1-\alpha}$
generated (or sampled) by single-tape Turing machines
running in time $n^{2-16 \alpha}$, for all sufficiently
small $\alpha > 0$. We also show that such machines
cannot sample a uniform $n$-bit input to the Inner
Product function together with the output.

The proofs combine a variant of the crossing-sequence
technique by Hennie [SWCT 1965] with extractors for block
sources, especially those by Chor and Goldreich [SICOMP
1988] and by Kamp, Rao, Vadhan, and Zuckerman [JCSS
2011].

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