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Extractors for Turing-Machine Sources

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2012, RANDOM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7408))

Abstract

We obtain the first deterministic randomness extractors for n-bit sources with min-entropy ≥ n 1 − α generated (or sampled) by single-tape Turing machines running in time n 2 − 16 α, for all sufficiently small α > 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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Author information

Authors and Affiliations

  1. Northeastern University, Boston, MA, 02115, USA

    Emanuele Viola

Authors
  1. Emanuele Viola
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Carnegie Mellon University, Gates Building 7203, 15213, Pittsburgh, PA, USA

    Anupam Gupta

  2. Department of Computer Science, University Kiel, Olshausenstraße 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Centre Universitaire d’Informatique, University of Geneva, Battelle A, 7 route de Drize, 1227, Carouge, Switzerland

    José Rolim

  4. Department of Computer Science, Foundation School of Engineering and Applied Science, Columbia University, Amsterdam Avenue 1214, 10027-7003, New York, NY, USA

    Rocco Servedio

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© 2012 Springer-Verlag Berlin Heidelberg

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Viola, E. (2012). Extractors for Turing-Machine Sources. In: Gupta, A., Jansen, K., Rolim, J., Servedio, R. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2012 2012. Lecture Notes in Computer Science, vol 7408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32512-0_56

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  • DOI: https://doi.org/10.1007/978-3-642-32512-0_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32511-3

  • Online ISBN: 978-3-642-32512-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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