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Pseudorandomness for Linear Length Branching Programs and Stack Machines

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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 show the existence of an explicit pseudorandom generator G of linear stretch such that for every constant k, the output of G is pseudorandom against:

  • Oblivious branching programs over alphabet {0,1} of length kn and size 2O(n/logn) on inputs of size n.

  • Non-oblivious branching programs over alphabet Σ of length kn, provided the size of Σ is a power of 2 and sufficiently large in terms of k.

  • The model of logarithmic space randomized Turing Machines (over alphabet {0,1}) extended with an unbounded stack that make k passes over their randomness.

The construction of the pseudorandom generator G is the same as in our previous work (FOCS 2011). The results here rely on a stronger analysis of the construction. For the last result we give a length-efficient simulation of stack machines by non-deterministic branching programs. (over a large alphabet) whose accepting computations have a unique witness.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering and ITCSC, Chinese University of Hong Kong, Hong Kong

    Andrej Bogdanov

  2. Institute for Theoretical Computer Science, IIIS, Tsinghua University, P.R. China

    Periklis A. Papakonstantinou & Andrew Wan

Authors
  1. Andrej Bogdanov
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  2. Periklis A. Papakonstantinou
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  3. Andrew Wan
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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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Bogdanov, A., Papakonstantinou, P.A., Wan, A. (2012). Pseudorandomness for Linear Length Branching Programs and Stack Machines. 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_38

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  • DOI: https://doi.org/10.1007/978-3-642-32512-0_38

  • 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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