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International Workshop on Approximation Algorithms for Combinatorial Optimization

International Workshop on Randomization and Approximation Techniques in Computer Science

APPROX 2013, RANDOM 2013: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques pp 655–670Cite as

Pseudorandomness for Regular Branching Programs via Fourier Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8096))

Abstract

We present an explicit pseudorandom generator for oblivious, read-once, permutation branching programs of constant width that can read their input bits in any order. The seed length is O(log2 n), where n is the length of the branching program. The previous best seed length known for this model was n 1/2 + o(1), which follows as a special case of a generator due to Impagliazzo, Meka, and Zuckerman (FOCS 2012) (which gives a seed length of s 1/2 + o(1) for arbitrary branching programs of size s). Our techniques also give seed length n 1/2 + o(1) for general oblivious, read-once branching programs of width \(2^{n^{o(1)}}\), which is incomparable to the results of Impagliazzo et al.

Our pseudorandom generator is similar to the one used by Gopalan et al. (FOCS 2012) for read-once CNFs, but the analysis is quite different; ours is based on Fourier analysis of branching programs. In particular, we show that an oblivious, read-once, regular branching program of width w has Fourier mass at most (2w 2)k at level k, independent of the length of the program.

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Authors and Affiliations

  1. Microsoft Research Silicon Valley, Mountain View, CA, USA

    Omer Reingold

  2. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    Thomas Steinke & Salil Vadhan

Authors
  1. Omer Reingold
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  2. Thomas Steinke
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  3. Salil Vadhan
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Editor information

Editors and Affiliations

  1. University of California, Berkeley, CA, USA

    Prasad Raghavendra

  2. Dept. of computer Science and Engineering, Pennsylvania State University, University Park, PA, USA

    Sofya Raskhodnikova

  3. Institute of Computer Science, University of Kiel, 24118, Kiel, Germany

    Klaus Jansen

  4. University of Geneva, Centre Universitaire d’Informatique, 1227, Carouge, Switzerland

    José D. P. Rolim

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Reingold, O., Steinke, T., Vadhan, S. (2013). Pseudorandomness for Regular Branching Programs via Fourier Analysis. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2013 2013. Lecture Notes in Computer Science, vol 8096. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40328-6_45

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  • DOI: https://doi.org/10.1007/978-3-642-40328-6_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40327-9

  • Online ISBN: 978-3-642-40328-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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