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Lower Bound on Average-Case Complexity of Inversion of Goldreich’s Function by Drunken Backtracking Algorithms

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Computer Science – Theory and Applications (CSR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6072))

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Abstract

We prove an exponential lower bound on the average time of inverting Goldreich’s function by drunken [AHI05] backtracking algorithms; therefore we resolve the open question stated in [CEMT09]. The Goldreich’s function [Gol00] has n binary inputs and n binary outputs. Every output depends on d inputs and is computed from them by the fixed predicate of arity d. Our Goldreich’s function is based on an expander graph and on the nonliniar predicates of a special type. Drunken algorithm is a backtracking algorithm that somehow chooses a variable for splitting and randomly chooses the value for the variable to be investigated at first. Our proof technique significantly simplifies the one used in [AHI05] and in [CEMT09].

Partially supported by RFBR grants 08-01-00640 and 09-01-12137-ofi_m, the Fundamental research program of the Russian Academy of Sciences, the president of Russia grant “Leading Scientific Schools” NSh-4392.2008.1 and by Federal Target Programme “Scientific and scientific-pedagogical personnel of the innovative Russia” 2009-2013.

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Authors and Affiliations

  1. Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, St. Petersburg, 191023, Russia

    Dmitry Itsykson

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  1. Dmitry Itsykson
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Editors and Affiliations

  1. Dept. of Theoretical Cybernetics, Kazan State University, 420008, Kazan, Russia

    Farid Ablayev

  2. Institut für Informatik, Technische Universität München, 85748, Garching, Germany

    Ernst W. Mayr

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Itsykson, D. (2010). Lower Bound on Average-Case Complexity of Inversion of Goldreich’s Function by Drunken Backtracking Algorithms. In: Ablayev, F., Mayr, E.W. (eds) Computer Science – Theory and Applications. CSR 2010. Lecture Notes in Computer Science, vol 6072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13182-0_19

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  • DOI: https://doi.org/10.1007/978-3-642-13182-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13181-3

  • Online ISBN: 978-3-642-13182-0

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