The Goldreich's function 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. Every Goldreich's function is defined by it's dependency graph G and predicate P. In 2000 O. Goldreich formulated a conjecture that if G is an expander and P is a random predicate of arity d then the corresponding function is one way. In 2005 M. Alekhnovich, E. Hirsch and D. Itsykson proved the exponential lower bound on the complexity of inversion of Goldreich's function based on linear predicate and random graph by myopic DPLL agorithms. In 2009 J. Cook, O. Etesami, R. Miller, and L. Trevisan extended this result to nonliniar predicates (but for a slightly weaker definition of myopic algorithms). Recently D. Itsykson and independently R. Miller proved the lower bound for drunken DPLL algorithms that invert Goldreich's function with nonlinear P and random G. All above lower bounds are randomized. The main contribution of this paper is the simpler proof of the exponential lower bound of the Goldreich's function inversion by myopic DPLL algorithms. A dependency graph in our construction may be based on an arbitrary expander, particulary it is possible to use an explicit expander; the predicate may be linear or slightly nonlinear. Our definition of myopic algorithms is more general than one used by J. Cook et al. Our construction may be used in the proof of lower bound for drunken algorithms as well.

Original languageEnglish
Title of host publicationComputer Science - Theory and Applications - 6th International Computer Science Symposium in Russia, CSR 2011, Proceedings
Pages134-147
Number of pages14
DOIs
StatePublished - 23 Jun 2011
Event6th International Computer Science Symposium in Russia, CSR 2011 - St. Petersburg, Russian Federation
Duration: 14 Jun 201118 Jun 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6651 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference6th International Computer Science Symposium in Russia, CSR 2011
Country/TerritoryRussian Federation
CitySt. Petersburg
Period14/06/1118/06/11

    Research areas

  • DPLL algorithm, expander, lower bounds, one-way function

    Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

ID: 49786634