DOI

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.

Язык оригиналаанглийский
Название основной публикацииComputer Science - Theory and Applications - 6th International Computer Science Symposium in Russia, CSR 2011, Proceedings
Страницы134-147
Число страниц14
DOI
СостояниеОпубликовано - 23 июн 2011
Событие6th International Computer Science Symposium in Russia, CSR 2011 - St. Petersburg, Российская Федерация
Продолжительность: 14 июн 201118 июн 2011

Серия публикаций

НазваниеLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Том6651 LNCS
ISSN (печатное издание)0302-9743
ISSN (электронное издание)1611-3349

конференция

конференция6th International Computer Science Symposium in Russia, CSR 2011
Страна/TерриторияРоссийская Федерация
ГородSt. Petersburg
Период14/06/1118/06/11

    Предметные области Scopus

  • Теоретические компьютерные науки
  • Компьютерные науки (все)

ID: 49786634