The Complexity of Inversion of Explicit Goldreich's Function by DPLL Algorithms

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 contribu...

• Type: Journal
• Year: 2011
• Where: CSR
• Authors: Dmitry Itsykson, Dmitry Sokolov
• Keywords: Binary Inputs, CSR 2011, Dependency Graph, Random Graph, Theoretical Computer Science