Journal of the ACM (JACM)
Journal of Computer and System Sciences
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Pseudorandom generators in propositional proof complexity
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Exponential Lower Bounds for the Running Time of DPLL Algorithms on Satisfiable Formulas
Journal of Automated Reasoning
Goldreich's One-Way Function Candidate and Myopic Backtracking Algorithms
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Effective preprocessing in SAT through variable and clause elimination
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Applications of SAT solvers to cryptanalysis of hash functions
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
The complexity of inversion of explicit goldreich's function by DPLL algorithms
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Lower bounds for myopic DPLL algorithms with a cut heuristic
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Pseudorandom generators with long stretch and low locality from random local one-way functions
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A dichotomy for local small-bias generators
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Theory of Computing Systems
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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].