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

We prove an exponential lower bound on the average time of inverting Goldreich’s function by drunken backtracking algorithms; this resolves the open question stated in Cook et al. (Proceedings of TCC, pp. 521–538, 2009 ). The Goldreich’s function has n binary inputs and n binary outputs. Every outpu...

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Bibliographic Details
Published in:Theory of computing systems Vol. 54; no. 2; pp. 261 - 276
Main Author: Itsykson, Dmitry
Format: Journal Article
Language:English
Published: Boston Springer US 01.02.2014
Springer Nature B.V
Subjects:
Algorithms
Analysis
Backtracking
Computer Science
Heuristic
Studies
Theory of Computation
Variables
Lower bound
Expander
DPLL
Goldreich’s function
ISSN:1432-4350, 1433-0490
Online Access:Get full text
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Summary:We prove an exponential lower bound on the average time of inverting Goldreich’s function by drunken backtracking algorithms; this resolves the open question stated in Cook et al. (Proceedings of TCC, pp. 521–538, 2009 ). 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 . Our Goldreich’s function is based on an expander graph and on the nonlinear predicates that are linear in Ω ( d ) variables. 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. After the submission to the journal we found out that the same result was independently obtained by Rachel Miller.
Bibliography:SourceType-Scholarly Journals-1
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content type line 14
ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-013-9514-8