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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Vydáno v:Theory of computing systems Ročník 54; číslo 2; s. 261 - 276
Hlavní autor: Itsykson, Dmitry
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.02.2014
Springer Nature B.V
Témata:
Algorithms
Analysis
Backtracking
Computer Science
Heuristic
Studies
Theory of Computation
Variables
Lower bound
Expander
DPLL
Goldreich’s function
ISSN:1432-4350, 1433-0490
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Shrnutí: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.
Bibliografie:SourceType-Scholarly Journals-1
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-013-9514-8