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: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
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Springer US
01.02.2014
Springer Nature B.V |
| Témata: | |
| ISSN: | 1432-4350, 1433-0490 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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 [Omega](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.[PUBLICATION ABSTRACT] 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. |
| Author | Itsykson, Dmitry |
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| Cites_doi | 10.1007/11814948_13 10.1145/375827.375835 10.1145/368273.368557 10.1016/S0022-0000(05)80043-1 10.1145/321033.321034 10.1109/SFCS.2000.892064 10.1007/11499107_5 10.1090/S0273-0979-06-01126-8 10.1145/7531.8928 10.1007/s00037-011-0034-0 10.1007/978-3-642-13182-0_19 10.1007/978-3-642-25591-5_48 |
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| DOI | 10.1007/s00224-013-9514-8 |
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| Snippet | We prove an exponential lower bound on the average time of inverting Goldreich’s function by
drunken
backtracking algorithms; this resolves the open question... We prove an exponential lower bound on the average time of inverting Goldreich's function by drunken backtracking algorithms; this resolves the open question... |
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| SubjectTerms | Algorithms Analysis Backtracking Computer Science Heuristic Studies Theory of Computation Variables |
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| Title | Lower Bound on Average-Case Complexity of Inversion of Goldreich’s Function by Drunken Backtracking Algorithms |
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