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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| creator | Itsykson, Dmitry |
| description | 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. |
| doi_str_mv | 10.1007/s00224-013-9514-8 |
| format | Article |
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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.</description><identifier>ISSN: 1432-4350</identifier><identifier>EISSN: 1433-0490</identifier><identifier>DOI: 10.1007/s00224-013-9514-8</identifier><identifier>CODEN: TCSYFI</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Algorithms ; Analysis ; Backtracking ; Computer Science ; Heuristic ; Studies ; Theory of Computation ; Variables</subject><ispartof>Theory of computing systems, 2014-02, Vol.54 (2), p.261-276</ispartof><rights>Springer Science+Business Media New York 2013</rights><rights>Springer Science+Business Media New York 2014</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-2b157b75e9ee0600b8065bd13f40683d72bd0c8149d9d90e6d034c80ae774c93</citedby><cites>FETCH-LOGICAL-c316t-2b157b75e9ee0600b8065bd13f40683d72bd0c8149d9d90e6d034c80ae774c93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00224-013-9514-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00224-013-9514-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Itsykson, Dmitry</creatorcontrib><title>Lower Bound on Average-Case Complexity of Inversion of Goldreich’s Function by Drunken Backtracking Algorithms</title><title>Theory of computing systems</title><addtitle>Theory Comput Syst</addtitle><description>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.</description><subject>Algorithms</subject><subject>Analysis</subject><subject>Backtracking</subject><subject>Computer Science</subject><subject>Heuristic</subject><subject>Studies</subject><subject>Theory of 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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.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s00224-013-9514-8</doi><tpages>16</tpages></addata></record> |
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| language | eng |
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| source | SpringerNature Journals; EBSCOhost Business Source Complete |
| subjects | Algorithms Analysis Backtracking Computer Science Heuristic Studies Theory of Computation Variables |
| title | Lower Bound on Average-Case Complexity of Inversion of Goldreich’s Function by Drunken Backtracking Algorithms |
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