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dc.contributor.authorLu, Chi-Jenen_US
dc.contributor.authorTsai, Shi-Chunen_US
dc.contributor.authorWu, Hsin-Lungen_US
dc.date.accessioned2014-12-08T15:42:24Z-
dc.date.available2014-12-08T15:42:24Z-
dc.date.issued2008-10-01en_US
dc.identifier.issn0018-9448en_US
dc.identifier.urihttp://dx.doi.org/10.1109/TIT.2008.928988en_US
dc.identifier.urihttp://hdl.handle.net/11536/28798-
dc.description.abstractFor delta is an element of (0, 1) and k, n is an element of N, we study the task of transforming a hard function f : {0, 1}(n) -> {0, 1}, with which any small circuit disagrees on (1 - delta)/2 fraction of the input, into a harder function f', with which any small circuit disagrees on (1 - delta(k))/2 fraction of the input. First, we show that such hardness amplification, when carried out in some black-box way, must require a high complexity. In particular, it cannot be realized by a circuit of depth d and size 2(o(k1/d)) or by a nondeterministic circuit of size o(k/log k) (and arbitrary depth) for any delta is an element of (0, 1). This extends the result of Viola, which only works when (1 - delta)/2 is small enough. Furthermore, we show that even without any restriction on the complexity of the amplification procedure, such a black-box hardness amplification must be inherently nonuniform in the following sense. To guarantee the hardness of the resulting function f', even against uniform machines, one has to start with a function f, which is hard against nonuniform algorithms with Omega(k log(1/delta)) bits of advice. This extends the result of Trevisan and Vadhan, which only addresses the case with (1 - delta)/2 = 2(-n). Finally, we derive similar lower bounds for any black-box construction of a pseudorandom generator (PRG) from a hard function. To prove our results, we link the task of hardness amplifications and PRG constructions, respectively, to some type of error-reduction codes, and then we establish lower bounds for such codes, which we hope could find interest in both coding theory and complexity theory.en_US
dc.language.isoen_USen_US
dc.subjectcomputational complexityen_US
dc.subjecthardness amplificationen_US
dc.subjectlist-decodable codeen_US
dc.subjectpseudorandom generatoren_US
dc.titleOn the complexity of hardness amplificationen_US
dc.typeArticle; Proceedings Paperen_US
dc.identifier.doi10.1109/TIT.2008.928988en_US
dc.identifier.journalIEEE TRANSACTIONS ON INFORMATION THEORYen_US
dc.citation.volume54en_US
dc.citation.issue10en_US
dc.citation.spage4575en_US
dc.citation.epage4586en_US
dc.contributor.department資訊工程學系zh_TW
dc.contributor.departmentDepartment of Computer Scienceen_US
dc.identifier.wosnumberWOS:000259407000012-
Appears in Collections:Conferences Paper