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dc.contributor.authorAaronson, Scott
dc.contributor.authorAmbainis, Andris
dc.contributor.authorBalodis, Kaspars
dc.contributor.authorBavarian, Mohammad
dc.date.accessioned2015-11-02T17:16:49Z
dc.date.available2015-11-02T17:16:49Z
dc.date.issued2014
dc.identifier.isbn978-3-662-43947-0
dc.identifier.isbn978-3-662-43948-7
dc.identifier.issn0302-9743
dc.identifier.issn1611-3349
dc.identifier.urihttp://hdl.handle.net/1721.1/99645
dc.description.abstractWe study the query complexity of Weak Parity: the problem of computing the parity of an n-bit input string, where one only has to succeed on a 1/2 + ε fraction of input strings, but must do so with high probability on those inputs where one does succeed. It is well-known that n randomized queries and n/2 quantum queries are needed to compute parity on all inputs. But surprisingly, we give a randomized algorithm for Weak Parity that makes only O(n/log[superscript 0.246](1/ε)) queries, as well as a quantum algorithm that makes O(n/√log(1/ε)) queries. We also prove a lower bound of Ω(n/log(1/ε)) in both cases, as well as lower bounds of Ω(logn) in the randomized case and Ω(√logn) in the quantum case for any ε > 0. We show that improving our lower bounds is intimately related to two longstanding open problems about Boolean functions: the Sensitivity Conjecture, and the relationships between query complexity and polynomial degree.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant 0844626)en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Alan T. Waterman Award)en_US
dc.description.sponsorshipNational Science Foundation (U.S.). Science and Technology Center (Award 0939370)en_US
dc.language.isoen_US
dc.publisherSpringer-Verlagen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/978-3-662-43948-7_3en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourceMIT web domainen_US
dc.titleWeak Parityen_US
dc.typeArticleen_US
dc.identifier.citationAaronson, Scott, Andris Ambainis, Kaspars Balodis, and Mohammad Bavarian. “Weak Parity.” Lecture Notes in Computer Science (2014): 26–38.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorAaronson, Scotten_US
dc.contributor.mitauthorBavarian, Mohammaden_US
dc.relation.journalAutomata, Languages, and Programmingen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dspace.orderedauthorsAaronson, Scott; Ambainis, Andris; Balodis, Kaspars; Bavarian, Mohammaden_US
dc.identifier.orcidhttps://orcid.org/0000-0003-3292-2520
dc.identifier.orcidhttps://orcid.org/0000-0003-1333-4045
mit.licenseOPEN_ACCESS_POLICYen_US


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