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dc.contributor.advisorDana Moshkovitz.en_US
dc.contributor.authorRamnarayan, Govinden_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.en_US
dc.date.accessioned2016-12-22T16:28:09Z
dc.date.available2016-12-22T16:28:09Z
dc.date.copyright2016en_US
dc.date.issued2016en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/106080
dc.descriptionThesis: S.M. in Computer Science and Engineering, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 45-46).en_US
dc.description.abstractIn this work we show a barrier towards proving a randomness-efficient parallel repetition, a promising avenue for achieving many tight inapproximability results. Feige and Kilian (STOC'95) proved an impossibility result for randomnessefficient parallel repetition for two prover games with small degree, i.e., when each prover has only few possibilities for the question of the other prover. In recent years, there have been indications that randomness-efficient parallel repetition (also called derandomized parallel repetition) might be possible for games with large degree, circumventing the impossibility result of Feige and Kilian. In particular, Dinur and Meir (CCC'11) construct games with large degree whose repetition can be derandomized using a theorem of Impagliazzo, Kabanets and Wigderson (SICOMP'12). However, obtaining derandomized parallel repetition theorems that would yield optimal inapproximability results has remained elusive. This paper presents an explanation for the current impasse in progress, by proving a limitation on derandomized parallel repetition. We formalize two properties which we call "fortification-friendliness" and "yields robust embeddings". We show that any proof of derandomized parallel repetition achieving almost-linear blow-up cannot both (a) be fortification-friendly and (b) yield robust embeddings. Unlike Feige and Kilian, we do not require the small degree assumption. Given that virtually all existing proofs of parallel repetition share these two properties, our no-go theorem highlights a major barrier to achieving almostlinear derandomized parallel repetition.en_US
dc.description.statementofresponsibilityby Govind Ramnarayan.en_US
dc.format.extent71 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectElectrical Engineering and Computer Science.en_US
dc.titleA no-go theorem for derandomized parallel repetitionen_US
dc.typeThesisen_US
dc.description.degreeS.M. in Computer Science and Engineeringen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
dc.identifier.oclc965242032en_US


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