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Some applications of randomness in computational complexity
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TitleInfo
Title
Some applications of randomness in computational complexity
Name
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Friedman
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Luke
NamePart
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1982-
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Luke Friedman
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author
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Eric
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Eric Allender
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chair
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Kopparty
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Swastik
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Swastik Kopparty
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Advisory Committee
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internal member
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Saks
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Michael
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Michael Saks
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Advisory Committee
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internal member
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Pitassi
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Toniann
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Toniann Pitassi
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Advisory Committee
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Rutgers University
Role
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degree grantor
Name
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Graduate School - New Brunswick
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Text
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theses
OriginInfo
DateCreated
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2013
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2013-05
Place
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xx
Language
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eng
Abstract
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In this dissertation we consider two different notions of randomness and their applications to problems in complexity theory. In part one of the dissertation we consider Kolmogorov complexity, a way to formalize a measure of the randomness of a single finite string, something that cannot be done using the usual distributional definitions. We let R be the set of random strings under this measure and study what resource-bounded machines can compute using R as an oracle. We show the surprising result that under proper definitions we can in fact define well-formed complexity classes using this approach, and that perhaps it is possible to exactly characterize standard classes such as BPP and NEXP in this way. In part two of the dissertation we switch gears and consider the use of randomness as a tool in propositional proof complexity, a sub-area of complexity theory that addresses the NP vs. coNP problem. Here we consider the ability of various proof systems to efficiently refute randomly generated unsatisfiable 3-CNF and 3-XOR formulas. In particular, we show that certain restricted proof systems based on Ordered Binary Decision Diagrams requires exponential-size refutations of these formulas. We also outline a new general approach for proving proof complexity lower bounds using random 3-CNF formulas and demonstrate its use on treelike resolution, a weak proof system.
Subject
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Topic
Computer Science
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Title
Rutgers University Electronic Theses and Dissertations
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ETD_4606
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electronic resource
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application/pdf
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Extent
viii, 125 p. : ill.
Note
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Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = statement of responsibility)
by Luke Friedman
Subject
(authority = ETD-LCSH)
Topic
Computational complexity
Subject
(authority = ETD-LCSH)
Topic
Random operators
Identifier
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http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000068854
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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NjNbRU
Identifier
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doi:10.7282/T32B8WNG
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
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The author owns the copyright to this work.
RightsHolder
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Name
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Friedman
GivenName
Luke
Role
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Permission or license
DateTime
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2013-04-09 11:49:19
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Luke Friedman
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Affiliation
Rutgers University. Graduate School - New Brunswick
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License
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Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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windows xp
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