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Two problems in noise tolerant computing
Descriptive
TitleInfo
Title
Two problems in noise tolerant computing
Name
(type = personal)
NamePart
(type = family)
Tang
NamePart
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Sijian
NamePart
(type = date)
1991-
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Sijian Tang
Role
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author
Name
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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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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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(type = personal)
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(type = family)
Allender
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Eric
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Eric Allender
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Advisory Committee
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internal member
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Kindler
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Guy
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Guy Kindler
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Advisory Committee
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outside member
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Rutgers University
Role
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degree grantor
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School of Graduate Studies
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Text
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theses
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2018
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2018-10
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2018
Place
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xx
Language
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eng
Abstract
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This thesis consists of 2 main results about computations under random noise. In both problems we consider the discrete input picked from the hamming cube {0,1}<sup>n</sup>. Noise is introduced by flipping each input bit randomly with some fixed probability.
In Chapter 2 we provide the first polynomial algorithm for noisy population recovery problem with finite support. This result directly implies a reverse Bonami-Beckner type inequality for sparse functions.
In Chapter 3 we study the noisy broadcast model and the generalized noisy decision tree (gnd-tree) model under noise cancellation adversary. Here noise cancellation adversary is a type of adversary that can correct the random noise. Under the noise cancellation adversary, we show an Ω(ε<sup>5</sup>·n log n) lower bound for the function $OR$ in the non-adaptive gnd-tree model. This implies an Ω(log(1/ε)<sup>-1</sup> ·n log log n) lower bound for a special kind of noisy broadcast model which we call the 2-Phase noisy broadcast model.
In Chapter 2 we provide the first polynomial algorithm for noisy population recovery problem with finite support. This result directly implies a reverse Bonami-Beckner type inequality for sparse functions.
In Chapter 3 we study the noisy broadcast model and the generalized noisy decision tree (gnd-tree) model under noise cancellation adversary. Here noise cancellation adversary is a type of adversary that can correct the random noise. Under the noise cancellation adversary, we show an Ω(ε<sup>5</sup>·n log n) lower bound for the function $OR$ in the non-adaptive gnd-tree model. This implies an Ω(log(1/ε)<sup>-1</sup> ·n log log n) lower bound for a special kind of noisy broadcast model which we call the 2-Phase noisy broadcast model.
Subject
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Topic
Mathematics
Subject
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Topic
Random noise theory
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Title
Rutgers University Electronic Theses and Dissertations
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ETD
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TitleInfo
Title
School of Graduate Studies Electronic Theses and Dissertations
Identifier
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rucore10001600001
Identifier
ETD_9193
Identifier
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doi:10.7282/t3-bhzn-nk34
PhysicalDescription
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (77 pages: illustrations)
Note
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Ph.D.
Note
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Includes bibliographical references
Note
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by Sijian Tang
Location
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NjNbRU
Genre
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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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Tang
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Sijian
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Permission or license
DateTime
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2018-09-14 01:28:08
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Sijian Tang
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Affiliation
Rutgers University. School of Graduate Studies
AssociatedObject
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Name
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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2018-09-26T22:58:30
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2018-09-26T22:58:30
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