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On circuit complexity classes and iterated matrix multiplication
Descriptive
TitleInfo
Title
On circuit complexity classes and iterated matrix multiplication
Name
(type = personal)
NamePart
(type = family)
Wang
NamePart
(type = given)
Fengming
NamePart
(type = date)
1980-
DisplayForm
Fengming Wang
Role
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(authority = RULIB)
author
Name
(type = personal)
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Allender
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(type = given)
Eric
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Eric Allender
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Advisory Committee
Role
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chair
Name
(type = personal)
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(type = family)
Saks
NamePart
(type = given)
Michael
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Michael Saks
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Advisory Committee
Role
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(authority = RULIB)
internal member
Name
(type = personal)
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(type = family)
Szegedy
NamePart
(type = given)
Mario
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Mario Szegedy
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
Impagliazzo
NamePart
(type = given)
Russell
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Russell Impagliazzo
Affiliation
Advisory Committee
Role
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(authority = RULIB)
outside member
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NamePart
Rutgers University
Role
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(authority = RULIB)
degree grantor
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Graduate School - New Brunswick
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school
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Text
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theses
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DateCreated
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2012
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(type = degree)
2012-01
Place
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xx
Language
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(type = code)
eng
Abstract
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In this thesis, we study small, yet important, circuit complexity classes within NC^1, such as ACC^0 and TC^0. We also investigate the power of a closely related problem called Iterated Matrix Multiplication and its implications in low levels of algebraic complexity theory. More concretely, 1. We show that extremely modest-sounding lower bounds for certain problems can lead to non-trivial derandomization results. a. If the word problem over S_5 requires constant-depth threshold circuits of size n^{1+epsilon} for some epsilon > 0, then any language accepted by uniform polynomial-size probabilistic threshold circuits can be solved in subexponential time (and more strongly, can be accepted by a uniform family of deterministic constant-depth threshold circuits of subexponential size.) b. If there are no constant-depth arithmetic circuits of size n^{1+epsilon} for the problem of multiplying a sequence of n 3-by-3 matrices, then for every constant d, black-box identity testing for depth-d arithmetic circuits with bounded individual degree can be performed in subexponential time (and even by a uniform family of deterministic constant-depth AC circuits of subexponential size). 2. ACC_m circuits are circuits consisting of unbounded fan-in AND, OR and MOD_m gates and unary NOT gates, where m is a fixed integer. We show that there exists a language in non-deterministic exponential time which can not be computed by any non-uniform family of ACC_m circuits of quasi-polynomial size and o(loglog n) depth, where $m$ is an arbitrarily chosen constant. 3. We show that there are families of polynomials having small depth-two arithmetic circuits that cannot be expressed by algebraic branching programs of width two. This clarifies the complexity of the problem of computing the product of a sequence of two-by-two matrices, which arises in several settings.
Subject
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Topic
Computer Science
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Title
Rutgers University Electronic Theses and Dissertations
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ETD_3715
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electronic resource
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application/pdf
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text/xml
Extent
viii, 79 p. : ill.
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = vita)
Includes vita
Note
(type = statement of responsibility)
by Fengming Wang
Subject
(authority = ETD-LCSH)
Topic
Programming languages (Electronic computers)
Subject
(authority = ETD-LCSH)
Topic
Cellular automata
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000064183
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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/T35D8QVQ
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
RightsDeclaration
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The author owns the copyright to this work.
RightsHolder
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Name
FamilyName
Wang
GivenName
Fengming
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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(qualifier = exact);
(point = start)
2011-12-09 22:07:49
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Name
Fengming Wang
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Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
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License
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
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Copyright protected
Availability
Status
Open
Reason
Permission or license
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526336
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