Testability of linear-invariant properties
Name
768836640-MIT.pdf
Description
Full printable version
Size
4.51 MB
Format
Adobe PDF
Checksum (MD5)
9051f57ca21dd00c3588c2d15fdd6a62
Author(s)
Bhattacharyya, Arnab
Advisor(s)
Ronitt Rubinfeld.
Date Issued
2011
Publisher
Massachusetts Institute of Technology
Abstract
Property Testing is the study of super-efficient algorithms that solve "approximate decision problems" with high probability. More precisely, given a property P, a testing algorithm for P is a randomized algorithm that makes a small number of queries into its input and distinguishes between whether the input satisfies P or whether the input is "far" from satisfying P, where "farness" of an object from P is measured by the minimum fraction of places in its representation that needs to be modified in order for it to satisfy P. Property testing and ideas arising from it have had significant impact on complexity theory, pseudorandomness, coding theory, computational learning theory, and extremal combinatorics. In the history of the area, a particularly important role has been played by linearinvariant properties, i.e., properties of Boolean functions on the hypercube which are closed under linear transformations of the domain. Examples of such properties include linearity, homogeneousness, Reed-Muller codes, and Fourier sparsity. In this thesis, we describe a framework that can lead to a unified analysis of the testability of all linear-invariant properties, drawing on techniques from additive combinatorics and from graph theory. We also show the first nontrivial lowerbound for the query complexity of a natural testable linear-invariant property.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 75-80).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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