Algebraic methods in pseudorandomness and circuit complexity
Name
965381860-MIT.pdf
Description
Full printable version
Size
5.64 MB
Format
Adobe PDF
Checksum (MD5)
cf39f44bae9fb6a488bdef221c0ae133
Author(s)
Remscrim, Zachary (Zachary N.)
Advisor(s)
Michael Sipser.
Date Issued
2016
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, we apply tools from algebra and algebraic geometry to prove new results concerning extractors for algebraic sets, AC⁰-pseudorandomness, the recursive Fourier sampling problem, and VC dimension. We present a new construction of an extractor which works for algebraic sets defined by polynomials over F₂ of substantially higher degree than the previous state-of-the-art construction. We exhibit a collection of natural functions that behave pseudorandomly with regards to AC⁰ tests. We also exactly determine the F₂-polynomial degree of the recursive Fourier sampling problem and use this to provide new partial results towards a circuit lower bound for this problem. Finally, we answer a question posed in [MR15] concerning VC dimension, interpolation degree and the Hilbert function.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 93-96).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
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