A Polylogarithmic PRG for Degree 2 Threshold Functions in the Gaussian Setting

Kane, Daniel M.

doi:10.4230/LIPIcs.CCC.2015.567

Document

A Polylogarithmic PRG for Degree 2 Threshold Functions in the Gaussian Setting

Author Daniel M. Kane

Part of: Volume: 30th Conference on Computational Complexity (CCC 2015)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Computational Complexity Conference (CCC)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2015-06-06

PDF

File

PDF

LIPIcs.CCC.2015.567.pdf

Filesize: 484 kB
15 pages

Document Identifiers

DOI: 10.4230/LIPIcs.CCC.2015.567
URN: urn:nbn:de:0030-drops-50534

Subject Classification

Keywords

polynomial threshold function
pseudorandom generator
Gaussian distribution

Metrics

Access Statistics
Total Accesses (updated on a weekly basis)

0

PDF Downloads

0

Metadata Views

Abstract

We construct and analyze a new pseudorandom generator for degree 2 polynomial threshold functions with respect to the Gaussian measure. In particular, we obtain one whose seed length is polylogarithmic in both the dimension and the desired error, a substantial improvement over existing constructions.

Our generator is obtained as an appropriate weighted average of pseudorandom generators against read once branching programs. The analysis requires a number of ideas including a hybrid argument and a structural result that allows us to treat our degree 2 threshold function as a function of a number of linear polynomials and one approximately linear polynomial.

Cite As Get BibTex

Daniel M. Kane. A Polylogarithmic PRG for Degree 2 Threshold Functions in the Gaussian Setting. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 567-581, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.CCC.2015.567

Author Details

Daniel M. Kane

Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail