NP-Hardness of Approximately Solving Linear Equations Over Reals
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Moshkovitz_NP-hardness.pdf
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275.53 KB
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Author(s)
Khot, Subhash
Moshkovitz Aaronson, Dana Hadar
Date Issued
June 2011
Journal
Proceedings of the 43rd ACM Symposium on Theory of Computing, ACM STOC 2011
Publisher
Association for Computing Machinery
Citation
Khot, Subhash and Dana Moshkovitz. "NP-Hardness of Approximately Solving Linear Equations Over Reals." Proceedings of the 43rd ACM Symposium on Theory of Computing, ACM STOC 2011, June 6-8, San Jose, California.
Version
Author's final manuscript
Abstract
In this paper, we consider the problem of approximately solving a system of homogeneous
linear equations over reals, where each equation contains at most three variables.
Since the all-zero assignment always satisfies all the equations exactly, we restrict the
assignments to be “non-trivial”. Here is an informal statement of our result: it is NP-hard
to distinguish whether there is a non-trivial assignment that satisfies $1-\delta$ fraction of the
equations or every non-trivial assignment fails to satisfy a constant fraction of the equations
with a ``margin" of $\Omega(\sqrt{\delta})$.
We develop linearity and dictatorship testing procedures for functions f : Rn 7--> R over
a Gaussian space, which could be of independent interest.
We believe that studying the complexity of linear equations over reals, apart from being
a natural pursuit, can lead to progress on the Unique Games Conjecture.
Description
URL lists article on conference site
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1145/1993636.1993692
