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- W2093750812 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 “nontrivial.” Here is an informal statement of our result: it is $mathcal{NP}$-hard to distinguish whether there is a nontrivial assignment that satisfies $1-delta$ fraction of the equations or every nontrivial 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 $f: mathbb{R}^n mapsto mathbb{R}$ over a Gaussian space, which could be of independent interest. Our research is motivated by a possible approach to proving the unique games conjecture." @default.
- W2093750812 created "2016-06-24" @default.
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- W2093750812 date "2010-01-01" @default.
- W2093750812 modified "2023-09-25" @default.
- W2093750812 title "NP-Hardness of Approximately Solving Linear Equations Over Reals." @default.
- W2093750812 hasPublicationYear "2010" @default.
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