1 research outputs found
NP-Hardness of Approximately Solving Linear Equations Over Reals
URL lists article on conference siteIn 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 ānon-trivialā. Here is an informal statement of our result: it is NP-hard
to distinguish whether there is a non-trivial assignment that satisfies fraction of the
equations or every non-trivial assignment fails to satisfy a constant fraction of the equations
with a ``margin" of .
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.National Science Foundation (U.S.) (NSF CAREER grant CCF-0833228)National Science Foundation (U.S.) (Expeditions grant CCF-0832795)U.S.-Israel Binational Science Foundation (BSF grant 2008059