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Hardness of Solving Sparse Overdetermined Linear Systems

2009
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ACM Transactions on Computation Theory
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A classic result due to Håstad established that for every constant ε > 0, given an overdetermined system of linear equations over a finite field Fq where each equation depends on exactly 3 variables and at least a fraction (1 − ε) of the equations can be satisfied, it is NP-hard to satisfy even a fraction'1 q + ε´of the equations. In this work, we prove the analog of Håstad's result for equations over the integers (as well as the reals). Formally, we prove that for every ε, δ > 0, given a

doi:10.1145/1595391.1595393
fatcat:xby4pxzqpra53adtfgmnwmf2vy