Lattice problems in NP ∩ coNP

@article{Aharonov2005LatticePI,
  title={Lattice problems in NP ∩ coNP},
  author={Dorit Aharonov and Oded Regev},
  journal={J. ACM},
  year={2005},
  volume={52},
  pages={749-765}
}
We show that the problems of approximating the shortest and closest vector in a lattice to within a factor of &nradic; lie in NP intersect coNP. The result (almost) subsumes the three mutually-incomparable previous results regarding these lattice problems: Banaszczyk [1993], Goldreich and Goldwasser [2000], and Aharonov and Regev [2003]. Our technique is based on a simple fact regarding succinct approximation of functions using their Fourier series over the lattice. This technique might be… 

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