We construct so-called distinguishers, sparse matrices that retain some properties of error correcting codes. They provide a technically and conceptually simple approach to magnification. We generalize and strengthen known general (not problem specific) magnification results and in particular achieve magnification thresholds below known lower bounds. For example, we show that fixed polynomial formula size lower bounds for NP are implied by slightly superlinear formula size lower bounds for approximating any sufficiently sparse problem in NP. We also show that the thresholds achieved are sharp. Additionally, our approach yields a uniform magnification result for the minimum circuit size problem. This seems to sidestep the localization barrier.

翻译：我们构造了所谓的区分器——一种保留纠错码某些性质的稀疏矩阵。它们为放大提供了技术上和概念上均简单的方法。我们推广并强化了已知的一般性（非问题特定）放大结果，尤其实现了低于已知下界的放大阈值。例如，我们证明：通过对NP中任意足够稀疏问题的逼近获得略超线性的公式规模下界，即可推出NP问题的固定多项式公式规模下界。我们还证明所实现的阈值具有尖锐性。此外，我们的方法能为最小电路规模问题产生均匀放大结果，这似乎规避了定位障碍。