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On the Complexity of Hardness Amplification
2008
IEEE Transactions on Information Theory
For 2 (0; 1) and k; n 2 , we study the task of transforming a hard function f : f0; 1g n ! f0; 1g, with which any small circuit disagrees on (1 0 )=2 fraction of the input, into a harder function f 0 , with which any small circuit disagrees on (1 0 k )=2 fraction of the input. First, we show that such hardness amplification, when carried out in some black-box way, must require a high complexity. In particular, it cannot be realized by a circuit of depth d and size 2 o(k ) or by a
doi:10.1109/tit.2008.928988
fatcat:7niutgi45vdwhcuhg66cr2lgkq