Limitations of Hardness vs. Randomness under Uniform Reductions

We consider (uniform) reductions from computing a function f to the task of distinguishing the output of some pseudorandom generator G from uniform. Impagliazzo and Wigderson [IW] and Trevisan and Vadhan [TV] exhibited such reductions for every function f in PSPACE. Moreover, their reductions are "black box," showing how to use any distinguisher T, given as oracle, in order to compute f (regardless of the complexity of T). The reductions are also adaptive, but only mildly (queries of the same length do not occur in different levels of adaptivity). Impagliazzo and Wigderson [IW] also exhibited such reductions for every function f in EXP, but those reductions are not black-box, because they only work when the oracle T is computable by small circuits. Our main results are that:

• Type: Conference
• Year: 2008
• Where: APPROX
• Authors: Dan Gutfreund, Salil P. Vadhan
• Keywords: Algorithms, APPROX 2008, Black-box Reductions, Nonadaptive Black-box Reductions, Reductions