Pseudorandomness and Average-Case Complexity via Uniform Reductions

DSpace/Manakin Repository

Pseudorandomness and Average-Case Complexity via Uniform Reductions

Citable link to this page


Title: Pseudorandomness and Average-Case Complexity via Uniform Reductions
Author: Trevisan, Luca; Vadhan, Salil

Note: Order does not necessarily reflect citation order of authors.

Citation: Trevisan, Luca and Salil Vadhan. 2007. Pseudorandomness and average-case complexity via uniform reductions. Computational Complexity, 16, no. 4: 331-364.
Full Text & Related Files:
Abstract: Impagliazzo and Wigderson (36th FOCS, 1998) gave the first construction of pseudorandom generators from a uniform complexity assumption on EXP (namely EXP [not equal to] BPP). Unlike results in the nonuniform setting, their result does not provide a continuous trade-off between worst-case hardness and pseudorandomness, nor does it explicitly establish an average-case hardness result.

In this paper:

1. We obtain an optimal worst-case to average-case connection for EXP: if EXP is not a subset of BPTIME(t(n)), EXP has problems that cannot be solved on a fraction 1/2 +1/t'(n) of the inputs by BPTIME(t'(n)) algorithms, for t'=t^{\Omega(1)}.

2. We exhibit a PSPACE-complete self-correctible and downward self-reducible problem. This slightly simplifies and strengthens the proof of Impaglaizzo and Wigderson, which used a a #P-complete problem with these properties.

3. We argue that the results of Impagliazzo and Wigderson, and the ones in this paper, cannot be proved via "black-box" uniform reductions.
Published Version:
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at
Citable link to this page:
Downloads of this work:

Show full Dublin Core record

This item appears in the following Collection(s)


Search DASH

Advanced Search