Average-case Complexity

@article{Bogdanov2008AveragecaseC,
  title={Average-case Complexity},
  author={Andrej Bogdanov and Luca Trevisan},
  journal={2008 49th Annual IEEE Symposium on Foundations of Computer Science},
  year={2008},
  pages={11-11}
}
We review the many open questions and the few things that are known about the average-case complexity of computational problems. We shall follow the presentations of Impagliazzo, of Goldreich, and of Bogdanov and the author, and focus on the following subjects. (i). Average-case tractability. What does it mean for a problem to have an "efficient on average'' algorithm with respect to a distribution of instances? There is more than one ``correct'' answer to this question, and a numberof… 
Special Issue On Worst-case Versus Average-case Complexity Editors’ Foreword
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It is shown unconditionally that error-prone average-case hardness is equivalent to errorless average- case hardness for P against NC1 and for UP ∩ coUP against P, and applied to get new equivalences between hitting set generators and pseudo-random generators.
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TLDR
This paper shows that several standard worst-case complexity assumptions are sufficient to imply non-trivial average-case hardness of NP or PH, and constructs quite efﷁcient complexity-theoretic pseudorandom generators under the assumption that the nondeterministic linear time is easy on average, which may be of independent interest.
Average-Case Completeness in Tag Systems
TLDR
This work shows that a tag system can efficiently simulate a Turing machine even when the input is provided in an extremely simple encoding which adds just log n carefully set bits to encode an arbitrary Turing machine input of length n.
One-Way Functions and a Conditional Variant of MKTP
TLDR
It is shown that McKTP is hard-on-average if and only if there are logspace-computable OWFs, which means the existence of OWFs is inextricably linked to the average-case hardness of this NP -complete problem.
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