J. Wang. Average-case intractable NP problems. In D.-Z. Du and K.-I. Ko, editors, Advances in Languages, Algorithms, and Complexity. Kluver Academic Publishers, 1997. to appear. 4  Home/Search Document Details and Download
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Polynomial on Average Under Natural Distributions - Schuler (Correct)
....by Levin, there is a reasonable notion of reducibility, which preserves solvability in time polynomial on average. Furthermore, there are NP problems that are for a certain distribution on the instances, complete under this reducibility for the class NP and a natural set of distributions (see [Wan97]) Note that it is necessary to restrict the set of distributions, since there are distributions m such that every algorithm which is polynomial on m average is already polynomially bounded in the worst case [LV92, Mil93] In a typical application instances of the problem are generated by some ....
J. Wang. Average-case intractable NP problems. In D.-Z. Du and K.-I. Ko, editors, Advances in Languages, Algorithms, and Complexity. Kluver Academic Publishers, 1997. to appear. 4
The Computational Complexity Column - Allender (1998) (Correct)
.... high probability (Monte Carlo randomization) or one that is guaranteed to be correct after what is likely to be a polynomial amount of time (Las Vegas randomization) 5 C mon guys, you re laying it on a bit thick, aren t you For a more optimistic view on average case complexity, please consult [Wang97a, Wang97b]. EWA These seemed at first to be potentially powerful generalizations of polynomial time. Randomized Monte Carlo and Las Vegas algorithms are a workhorse of cryptography, and have important applications in computational geometry, pattern matching, on line algorithms and computer algebra (see ....
J. Wang. Average-case intractable NP problems. In D.-Z. Du and K.-I. Ko, editors, Advances in Languages, Algorithms, and Complexity, Kluwer Academic Publishers, pp. 313-378, 1997.
Average-case Computational Complexity Theory - Wang (1996) (28 citations) Self-citation (Wang) (Correct)
....similarly to Lemma 3.6, it is straightforward to show the 8 Requiring that the good input domain be certifiable is sometimes impossible. In such a case, we may need to construct a reduction that produces a witness along with the yes no answer, so that the correctness of the answer can be verified [Wan97]. 1. Average Case Computational Complexity Theory 19 following lemma for distributional decision problems. The lemma is also true for search problems. Lemma 4.4 (1) If (A; is ap time randomly reducible to (B; and (B; is in RAP, then so is (A; 2) The ap time randomized reductions are ....
....a certain matrix transformation problem with a flat distribution is complete for DistNP. Some additional distributional problems are shown to be average case NP complete under randomized reductions in [VR92] Due to space limitations, exposition of these results will be given in a separate paper [Wan97]. To demonstrate the idea of using randomized reductions, we show that a certain halting problem with a flat distribution is complete for DistNP under p time randomized reductions. We then show, in the next section, that polynomial time sampling does not generate harder instances than uniformly ....
J. Wang. Average-case intractable NP problems. In Advances in Complexity and Algorithms (D.-Z. Du and K.-I. Ko eds), Kluwer Academic Publishers. 1997, to appear.
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