Average case complete problems
SIAM Journal on Computing
Structural complexity 1
Cook reducibility is faster than Karp reducibility in NP
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Journal of Computer and System Sciences
On the greedy algorithm for satisfiability
Information Processing Letters
On the theory of average case complexity
Journal of Computer and System Sciences
Structural properties of complete problems for exponential time
Complexity theory retrospective II
Average-case computational complexity theory
Complexity theory retrospective II
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
A personal view of average-case complexity
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
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In this paper we separate many-one reducibility from truthtable reducibility for distributional problems in DistNP under the hypothesis that P ≠ NP. As a first example we consider the 3-Satisfiability problem (3SAT) with two different distributions on 3CNF formulas. We show that 3SAT using a version of the standard distribution is truth-table reducible but not many-one reducible to 3SAT using a less redundant distribution unless P = NP. We extend this separation result and define a distributional complexity class C with the following properties: (1) C is a subclass of DistNP, this relation is proper unless P = NP. (2) C contains DistP, but it is not contained in AveP unless DistNP ⊆ AveZPP. (3) C has a ≤mp-complete set. (4) C has a ≤ttp-complete set that is not ≤mp-complete unless P = NP. This shows that under the assumption that P ≠ NP, the two completeness notions differ on some non-trivial subclass of DistNP.