On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
Resettable zero-knowledge (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Which Problems Have Strongly Exponential Complexity?
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Note: Computational complexity of some restricted instances of 3-SAT
Discrete Applied Mathematics
Computational complexity of quantified Boolean formulas with fixed maximal deficiency
Theoretical Computer Science
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Consider a formula that contains n variables with the form Φ = Φ2 ∧ Φ3, where Φ2 is an instance of 2-SAT containing m2 2-clauses and Φ3 is an instance of 3-SAT containing m3 3-clauses. Φ is an instance of (2 + f(n))-SAT if m3/(m2 + m3) ≤ f(n). We prove that (2 + f(n))-SAT is in P if f(n) = O(log n/n2), and in NPC if f(n) = 1/n2-ε(∀ε: 0 n)k/n2)-SAT (k ≥ 2), for natural problems in NP - NPC - P (denoted as NPI) with respect to this (2 + f(n))-SAT model. We prove that the restricted version of it is not in NPC under P ≠ NP. Actually, it is indeed in NPI under some stronger but plausible assumption, specifically, the exponential-time hypothesis.