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
Soundness in the Public-Key Model
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
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
Counting for Satisfiability by Inverting Resolution
Artificial Intelligence Review
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Consider a formula which contains n variables and m clauses with the form 驴 = 驴驴 驴 驴驴, where 驴驴 is an instance of 2-SAT which contains m驴 2-clauses and 驴驴 is an instance of 3-SAT which contains m驴 3-clauses. 驴 is an instance of (2 + f(n))-SAT if (m驴/m驴 + m驴) 驴 f(n). We prove that (2 + f(n))-SAT is in P if f(n) = O(log n/n驴), and in NPC if f(n) =1/(n驴-驴) (驴驴 : 0 n)k/n驴)-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 the assumption P 驴 NP. Actually it is indeed in NPI under some stronger but plausible assumption, specifically, the Exponential-Time Hypothesis (ETH) which was introduced by Impagliazzo and Paturi.