2012 IEEE 27th Conference on Computational Complexity (1999)

Atlanta, Georgia

May 4, 1999 to May 6, 1999

ISSN: 1093-0159

ISBN: 0-7695-0075-7

pp: 237

Ramamohan Paturi , University of California at San Diego

Russell Impagliazzo , University of California at San Diego

ABSTRACT

The problem of k-SAT is to determine if the given k-CNF has a satisfying solution. It is a celebrated open question as to whether it requires exponential time to solve k-SAT for k \geq 3.Define s_k (for k\geq 3) to be the infimum of \{\delta: \mbox{there exists an O(2^{\delta n})} \mbox{ algorithm for solving k-SAT} \}. Define {\bf ETH} (Exponential-Time Hypothesis) for k-SAT as follows: for k\geq 3, s_k >0. In other words, for k \geq 3, k-SAT does not have a subexponential-time algorithm.In this paper, we show that s_k is an increasing sequence assuming \eth\ for k-SAT. Let s_\infty be the limit of s_k. We will in fact show that s_k \leq (1-d/(ek))s_\infty for some constant d >0.

INDEX TERMS

Satisfiability, NP-completeness, Reductions, Complexity Theory

CITATION

Ramamohan Paturi,
Russell Impagliazzo,
"The Complexity of k-SAT",

*2012 IEEE 27th Conference on Computational Complexity*, vol. 00, no. , pp. 237, 1999, doi:10.1109/CCC.1999.766282