Complexity of k-SAT

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⩾3. Define s_k (for k⩾3) to be the infimum of {δ: there exists an O(2 ^δn) algorithm for solving k-SAT}. Define ETH (Exponential-Time Hypothesis) for k-SAT as follows: for k⩾3, s_k >0. In other words, for k⩾3, k-SA 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_∞ be the limit of s_k. We in fact show that s_k⩽(1-d/k) s_∞ for some constant d>0