Local Search Algorithms for kSAT

Problem Definition

The CNF Satisfiability problem is to determine, given a CNF formula F with n variables, whether or not there exists a satisfying assignment for F. If each clause of F contains at most k literals, then F is called a k-CNF formula and the problem is called k-SAT, which is one of the most fundamental NP-complete problems. The trivial algorithm is to search 2ⁿ 0/1-assignments for the n variables. But since [6], several algorithms which run significantly faster than this O(2ⁿ) bound have been developed. As a simple exercise, consider the following straightforward algorithm for 3-SAT, which gives us an upper bound of 1.913ⁿ: Choose an arbitrary clause in F, say $(x_1 \vee \overline{x_2} \vee x_3)$. Then generate seven new formulas by substituting to these x ₁, x ₂ and x ₃ all the possible values excepting $(x_1, x_2, x_3) = (0,1,0)$ which obviously unsatisfies F. Now one can check the satisfiability of these seven formulas and conclude that Fis satisfiable iff at...