Recombination Operators for Satisfiability Problems

The satisfiability problem (SAT) [6] consists in finding a truth assignment that satisfies a wellformed Boolean expression. An instance of the SAT problem is defined by a set of boolean variables (also called atoms) X = {x1, ..., xn} and a boolean formula φ: {0, 1}n → {0, 1}. A literal is a variable or its negation. A (truth) assignment is a function v:X → {0, 1}. The formula is said to be satisfiable if there exists an assignment satisfying φ and unsatisfiable otherwise. The formula φ is in conjunctive normal form (CNF) if it is a conjunction of clauses where a clause is a disjunction of literals. In this paper, φ is supposed to be in CNF. SAT is originally stated as a decision problem but we are also interesting here in the MAX-SAT problem which consists in finding an assignment which satisfies the maximum number of clauses in φ.