An incomplete method for solving the propositional satisfiability problem (or a general constraint satisfaction problem) is one that does not provide the guarantee that it will eventually either report a satisfying assignment or declare that the given formula is unsatisfiable. In practice, most such methods are biased towards the satisfiable side: they are typically run with a pre-set resource limit, after which they either produce a valid solution or report failure; they never declare the formula to be unsatisfiable. These are the kind of algorithms we will discuss in this chapter. In complexity theory terms, such algorithms are referred to as having one-sided error. In principle, an incomplete algorithm could instead be biased towards the unsatisfiable side, always providing proofs of unsatisfiability but failing to find solutions to some satisfiable instances, or be incomplete with respect to both satisfiable and unsatisfiable instances (and thus have two-sided error). Unlike systematic solvers often based on an exhaustive branching and backtracking search, incomplete methods are generally based on stochastic local search,

www.elsevier.com/locate/artint A comparative runtime analysis of heuristic algorithms for satisfiability problems