Recently several local hill-climbing procedures for propositional satisability havebeen proposed, which are able to solve large and di cult problems beyond the reach ofconventional algorithms like Davis-Putnam. By the introduction of some new variants of these procedures, we provide strong experimental evidence to support the conjecture that neither greediness nor randomness is important in these procedures. One of the variants introduced seems to o er signi cant improvements over earlier procedures. In addition, we investigate experimentally how their performance depends on their parameters. Our results suggest that run-time scales less than simply exponentially in the problem size. 1

In this paper, tabu search for SAT is investigated from an experimental point of view. To this end, TSAT, a basic tabu search algorithm for SAT, is introduced and compared with Selman et al. Random Walk Strategy GSAT procedure, in short RWS-GSAT. TSAT does not involve the additional

Conventional ways of using local search are difficult to generalize. Increased efficiency is the only goal, generality often being disregarded. This is manifested in the highly monolithic encodings of complex problems and the application of highly specific satisfaction methods. Other approaches take the general constraint programming framework as a starting point and try to introduce local search methods for constraint satisfaction. These methods frequently fail because they have only a very limited view of the unknown search-space structure. The present paper attempts to overcome the drawbacks of these two approaches by using global constraints. The use of global constraints for local search allows us to revise a current state on a more global level with domain-specific knowledge, while preserving features like reusability and maintenance. The proposed strategy is demonstrated on a dynamic job-shop scheduling problem.

Abstract. We describe a branch and cut algorithm for both MAX-SAT and weighted MAX-SAT. This algorithm uses the GSAT procedure as a primal heuristic. At each nodewe solve a linear programming (LP) relaxation of the problem. Two styles of separating cuts are added: resolution cuts and odd cycle inequalities. We compare our algorithm to an extension of the Davis Putnam Loveland (EDPL) algorithm. Our algorithm is more e ective than EDPL on some problems, notably MAX-2-SAT. EDPL is more e ective on some other classes of problems. 1.

We describe a branch and cut algorithm for both MAX-SAT and weighted MAX-SAT. This algorithm uses the GSAT procedure as a primal heuristic. At each nodewe solve a linear programming (LP) relaxation of the problem. Two styles of separating cuts are added: resolution cuts and odd cycle inequalities. We compare our algorithm to an extension of the Davis Putnam Loveland (EDPL) algorithm and a Semi-Definite Programming (SDP) approach. Our algorithm is more effective than EDPL on some problems, notably MAX-2-SAT. EDPL and SDP are more effective on some other classes of problems.

This paper has two related themes. Firstly, artificial SAT problems to show that certain chains of variable dependency have a harmful effect on local search, sometimes causing exponential scaling on intrinsically easy problems. Secondly, systematic, local and hybrid SAT algorithms are evaluated on Hamiltonian cycle problems, exposing weaknesses in all three. The connection between the two themes is that some Hamiltonian cycle problems also cause local search to scale badly, indicating that pathological variable dependencies occur in more realistic applications. More generally, the results highlight the need for alternative models and search algorithms, and new examples of both are described.

The satisfiability problem (SAT) is a fundamental problem in mathematical logic, constraint satisfaction, VLSI engineering, and computing theory. Methods to solve the satisfiability problem play an important role in the development of computing theory and systems. In this paper, we give a BDD (Binary Decision Diagrams) SAT solver for practical asynchronous circuit design. The BDD SAT solver consists of a structural SAT formula preprocessor and a complete, incremental SAT algorithm that is able to nd an optimal solution. The preprocessor compresses a large size SAT formula representing the circuit into a number of smaller SAT formulas. This avoids the problem of solving very large SAT formulas. Each small size SAT formula is solved by the BDD SAT algorithm e ciently. Eventually, the results of these subproblems are integrated together that contribute to the solution of the original problem. According to recent industrial assessments, this BDD SAT solver provides solutions to the practical, industrial asynchronous circuit design problem.

We introduce a greedy local search procedure called GSAT for solving propositional satis ability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the Davis-Putnam procedure or resolution. We also show that GSAT can solve structured satisfiability problems quickly. In particular, we solve encodings of graph coloring problems, N-queens, and Boolean induction. General application strategies and limitations of the approach are also discussed. GSAT is best viewed as a model-finding procedure. Its good performance suggests that it may beadvantageous to reformulate reasoning tasks that have traditionally been viewed as theorem-proving problems as model-finding tasks.