Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its importance, little is known of the ultimate strengths and limitations of the technique. This paper presents the first precise characterization of clause learning as a proof system (CL), and begins the task of understanding its power by relating it to the well-studied resolution proof system. In particular, we show that with a new learning scheme, CL can provide exponentially shorter proofs than many proper refinements of general resolution (RES) satisfying a natural property. These include regular and Davis-Putnam resolution, which are already known to be much stronger than ordinary DPLL. We also show that a slight variant of CL with unlimited restarts is as powerful as RES itself. Translating these analytical results to practice, however, presents a challenge because of the nondeterministic nature of clause learning algorithms. We propose a novel way of exploiting the underlying problem structure, in the form of a high level problem description such as a graph or PDDL specification, to guide clause learning algorithms toward faster solutions. We show that this leads to exponential speed-ups on grid and randomized pebbling problems, as well as substantial improvements on certain ordering formulas. 1.

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SAT Competition 2002 held in March--May 2002 in conjunction with SAT 2002 (the Fifth International Symposium on the Theory and Applications of Satisfiability Testing). About 30 solvers and 2300 benchmarks took part in the competition, which required more than 2 CPU years to complete the evaluation. In this report

Abstract. In 1997 we presented ten challenges for research on satisfiability testing [1]. In this paper we review recent progress towards each of these challenges, including our own work on the power of clause learning and randomized restart policies. 1

The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worst-case exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern generation [138, 221], planning [129, 197], scheduling [103], and even challenging problems from algebra [238]. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers [e.g. 13,

Abstract. Structural logical formulas sometimes yield a substantial fraction of so called equivalence clauses after translation to CNF. Probably the best known example of this is the parity-family. Large instances of such CNF formulas cannot be solved in reasonable time if no detection of, and extra reasoning with, these clauses is incorporated. That is, in solving these formulas, there is a more or less separate algorithmic device dealing with the equivalence clauses, called equivalence reasoning, and another dealing with the remaining clauses. In this paper we propose a way to align these two reasoning devices by introducing parameters for which we establish optimal values over a variety of existing benchmarks. We obtain a truly convincing speed-up in solving such formulas with respect to the best solving methods existing so far. 1

Preprocessing is an often used approach for solving hard instances of propositional satisfiability (SAT). Preprocessing can be used for reducing the number of variables and for drastically modifying the set of clauses, either by eliminating irrelevant clauses or by inferring new clauses. Over the years, a large number of formula manipulation techniques has been proposed, that in some situations have allowed solving instances not otherwise solvable with stateof -the-art SAT solvers. This paper proposes probing-based preprocessing, an integrated approach for preprocessing propositional formulas, that for the first time integrates in a single algorithm most of the existing formula manipulation techniques. Moreover, the new unified framework can be used to develop new techniques. Preliminary experimental results illustrate that probing-based preprocessing can be effectively used as a preprocessing tool in state-of-theart SAT solvers.

DPLL based clause learning algorithms for satisfiability testing are known to work very well in practice. However, like most branch-and-bound techniques, their performance depends heavily on the variable order used in making branching decisions. We propose a novel way of exploiting the underlying problem structure to guide clause learning algorithms toward faster solutions. The key idea is to use a higher level problem description, such as a graph or a PDDL specification, to generate a good branching sequence as an aid to SAT solvers.

Abstract. We present a method—called quantifier tree reconstruction—that allows to efficiently recover ex-post a portion of the internal structure of QBF instances which was hidden as a consequence of the cast to prenex normal form. Means to profit from a quantifier tree are presented for all the main families of QBF solvers. Surprising experiments on QBFLIB instances are also reported. 1

Abstract. We present a new and more efficient heuristic by restricting lookahead saturation (LAS) with NVO (neighbourhood variable ordering) and DEW (dynamic equality weighting). We report on the integration of this heuristic in Satz, a high-performance SAT solver, showing empirically that it significantly improves the performance on an extensive range of benchmark problems that exhibit hard structure. 1