HypBinRes, a particular form of hyper-resolution, was first employed in the SAT solver 2CLS+EQ. In 2CLS+EQ, HypBinRes and equality reduction are used at every node of a DPLL search tree, pruning much of the search tree.

It has been widely observed that there is no single “dominant ” SAT solver; instead, different solvers perform best on different instances. Rather than following the traditional approach of choosing the best solver for a given class of instances, we advocate making this decision online on a per-instance basis. Building on previous work, we describe SATzilla, an automated approach for constructing per-instance algorithm portfolios for SAT that use so-called empirical hardness models to choose among their constituent solvers. This approach takes as input a distribution of problem instances and a set of component solvers, and constructs a portfolio optimizing a given objective function (such as mean runtime, percent of instances solved, or score in a competition). The excellent performance of our SATzilla portfolios has been independently verified in the 2007 SAT Competition, where our SATzilla-07 solvers won three gold, one silver and one bronze medal. In this article, we go well beyond SATzilla-07 by making the portfolio construction scalable and completely automated, and improving it by integrating local search solvers as candidate solvers, by predicting performance score instead of runtime, and by using hierarchical hardness models that take into account different types of SAT instances. We demonstrate the effectiveness of these new techniques in extensive experimental results on data sets including instances from the most recent SAT competition. 1.

Deciding whether a propositional formula in conjunctive normal form is satisfiable (SAT) is an NP-complete problem. The problem becomes linear when the formula contains binary clauses only. Interestingly, the reduction to SAT of a number of well-known and important problems -- such as classical AI planning and automatic test pattern generation for circuits -- yields formulas containing many binary clauses. In this paper we introduce and experiment with 2-SIMPLIFY, a formula simplifier targeted at such problems. 2-SIMPLIFY constructs the transitive closure of the implication graph corresponding to the binary clauses in the formula and uses this graph to deduce new unit literals. The deduced literals are used to simplify the formula and update the graph, and so on, until stabilization. Finally, we use the graph to construct an equivalent, simpler set of binary clauses. Experimental evaluation of this simplifier on a number of bench-mark formulas produced by encoding AI planning problems prove 2-SIMPLIFY to be a useful tool in many circumstances.

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. Binary clause reasoning has found some successful applications in SAT, and it is natural to investigate its use in various extensions of SAT. In this paper we investigate the use of binary clause reasoning in the context of solving Quantified Boolean Formulas (QBF). We develop a DPLL based QBF solver that employs extended binary clause reasoning (hyper-binary resolution) to infer new binary clauses both before and during search. These binary clauses are used to discover additional forced literals, as well as to perform equality reduction. Both of these transformations simplify the theory by removing one of its variables. When applied during DPLL search this stronger inference can offer significant decreases in the size of the search tree, but it can also be costly to apply. We are able to show empirically that despite the extra costs, binary clause reasoning can improve our ability to solve QBF. 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,

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.

Abstract. In this paper we investigate the use of preprocessing when solving Quantified Boolean Formulas (QBF). Many different problems can be efficiently encoded as QBF instances, and there has been a great deal of recent interest and progress in solving such instances efficiently. Ideas from QBF have also started to migrate to CSP with the exploration of Quantified CSPs which offer an intriguing increase in representational power over traditional CSPs. Here we show that QBF instances can be simplified using techniques related to those used for preprocessing SAT. These simplifications can be performed in polynomial time, and are used to preprocess the instance prior to invoking a worst case exponential algorithm to solve it. We develop a method for preprocessing QBF instances that is empirically very effective. That is, the preprocessed formulas can be solved significantly faster, even when we account for the time required to perform the preprocessing. Our method significantly improves the efficiency of a range of state-of-the-art QBF solvers. Furthermore, our method is able to completely solve some instances just by preprocessing, including some instances that to our knowledge have never been solved before by any QBF solver. 1

Abstract. Boolean satisfiability (SAT) and its extensions are becoming a core technology for the analysis of systems. The SAT-based approach divides into three steps: encoding, preprocessing, and search. It is often argued that by encoding arbitrary Boolean formulas in conjunctive normal form (CNF), structural properties of the original problem are not reflected in the CNF. This should result in the fact that CNF-level preprocessing and SAT solver techniques have an inherent disadvantagecompared to related techniques applicable on the level of more structural SAT instance representations such as Boolean circuits. In this work we study the effect of a CNF-level simplification technique called blocked clause elimination (BCE). We show that BCE is surprisingly effective both in theory and in practice on CNFs resulting from a standard CNF encoding for circuits: without explicit knowledge of the underlying circuit structure, it achieves the same level of simplification as a combination of circuit-level simplifications and previously suggested polarity-based CNF encodings. Experimentally, we show that by applying BCE in preprocessing, further formula reduction and faster solving can be achieved, giving promise for applying BCE to speed up solvers. 1

Abstract. We develop and analyze clause elimination procedures, a specific family of simplification techniques for conjunctive normal form (CNF) formulas. Extending known procedures such as tautology, subsumption, and blocked clause elimination, we introduce novel elimination procedures based on hidden and asymmetric variants of these techniques. We analyze the resulting nine (including five new) clause elimination procedures from various perspectives: size reduction, BCP-preservance, confluence, andlogical equivalence. For the variants not preserving logical equivalence, we show how to reconstruct solutions to original CNFs from satisfying assignments to simplified CNFs. We also identify a clause elimination procedure that does a transitive reduction of the binary implication graph underlying any CNF formula purely on the CNF level. 1