has seen much interest in not just the theoretical computer science community, but also in areas where practical solutions to this problem enable significant practical applications. Since the first development of the basic search based algorithm proposed by Davis, Putnam, Logemann and Loveland (DPLL) about forty years ago, this area has seen active research effort with many interesting contributions that have culminated in state-of-the-art SAT solvers today being able to handle problem instances with thousands, and in same cases even millions, of variables. In this paper we examine some of the main ideas along this passage that have led to our current capabilities. Given the depth of the literature in this field, it is impossible to do this in any comprehensive way; rather we focus on techniques with consistent demonstrated efficiency in available solvers. For the most part, we focus on techniques within the basic DPLL search framework, but also briefly describe other approaches and look at some possible future research directions. 1.

Abstract. In this paper we introduce MINIMAXSAT, a new Max-SAT solver that incorporates the best SAT and Max-SAT techniques. It can handle hard clauses (clauses of mandatory satisfaction as in SAT), soft clauses (clauses whose falsification is penalized by a cost as in Max-SAT) as well as pseudo-boolean objective functions and constraints. Its main features are: learning and backjumping on hard clauses; resolution-based and subtraction-based lower bounding; and lazy propagation with the two-watched literals scheme. Our empirical evaluation on a wide set of optimization benchmarks indicates that its performance is usually close to the best specialized alternative and, in some cases, even better. 1

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

In this paper we introduce MINIMAXSAT, a new Max-SAT solver that is built on top of MIN-ISAT+. It incorporates the best current SAT and Max-SAT techniques. It can handle hard clauses (clauses of mandatory satisfaction as in SAT), soft clauses (clauses whose falsification is penalized by a cost as in Max-SAT) as well as pseudo-boolean objective functions and constraints. Its main features are: learning and backjumping on hard clauses; resolution-based and substractionbased lower bounding; and lazy propagation with the two-watched literal scheme. Our empirical evaluation comparing a wide set of solving alternatives on a broad set of optimization benchmarks indicates that the performance of MINIMAXSAT is usually close to the best specialized alternative and, in some cases, even better. 1.

Abstract. Advances in local-search SAT solvers have traditionally been presented in the context of local search solvers only. The most recent and rather comprehensive comparisons between UnitWalk and several versions of WalkSAT demonstrate that neither solver dominates on all benchmarks. QingTing2 (a ‘dragonfly ’ in Mandarin) is a SAT solver script that relies on a novel switching strategy to invoke one of the two local search solvers: WalkSAT or QingTing1. The local search solver Qing-Ting1 implements the UnitWalk algorithm with a new unit-propagation technique. The experimental methodology we use not only demonstrates the effectiveness of the switching strategy and the efficiency of the new unit-propagation implementation – it also supports, on the very same instances, statistically significant performance evaluation between local search and other state-of-the-art DPLL-based SAT solvers. The resulting comparisons show a surprising pattern of solver dominance, completely unanticipated when we began this work. 1

In recent years backtrack search SAT solvers have been the subject of dramatic improvements. These improvements allowed SAT solvers to successfully replace BDDs in many areas of formal verification, and also motivated the development of many new challenging problem instances, many of which too hard for the current generation of SAT solvers. As a result, further improvements to SAT technology are expected to have key consequences in formal verification. The objective of this paper is to propose heuristic approaches to the backtrack step of backtrack search SAT solvers, with the goal of increasing the ability of the SAT solver to search different parts of the search space. The proposed heuristics to the backtrack step are inspired by the heuristics proposed in recent years for the branching step of SAT solvers, namely VSIDS and some of its improvements. The preliminary experimental results are promising, and motivate the integration of heuristic backtracking in state-of-the-art SAT solvers.

Abstract. In this paper, we present a new SAT solver that combines a recently proposed local search algorithm — unitwalk — with efficient unit propagation techniques. Unlike many other local-search SAT algorithms, unitwalk’s search relies heavily on unit propagation. In our solver, QingTing 1, unit propagation is implemented with an efficient unit propagation algorithm using an underlying lazy data structure. By comparing it to a more basic data structure, we empirically show how our approach is able to significantly reduce memory access in terms of clause and literal visits. Experiments also show that QingTing is up to five times faster than the original unitwalk solver on a wide range of benchmarks and competitive with other state-of-the-art SAT solvers. 1

Abstract: Recent work has shown the value of using propositional SAT solvers, as opposed to pure BDD solvers, for solving many real-world Boolean Satisfiability problems including Bounded Model Checking problems (BMC). We propose a SAT solver paradigm which combines the use of BDDs and search methods to support efficient implementation of complex search heuristics and effective use of early (preprocessor) learning. We implement many of these ideas in software called SBSAT. We show that SBSAT solves many of the benchmarks tested competitively or substantially faster than state-of-the-art SAT solvers. SBSAT differs from standard propositional SAT solvers by working directly with non-CNF propositional input; its input format is BDDs. This allows some BDD-style processing to be used as a preprocessing tool. After preprocessing, the BDDs are transformed into state machines (different state machines than the ones used in the original model checking problem) and a good deal of lookahead information is precomputed and memoized. This provides for fast implementation of a new form of lookahead, called local-function-complete lookahead (contrasting with the depth-first lookahead of

This paper describes the CQuest SAT solver. This solver is essentially a translation from Java to C++ of the JQuest2 SAT solver [4]. All of the Quest generation solvers [3, 4] were mainly inspired in Grasp [5] and Chaff [6]. These solvers perform backtrack search enhanced with clause recording. In addition, Chaff’s lazy data structures are implemented in CQuest, in order to obtain fast unit propagation, namely on (large) recorded clauses. BerkMin [2] also inspired the CQuest SAT solver with respect to the variable branching heuristic. Experimental results have proved that CQuest is a competitive solver, specially when considering industrial benchmarks. 1

A growing number of problem domains are successfully being tackled by SAT solvers. This thesis contributes to that trend by pushing the state-of-the-art of core SAT algorithms and their implementation, but also in several important application areas. It consists of five papers: the first details the implementation of the SAT solver MINISAT and the other four papers discuss specific issues related to different application domains. In the first paper, catering to the trend of extending and adapting SAT solvers, we present a detailed description of MINISAT, a SAT solver designed for that particular purpose. The description additionally bridges a gap between theory and practice, serving as a tutorial on modern SAT solving algorithms. Among other things, we describe how to solve a series of related SAT problems efficiently, called incremental SAT solving. For finding finite first order models the MACE-style method that is based on SAT solving is well-known. In the second paper we improve the basic method with several techniques that can be loosely classified as either transformations