Bart Selman

Chapter 2 Satisfiability Solvers

Publisher Summary The past few years have seen 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 general-purpose tool in areas as diverse as software and hardware verification, automatic test-pattern generation, planning, scheduling, and even challenging problems from algebra. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers, exploration of new techniques, and creation of an extensive suite of real-world instances as well as challenging hand-crafted benchmark problems. Modern SAT solvers provide a black-box procedure that can often solve hard structured problems with over a million variables and several million constraints. This chapter describes the main solution techniques used in modern SAT solvers, classifying them as complete and incomplete methods. It discusses recent insights explaining the effectiveness of these techniques on practical SAT encodings and presents several extensions of the SAT approach currently under development. These extensions further expand the range of applications to include multiagent and probabilistic reasoning.