Effective SAT solving

Abstract

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 that make the reduction to SAT result in fewer clauses or techniques that are designed to speed up the search of the SAT solver. The resulting tool, called Paradox, won the SAT/Models division of the CASC competition in 2003 and has not been beaten since by a single general purpose model finding tool.

In the last decade the interest in methods for safety property verification that are based on SAT solving has been steadily growing. One example of such a method is temporal induction. The method requires a sequence of increasingly stronger induction proofs to be performed. In the third paper we show how this sequence of proofs can be solved efficiently using incremental SAT solving.

The last two papers consider two frequently occurring types of encodings: (1) the problem of encoding circuits into CNF, and (2) encoding 0-1 integer linear programming into CNF and how to use incremental SAT to solve the intended ptimization problem.

There are several encoding patterns that occur over and over again in this thesis but also elsewhere. The most noteworthy are: incremental SAT, lazy encoding of constraints, and bit-wise encoding of arithmetic influenced by hardware designs for adders and multipliers.

The general conclusion is: deploying SAT solvers effectively requires implementations that are efficient, yet easily adaptable to specific application needs. Moreover, to get the best results, it is worth spending effort to make sure that one uses the best codings possible for an application. However, it is important to note that this is not absolutely necessary. For some applications naive problem codings work just fine which is indeed part of the appeal of using SAT solving.