Chapter 29 - Boolean Satisfiability: Creating Solvers Optimized for Specific Problem Instances

Abstract

The Boolean satisfiability problem is well-known in computer science. Given a Boolean formula, the goal is to find an assignment to the variables so that the formula evaluates to true or 1, or to prove that such an assignment does not exist. It has many applications, including theorem proving, automatic test pattern generation, and formal verification. Boolean satisfiability (SAT) is a classic NP-complete problem with a broad range of applications. There are many projects that use reconfigurable computing to solve it. This chapter presents a review of the subject with emphasis on a particular approach that employs a backtrack search algorithm and generates solver hardware according to the problem instance. This approach uses the reconfigurability and fine-grained parallelism provided by field-programmable gate arrays (FPGAs). This chapter introduces the SAT formulation and applications. It describes the algorithms to solve the SAT problem and describes in detail two SAT solvers that use reconfigurable computing. Many projects have designed Boolean satisfiability solvers with reconfigurable computing. These projects demonstrate the performance potential of these solvers through fine-grained custom hardware and massively parallel processing. Significant progress has been made in software algorithms as well, and recently, reconfigurable computing solutions have not kept up in incorporating these innovations. This is partly because the tools for reconfigurable computing are not yet mature.