Searching for Truth: Techniques for Satisfiability of Boolean Formulas

The problem of determining whether a propositional Boolean formula can be true is called the Boolean Satisfiability Problem or SAT. SAT is an important and widely studied problem in computer science. In practice, SAT is a core problem in many applications such as Electronic Design Automation (EDA) and Artificial Intelligence (AI). This thesis investigates various problems in the design and implementation of SAT solvers. Even though researchers have been studying SAT solving algorithms for a long time, efforts were mainly concentrated on improving the algorithms to prune search spaces. In this thesis, the implementation issues of SAT solvers are studied and some of the most widely used techniques are quantitatively evaluated. SAT solvers developed by utilizing the results of the analysis can achieve 10-100x speedup over existing SAT solvers. For some applications, certain capabilities are required for the SAT solvers. For mission critical applications, the SAT solvers are often required to provide some means for a third party to verify the results. In the thesis a method to provide such a certification is discussed. The second capability discussed in the thesis is to find a small unsatisfiable sub-formula from an unsatisfiable SAT instance. This capability is useful for debugging purposes for some applications. The thesis discusses how these two capabilities are related and how to implement them in existing SAT solvers. For some reasoning tasks, propositional formulas are insufficient. This thesis discusses the problem of deciding the satisfiability of Quantified Boolean Formulas