Abstract Solving Quantified Boolean Formulas Horst Samulowitz Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2008 Many real-world problems do not have a simple algorithmic solution and casting these problems as search problems is often not only the simplest way of casting them, but also the most efficient way of solving them. In this thesis we will present several techniques to advance search-based algorithms in the context of solving quantified boolean formulas (QBF). QBF enables complex realworld problems including planning, two-player games and verification to be captured in a compact and quite natural fashion. We will discuss techniques ranging from straight forward pre-processing methods utilizing strong rules of inference to more sophisticated online approaches such as dynamic partitioning. Furthermore, we will show that all of the presented techniques achieve an essential improvement of the search process when solving QBF. At the same time the displayed empirical results also reveal the orthogonality of the different techniques with respect to performance. Generally speaking each approach performs well on a particular subset of benchmarks, but performs poorly on others. Consequently, an adaptive employment of the available techniques that maximizes the performance would result in further improvements. We will demonstrate that such an adaptive approach can pay off in practice, by presenting the results of using machine learning methods to dynamically select the best variable ordering heuristics during search.

Abstract Solving Quantified Boolean Formulas Horst Samulowitz Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2008 Many real-world problems do not have a simple algorithmic solution and casting these problems as search problems is often not only the simplest way of casting them, but also the most efficient way of solving them. In this thesis we will present several techniques to advance search-based algorithms in the context of solving quantified boolean formulas (QBF). QBF enables complex realworld problems including planning, two-player games and verification to be captured in a compact and quite natural fashion. We will discuss techniques ranging from straight forward pre-processing methods utilizing strong rules of inference to more sophisticated online approaches such as dynamic partitioning. Furthermore, we will show that all of the presented techniques achieve an essential improvement of the search process when solving QBF. At the same time the displayed empirical results also reveal the orthogonality of the different techniques with respect to performance. Generally speaking each approach performs well on a particular subset of benchmarks, but performs poorly on others. Consequently, an adaptive employment of the available techniques that maximizes the performance would result in further improvements. We will demonstrate that such an adaptive approach can pay off in practice, by presenting the results of using machine learning methods to dynamically select the best variable ordering heuristics during search.