Dynamic Local Search for SAT: Design, Insights and Analysis

In Boolean logic, a formula is satisfiable if a variable assignment exists that will make the formula equivalent to true, and the propositional satisfiability problem (SAT) is to determine if a given formula is satisfiable. SAT is one of the most fundamental problems in computer science, and since many relevant combinatorial problems can be encoded into SAT, it is of substantial theoretical and practical interest. A popular and successful approach to solving combinatorial problems such as SAT is Stochastic Local Search (SLS). In this dissertation we focus on SLS algorithms for SAT, which can find satisfying variable assignments effectively, but cannot determine if no satisfying variable assignment exists. Our primary goal is to advance the state-of-the-art for SLS algorithms for SAT. We accomplish this goal explicitly by developing new SLS algorithms that outperform the existing algorithms on interesting benchmark problems, and implicitly by advancing the understanding of current algorithms and introducing tools for developing new algorithms. The prevalent theme of our work is Dynamic Local Search (DLS), where DLS algorithms use their search history to dynamically change their behaviour. The cornerstone of this dissertation is UBCSAT, a software framework we developed for efficiently implementing and empirically evaluating SLS algorithms for SAT. We present the SCALING AND PROBABILISTIC SMOOTHING (SAPS) algorithm, which is amongst the state-of-the-art SLS algorithms for SAT. We provide an in-depth study of a class of DLS algorithms, analyze their performance and significantly advance the understanding of their behaviour. We also advance the understanding of the role of random decisions in SLS algorithms, by providing an empirical analysis on both the quality and quantity of random decisions. The capstone of this dissertation is a new conceptual model for representing and designing SLS algorithms for SAT. We introduce a new software design architecture that implements our model and is specifically designed to leverage recent tools to automate many of the tedious aspects of algorithm design. We demonstrate that by following our new algorithm design approach, we have achieved significant improvements over previous state-of-the-art SLS algorithms for SAT on encodings of software verification benchmark instances.