Browse Theses

In this dissertation, we examine complete search algorithms for SAT, the satisfiability problem for propositional formulas in conjunctive normal form. SAT is NP-complete, easy to think about, and one of the most important computational problems in the field of Artificial Intelligence. From an empirical perspective, the central problem associated with these algorithms is to implement one that runs as quickly as possible on a wide range of hard SAT problems. This in turn require identifying a set of useful techniques and programming guidelines. Another important problem is to identify the techniques that do not work well in practice, and provide qualitative reasons for their poor performance whenever possible. This dissertation addresses all four of these problems.

Our thesis is that any efficient SAT search algorithm should perform only a few key technique at each node of the search tree. Furthermore, any implementation of such an algorithm should perform these techniques in quadratic time total down any path of the search tree, and use only a linear amount of space. We have justified these claims by writing POSIT (for PrOpositional SatIsfiability Testbed), a SAT tester which runs more quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3$\sb{-}$U1, POSIT can solve hard random 400-variable 3-SAT problems in about 2 hours on the average. In general, it can solve hard n-variable random 3-SAT problems with search trees of size $O(2\sp{n/18.7}).$

In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NP-complete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.