Theoretical Analysis of Davis-Putnam Procedure and Propositional Satisfiability

This paper presents a statistical analysis of the Davis-Putnam procedure and propositional satisfiability problems (SAT). SAT has been researched in AI because of its strong relationship to automated reasoning and recently it is used as a benchmark problem of constraint satisfaction algorithms. The Davis-Putnam procedure is a wellknown satisfiability checking algorithm based on tree search technique. In this paper, I analyze two average case complexities for the Davis-Putnam procedure, the complexity for satisfiability checking and the complexity for finding all solutions. I also discuss the probability of satisfiability. The complexities and the probability strongly depend on the distribution of formulas to be tested and I use the fixed clause length model as the distribution model. The result of the analysis coincides with the experimental result well.