Theoretical analysis of Davis-Putnam procedure and propositional satisfiability

Authors:
Nobuhiro Yugami
Affiliations:
Fujitsu Laboratories, Kawasaki, Japan
Venue:
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Year:
1995

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Abstract

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 well-known 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.