Implementing the Davis–Putnam Method

The method proposed by Davis, Putnam, Logemann, and Loveland for propositional reasoning, often referred to as the Davis–Putnam method, is one of the major practical methods for the satisfiability (SAT) problem of propositional logic. We show how to implement the Davis–Putnam method efficiently using the trie data structure for propositional clauses. A new technique of indexing only the first and last literals of clauses yields a unit propagation procedure whose complexity is sublinear to the number of occurrences of the variable in the input. We also show that the Davis–Putnam method can work better when unit subsumption is not used. We illustrate the performance of our programs on some quasigroup problems. The efficiency of our programs has enabled us to solve some open quasigroup problems.

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