Implementing the Davis-Putnam Algorithm by Tries

The Davis-Putnam method is one of the major practical methods for the satiss-ability (SAT) problem of propositional logic. We show how to implement the Davis-Putnam method eeciently using the trie data structure for propositional clauses by presenting seven implementations of the method. We propose a new technique for implementing unit propagation whose complexity is sublinear to the number of occurrences of the variable in the input. We present the performance of our programs on some quasigroup problems. The eeciency of our programs allowed us to solve some open quasigroup problems.