A Rearrangement Search Strategy for Determining Propositional Satisfiability

Ramin Zabih, David McAllester

We present a simple algorithm for determining the satisfiability of propositional formulas in Conjunctive Normal Form. As the procedure searches for a satisfying truth assignment it dynamically rearranges the order in which variables are considered. The choice of which variable to assign a truth value next is guided by an upper bound on the size of the search remaining; the procedure makes the choice which yields the smallest upper bound on the size of the remaining search. We describe several upper bound functions and discuss the tradeoff between accurate upper bound functions and the overhead required to compute the upper bounds. Experimental data shows that for one easily computed upper bound the reduction in the size of the search spa,ce more than compensates for the 0verhea.d involved in selecting the next variable.

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