On finding minimal-models using DPLL-based SAT solver

We present a method to find minimal models using a SAT solver based on DPLL (Davis-Putnam-Logeman-Loveland) procedure. The algorithm of the method is described together with its correctness proof. A DPLL-based SAT solver outperforms MM-MGTP, a theorem prover of first-order logic which is adapted to finding minimal models, in solving SAT instances of the Random category in the standard SAT benchmarks. Still it is much slower than MM-MGTP in solving many other SAT instances. This is mainly due to its inappropriate strategies for model search. It remains to be solved how we can determine the order of decision variables appropriately.