Toward good elimination orders for symbolic SAT solving

Fundamentally different from DPLL, a new approach to SAT has recently emerged that abandons search and enlists BDDs to symbolically represent clauses of the CNF. These BDDs are conjoined according to a schedule where some variables may be eliminated by quantification at each step to reduce the size of the intermediate BDDs. SAT solving then reduces to checking whether the final BDD is the zero constant. For this approach to be practical, finding a good quantification schedule is critical. We study the use of a variable elimination algorithm for this purpose, as well as two specific methods for the generation of good elimination orders based on CNF structure. While neither method appears to dominate, we show how one can heuristically select the better using the notion of width. We implement a symbolic SAT solver based on these techniques and evaluate its efficiency and robustness on a set of benchmarks against five other solvers, each having unique characteristics, including winners of the most recent SAT competition.