In an earlier work we showed how a competitive satisfiability solver for the modal logic K can be built on top of a BDD package. In this work we study optimization issues for such solvers. We focus on two types of optimizations. First we study variable ordering, which is known to be of critical importance to BDD-based algorithms. Second, we study modal extensions of the pure-literal rule. Our results show that the payoff of the variable-ordering optimization is rather modest, while the payoff of the pure-literal optimization is quite significant. We benchmark our optimized solver against both native solvers (DLP) and translation-based solvers (MSPASS and SEMPROP). Our results indicate that the BDD-based approach dominates for modally heavy formulas, while search-based approaches dominate for propositionally-heavy formulas.
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