Lifting (D)QBF Preprocessing and Solving Techniques to (D)SSAT

Dependency stochastic Boolean satisfiability (DSSAT) generalizes stochastic Boolean satisfiability (SSAT) in existential variables being Henkinized allowing their dependencies on randomized variables to be explicitly specified. It allows NEX-PTIME problems of reasoning under uncertainty and partial information to be compactly encoded. To date, no decision procedure has been implemented for solving DSSAT formulas. This work provides the first such tool by converting DSSAT into SSAT with dependency elimination, similar to converting dependency quantified Boolean formula (DQBF) to quantified Boolean formula (QBF). Moreover, we extend (D)QBF preprocessing techniques and implement the first standalone (D)SSAT preprocessor. Experimental results show that solving DSSAT via dependency elimination is highly applicable and that existing SSAT solvers may benefit from preprocessing.