Solving Stochastic Boolean Satisfiability under Random-Exist Quantification

Stochastic Boolean Satisfiability (SSAT) is a powerful formalism to represent computational problems with uncertainty, such as belief network inference and propositional probabilistic planning. Solving SSAT formulas lies in the PSPACEcomplete complexity class same as solving Quantified Boolean Formulas (QBFs). While many endeavors have been made to enhance QBF solving in recent years, SSAT has drawn relatively less attention. This paper focuses on random-exist quantified SSAT formulas, and proposes an algorithm combining modern satisfiability (SAT) techniques and model counting to improve computational efficiency. Unlike prior exact SSAT algorithms, the proposed method can be easily modified to solve approximate SSAT by deriving upper and lower bounds of satisfying probability. Experimental results show that our method outperforms the stateof-the-art algorithm on random k-CNF and AIrelated formulas in both runtime and memory usage, and has effective application to approximate SSAT on VLSI circuit benchmarks.