Stochastic Boolean satisfiability (SSAT) is an expressive language to formulate decision problems with randomness. Solving SSAT formulas has the same PSPACE-complete computational complexity as solving quantified Boolean formulas (QBFs). Despite its broad applications and profound theoretical values, SSAT has received relatively little attention compared to QBF. In this paper, we focus on exist-random quantified SSAT formulas, also known as E-MAJSAT, which is a special fragment of SSAT commonly applied in probabilistic conformant planning, posteriori hypothesis, and maximum expected utility. Based on clause selection, a recently proposed QBF technique, we propose an algorithm to solve E-MAJSAT. Moreover, our method can provide an approximate solution to E-MAJSAT with a lower bound when an exact answer is too expensive to compute. Experiments show that the proposed algorithm achieves significant performance gains and memory savings over the state-of-the-art SSAT solvers on a number of benchmark formulas, and provides useful lower bounds for cases where prior methods fail to compute exact answers.

Stochastic Boolean Satisfiability (SSAT) is a powerful formalism to represent computational problems with uncertainly, such as belief network inference and propositional probabilistic planning. Solving SSAT formulas lies in the same complexity class (PSPACE-complete) as solving Quantified Boolean Formula (QBF). While many endeavors have been made to enhance QBF solving, SSAT has drawn relatively less attention in recent years. This paper focuses on random-exist quantified SSAT formulas, and proposes an algorithm combining binary decision diagram (BDD), logic synthesis, and modern SAT techniques 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 state-of-the-art algorithm on random k-CNF formulas and has effective application to approximate SSAT on circuit benchmarks.