A Generalization of SAT and #SAT for Robust Policy Evaluation

Both SAT and #SAT can represent difficult problems in seemingly dissimilar areas such as planning, verification, and probabilistic inference. Here, we examine an expressive new language, #SAT, that generalizes both of these languages. #SAT problems require counting the number of satisfiable formulas in a concisely-describable set of existentially quantified, propositional formulas. We characterize the expressiveness and worst-case difficulty of #SAT by proving it is complete for the complexity class #P NP [1], and re- lating this class to more familiar complexity classes. We also experiment with three new

general-purpose #SAT solvers on a battery of problem distributions including a simple logistics domain. Our experiments show that, despite the formidable worst-case complex-

ity of #P NP [1], many of the instances can be solved efficiently by noticing and exploiting a particular type of frequent structure.