Biblio

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2016-12-05
Erik Zawadzki, Andre Platzer, Geoffrey Gordon.  2014.  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.