{"type":"ScholarlyArticle","title":"A Generalization of SAT and #SAT for Robust Policy Evaluation","authors":[{"name":"Erik Peter Zawadzki","slug":"erik-peter-zawadzki","given":"Erik Peter","family":"Zawadzki","affiliation":""},{"name":"André Platzer","slug":"andre-platzer","given":"André","family":"Platzer","affiliation":""},{"name":"Geoffrey J. Gordon","slug":"geoffrey-j-gordon","given":"Geoffrey J.","family":"Gordon","affiliation":""}],"abstract":"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 that it is complete for the complexity class #P^{NP[1]} , and relating 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 complexity of #P^{NP[1]} , many of the instances can be solved efficiently by noticing and exploiting a particular type of frequent structure.","doi":null,"url":"https://ijcai.org/proceedings/2013/380","pdf":"https://ijcai.org/proceedings/2013/0380.pdf","markdown":"https://ijcai.org/proceedings/2013/380.md","bibtex":"https://ijcai.org/proceedings/2013/bibtex/380","volume":{"slug":"2013","title":"Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2013","url":"https://ijcai.org/proceedings/2013/","year":2013,"location":"Beijing, China","dates":"3–9 August 2013","editors":"Francesca Rossi","isbn":"978-1-57735-633-2","publisher":"AAAI Press / International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":380,"pages":{"first":2583,"last":2589},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}