@MISC{Gomes08modelcounting, author = {Carla P. Gomes and Ashish Sabharwal and Bart Selman}, title = {Model Counting}, year = {2008} }

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Abstract

Propositional model counting or #SAT is the problem of computing the number of models for a given propositional formula, i.e., the number of distinct truth assignments to variables for which the formula evaluates to true. For a propositional formula F, we will use #F to denote the model count of F. This problem is also referred to as the solution counting problem for SAT. It generalizes SAT and is the canonical #P-complete problem. There has been significant theoretical work trying to characterize the worst-case complexity of counting problems, with some surprising results such as model counting being hard even for some polynomial-time solvable problems like 2-SAT. The model counting problem presents fascinating challenges for practitioners and poses several new research questions. Efficient algorithms for this problem will have a significant impact on many application areas that are inherently beyond SAT (‘beyond ’ under standard complexity theoretic assumptions), such as bounded-length adversarial and contingency planning, and probabilistic reasoning. For example, various probabilistic inference problems, such as Bayesian net reasoning, can be effectively translated into model counting problems [cf.