Chaff: engineering an efficient SAT solver
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Enhancing Davis Putnam with extended binary clause reasoning
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A compiler for deterministic, decomposable negation normal form
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Algorithms and Complexity Results for #SAT and Bayesian Inference
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Performing incremental Bayesian inference by dynamic model counting
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
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Performing Bayesian inference by weighted model counting
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DPLL with a trace: from SAT to knowledge compilation
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Compiling Bayesian networks with local structure
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Heuristics for fast exact model counting
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Encoding CNFs to empower component analysis
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
sharpSAT: counting models with advanced component caching and implicit BCP
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Solution Enumeration for Projected Boolean Search Problems
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Volume Computation for Boolean Combination of Linear Arithmetic Constraints
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Solving #SAT and Bayesian inference with backtracking search
Journal of Artificial Intelligence Research
Exact cover via satisfiability: an empirical study
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Survey: The consequences of eliminating NP solutions
Computer Science Review
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Many real-world problems, including inference in Bayes Nets, can be reduced to #SAT, the problem of counting the number of models of a propositional theory. This has motivated the need for efficient #SAT solvers. Currently, such solvers utilize a modified version of DPLL that employs decomposition and caching, techniques that significantly increase the time it takes to process each node in the search space. In addition, the search space is significantly larger than when solving SAT since we must continue searching even after the first solution has been found. It has previously been demonstrated that the size of a DPLL search tree can be significantly reduced by doing more reasoning at each node. However, for SAT the reductions gained are often not worth the extra time required. In this paper we verify the hypothesis that for #SAT this balance changes. In particular, we show that additional reasoning can reduce the size of a #SAT solver's search space, that this reduction cannot always be achieved by the already utilized technique of clause learning, and that this additional reasoning can be cost effective.