Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
On the hardness of approximate reasoning
Artificial Intelligence
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Stochastic Boolean Satisfiability
Journal of Automated Reasoning
Counting Models Using Connected Components
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Algorithms and Complexity Results for #SAT and Bayesian Inference
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A new look at survey propagation and its generalizations
Journal of the ACM (JACM)
Towards efficient sampling: exploiting random walk strategies
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Model counting: a new strategy for obtaining good bounds
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Performing Bayesian inference by weighted model counting
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Approximate counting by sampling the backtrack-free search space
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
From sampling to model counting
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
MAP complexity results and approximation methods
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
A new approach to model counting
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Characterizing propagation methods for boolean satisfiability
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Constructing free-energy approximations and generalized belief propagation algorithms
IEEE Transactions on Information Theory
Message-passing and local heuristics as decimation strategies for satisfiability
Proceedings of the 2009 ACM symposium on Applied Computing
Exploiting problem structure for solution counting
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Upper bounds on the number of solutions of binary integer programs
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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We consider the problem of estimating the model count (number of solutions) of Boolean formulas, and present two techniques that compute estimates of these counts, as well as either lower or upper bounds with different trade-offs between efficiency, bound quality, and correctness guarantee. For lower bounds, we use a recent framework for probabilistic correctness guarantees, and exploit message passing techniques for marginal probability estimation, namely, variations of Belief Propagation (BP). Our results suggest that BP provides useful information even on structured loopy formulas. For upper bounds, we perform multiple runs of the MiniSat SAT solver with a minor modification, and obtain statistical bounds on the model count based on the observation that the distribution of a certain quantity of interest is often very close to the normal distribution. Our experiments demonstrate that our model counters based on these two ideas, BPCount and MiniCount, can provide very good bounds in time significantly less than alternative approaches.