Random generation of combinatorial structures from a uniform
Theoretical Computer Science
On selecting a satisfying truth assignment (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
On the hardness of approximate reasoning
Artificial Intelligence
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Counting Models Using Connected Components
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Journal of Symbolic Computation
A compiler for deterministic, decomposable negation normal form
Eighteenth national conference on Artificial intelligence
Towards efficient sampling: exploiting random walk strategies
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
The good old Davis-Putnam procedure helps counting models
Journal of Artificial Intelligence Research
Using DPLL for efficient OBDD construction
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Assertion-based repair of complex data structures
Proceedings of the twenty-second IEEE/ACM international conference on Automated software engineering
On probabilistic inference by weighted model counting
Artificial Intelligence
Model counting: a new strategy for obtaining good bounds
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Volume Computation for Boolean Combination of Linear Arithmetic Constraints
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
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
Leveraging belief propagation, backtrack search, and statistics for model counting
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Exploiting problem structure for solution counting
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
SampleSearch: Importance sampling in presence of determinism
Artificial Intelligence
Measuring plan coverage and overlap for agent reasoning
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
A generalization of SAT and #SAT for robust policy evaluation
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Anytime approximation in probabilistic databases
The VLDB Journal — The International Journal on Very Large Data Bases
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We introduce ApproxCount, an algorithm that approximates the number of satisfying assignments or models of a formula in propositional logic. Many AI tasks, such as calculating degree of belief and reasoning in Bayesian networks, are computationally equivalent to model counting. It has been shown that model counting in even the most restrictive logics, such as Horn logic, monotone CNF and 2CNF, is intractable in the worst-case. Moreover, even approximate model counting remains a worst-case intractable problem. So far, most practical model counting algorithms are based on backtrack style algorithms such as the DPLL procedure. These algorithms typically yield exact counts but are limited to relatively small formulas. Our ApproxCount algorithm is based on SampleSat, a new algorithm that samples from the solution space of a propositional logic formula near-uniformly. We provide experimental results for formulas from a variety of domains. The algorithm produces good estimates for formulas much larger than those that can be handled by existing algorithms.