CNF satisfiability test by counting and polynomial average time
SIAM Journal on Computing
On deterministic approximation of DNF
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Counting the number of solutions for instances of satisfiability
Theoretical Computer Science
Information Processing Letters
On the hardness of approximate reasoning
Artificial Intelligence
Number of models and satisfiability of sets of clauses
Theoretical Computer Science
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
An algorithm for counting maximum weighted independent sets and its applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Stochastic Boolean Satisfiability
Journal of Automated Reasoning
Counting Satisfying Assignments in 2-SAT and 3-SAT
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Comparing phase transitions and peak cost in PP-complete satisfiability problems
Eighteenth national conference on Artificial intelligence
A compiler for deterministic, decomposable negation normal form
Eighteenth national conference on Artificial intelligence
Algorithms for four variants of the exact satisfiability problem
Theoretical Computer Science
Counting for Satisfiability by Inverting Resolution
Artificial Intelligence Review
Phase transitions of PP-complete satisfiability problems
Discrete Applied Mathematics
Conditioning probabilistic databases
Proceedings of the VLDB Endowment
Online Rule Learning via Weighted Model Counting
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Counting models using extension rules
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Journal of Artificial Intelligence Research
Solving #SAT and Bayesian inference with backtracking search
Journal of Artificial Intelligence Research
Phase transitions of PP-complete satisfiability problems
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Counting solutions of CSPs: a structural approach
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
On Decomposability and Interaction Functions
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Semiring-induced propositional logic: definition and basic algorithms
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Feasibility analysis for robustness quantification by symbolic model checking
Formal Methods in System Design
Using DPLL for efficient OBDD construction
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
A new approach to model counting
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Geometric aspects related to solutions of #kSAT
MICAI'05 Proceedings of the 4th Mexican international conference on Advances in Artificial Intelligence
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
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
Probabilistic databases with MarkoViews
Proceedings of the VLDB Endowment
Mining frequent subgraphs over uncertain graph databases under probabilistic semantics
The VLDB Journal — The International Journal on Very Large Data Bases
Anytime approximation in probabilistic databases
The VLDB Journal — The International Journal on Very Large Data Bases
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As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F. Let m and n be the number of clauses and variables of F, respectively, and let p denote the probability that a literal l of F occurs in a clause C of F, then the average running time of CDP is shown to be O(mdn), where d=[-1/log2(1-p)].The practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas.