NP is as easy as detecting unique solutions
Theoretical Computer Science
On the hardness of approximate reasoning
Artificial Intelligence
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
On the computational power of PP and (+)P
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
A new approach to model counting
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Better bug reporting with better privacy
Proceedings of the 13th international conference on Architectural support for programming languages and operating systems
Random stimulus generation using entropy and XOR constraints
Proceedings of the conference on Design, automation and test in Europe
Measuring channel capacity to distinguish undue influence
Proceedings of the ACM SIGPLAN Fourth Workshop on Programming Languages and Analysis for Security
Using Model Counting to Find Optimal Distinguishing Tests
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Variable Influences in Conjunctive Normal Forms
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Using more reasoning to improve #SAT solving
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Counting CSP solutions using generalized XOR constraints
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Probabilistic planning via heuristic forward search and weighted model counting
Journal of Artificial Intelligence Research
From sampling to model counting
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Experiments with massively parallel constraint solving
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Short XORs for model counting: from theory to practice
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Solution counting algorithms for constraint-centered search heuristics
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
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
Computing the density of states of Boolean formulas
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
When boolean satisfiability meets gaussian elimination in a simplex way
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
SCSat: a soft constraint guided SAT solver
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
A scalable and nearly uniform generator of SAT witnesses
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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Model counting is the classical problem of computing the number of solutions of a given propositional formula. It vastly generalizes the NP-complete problem of propositional satisfiability, and hence is both highly useful and extremely expensive to solve in practice. We present a new approach to model counting that is based on adding a carefully chosen number of so-called streamlining constraints to the input formula in order to cut down the size of its solution space in a controlled manner. Each of the additional constraints is a randomly chosen XOR or parity constraint on the problem variables, represented either directly or in the standard CNF form. Inspired by a related yet quite different theoretical study of the properties of XOR constraints, we provide a formal proof that with high probability, the number of XOR constraints added in order to bring the formula to the boundary of being unsatisfiable determines with high precision its model count. Experimentally, we demonstrate that this approach can be used to obtain good bounds on the model counts for formulas that are far beyond the reach of exact counting methods. In fact, we obtain the first non-trivial solution counts for very hard, highly structured combinatorial problem instances. Note that unlike other counting techniques, such as Markov Chain Monte Carlo methods, we are able to provide high-confidence guarantees on the quality of the counts obtained.