Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
On Boolean Functions Encodable as a Single Linear Pseudo-Boolean Constraint
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
New Encodings of Pseudo-Boolean Constraints into CNF
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Circuit complexity and decompositions of global constraints
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Construction of efficient BDDs for bounded arithmetic constraints
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
Why cumulative decomposition is not as bad as it sounds
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Pseudo-Boolean Solving by incremental translation to SAT
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
Explaining propagators for s-DNNF circuits
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Conflict directed lazy decomposition
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
A compact encoding of pseudo-boolean constraints into SAT
KI'12 Proceedings of the 35th Annual German conference on Advances in Artificial Intelligence
A new look at BDDs for Pseudo-Boolean constraints
Journal of Artificial Intelligence Research
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Pseudo-Boolean constraints are omnipresent in practical applications, and therefore a significant effort has been devoted to the development of good SAT encoding techniques for these constraints. Several of these encodings are based on building Binary Decision Diagrams (BDDs) and translating these into CNF. Indeed, BDD-based encodings have important advantages, such as sharing the same BDD for representing many constraints. Here we first prove that, unless NP = Co-NP, there are Pseudo-Boolean constraints that admit no variable ordering giving a polynomial (Reduced, Ordered) BDD. As far as we know, this result is new (in spite of some misleading information in the literature). It gives several interesting insights, also relating proof complexity and BDDs. But, more interestingly for practice, here we also show how to overcome this theoretical limitation by coefficient decomposition. This allows us to give the first polynomial arc-consistent BDD-based encoding for Pseudo-Boolean constraints.