Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Efficient conflict driven learning in a boolean satisfiability solver
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Maintaining Arc-Consistency within Dynamic Backtracking
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
The Quest for Efficient Boolean Satisfiability Solvers
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Checking satisfiability of a conjunction of BDDs
Proceedings of the 40th annual Design Automation Conference
Constraint Processing
Constraint programming viewed as rule-based programming
Theory and Practice of Logic Programming
Solving set constraint satisfaction problems using ROBDDs
Journal of Artificial Intelligence Research
Modelling for lazy clause generation
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
Propagation via lazy clause generation
Constraints
Fast Set Bounds Propagation using BDDs
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
A constraint store based on multivalued decision diagrams
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Propagation = lazy clause generation
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Efficient reasoning for nogoods in constraint solvers with BDDs
PADL'08 Proceedings of the 10th international conference on Practical aspects of declarative languages
Fast set bounds propagation using a BDD-SAT hybrid
Journal of Artificial Intelligence Research
MDD propagators with explanation
Constraints
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
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Finite-domain constraint solvers based on Binary Decision Diagrams (BDDs) are a powerful technique for solving constraint problems over finite set and integer variables represented as Boolean formulæ. Boolean Satisfiability (SAT) solvers are another form of constraint solver that operate on constraints on Boolean variables expressed in clausal form. Modern SAT solvers have highly optimized propagation mechanisms and also incorporate efficient conflict-clause learning algorithms and effective search heuristics based on variable activity, but these techniques have not been widely used in finite-domain solvers. In this paper we show how to construct a hybrid BDD and SAT solver which inherits the advantages of both solvers simultaneously. The hybrid solver makes use of an efficient algorithm for capturing the inferences of a finite-domain constraint solver in clausal form, allowing us to automatically and transparently construct a SAT model of a finite-domain constraint problem. Finally, we present experimental results demonstrating that the hybrid solver can outperform both SAT and finite-domain solvers by a substantial margin.