On the parallel complexity of discrete relaxation in constraint satisfaction networks
Artificial Intelligence
GRASP—a new search algorithm for satisfiability
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
Boosting combinatorial search through randomization
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A linear-time transformation of linear inequalities into conjunctive normal form
Information Processing Letters
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
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
SATO: An Efficient Propositional Prover
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
BerkMin: A Fast and Robust Sat-Solver
Proceedings of the conference on Design, automation and test in Europe
Using CSP look-back techniques to solve real-world SAT instances
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Mapping problems with finite-domain variables to problems with boolean variables
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Universal Booleanization of Constraint Models
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Consistency checking of all different constraints over bit-vectors within a SAT solver
Proceedings of the 2008 International Conference on Formal Methods in Computer-Aided Design
Cardinality Networks and Their Applications
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
SAT Encoding and CSP Reduction for Interconnected Alldiff Constraints
MICAI '09 Proceedings of the 8th Mexican International Conference on Artificial Intelligence
Graph transformation units guided by a sat solver
ICGT'10 Proceedings of the 5th international conference on Graph transformations
Pseudo-Boolean Solving by incremental translation to SAT
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
Parallel search for maximum satisfiability
AI Communications - 18th RCRA International Workshop on “Experimental evaluation of algorithms for solving problems with combinatorial explosion”
Restoring CSP Satisfiability with MaxSAT
Fundamenta Informaticae - RCRA 2009 Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion
Optimizing MiniSAT variable orderings for the relational model finder kodkod
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
A cardinality solver: more expressive constraints for free
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Deliberative, search-based mitigation strategies for model-based software health management
Innovations in Systems and Software Engineering
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Motivated by the performance improvements made to SAT solvers in recent years, a number of different encodings of constraints into SAT have been proposed. Concrete examples are the different SAT encodings for ≤ 1 (x1, . . . , xn) constraints. The most widely used encoding is known as the pairwise encoding, which is quadratic in the number of variables in the constraint. Alternative encodings are in general linear, and require using additional auxiliary variables. In most settings, the pairwise encoding performs acceptably well, but can require unacceptably large Boolean formulas. In contrast, linear encodings yield much smaller Boolean formulas, but in practice SAT solvers often perform unpredictably. This lack of predictability is mostly due to the large number of auxiliary variables that need to be added to the resulting Boolean formula. This paper studies one specific encoding for ≤ 1 (x1, . . . , xn) constraints, and shows how a state-of-the-art SAT solver can be adapted to overcome the problem of adding additional auxiliary variables. Moreover, the paper shows that a SAT solver may essentially ignore the existence of auxiliary variables. Experimental results indicate that the modified SAT solver becomes significantly more robust on SAT encodings involving ≤ 1 (x1, . . . , xn) constraints.