A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Algorithms for maximum satisfiability using unsatisfiable cores
Proceedings of the conference on Design, automation and test in Europe
Sorting networks and their applications
AFIPS '68 (Spring) Proceedings of the April 30--May 2, 1968, spring joint computer conference
Towards robust CNF encodings of cardinality constraints
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Solving Pseudo-Boolean Modularity Constraints
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Grounding formulas with complex terms
Canadian AI'11 Proceedings of the 24th Canadian conference on Advances in artificial intelligence
Synthesizing shortest linear straight-line programs over GF(2) using SAT
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Perfect hashing and CNF encodings of cardinality constraints
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
A compact encoding of pseudo-boolean constraints into SAT
KI'12 Proceedings of the 35th Annual German conference on Advances in Artificial Intelligence
Automated reencoding of boolean formulas
HVC'12 Proceedings of the 8th international conference on Hardware and Software: verification and testing
The route to success: a performance comparison of diagnosis algorithms
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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We introduce Cardinality Networks , a new CNF encoding of cardinality constraints. It improves upon the previously existing encodings such as the sorting networks of [ES06] in that it requires much less clauses and auxiliary variables, while arc consistency is still preserved: e.g., for a constraint x 1 + ... + x n ≤ k , as soon as k variables among the x i 's become true, unit propagation sets all other x i 's to false. Our encoding also still admits incremental strengthening: this constraint for any smaller k is obtained without adding any new clauses, by setting a single variable to false. Here we give precise recursive definitions of the clause sets that are needed and give detailed proofs of the required properties. We demonstrate the practical impact of this new encoding by careful experiments comparing it with previous encodings on real-world instances.