The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Shatter: efficient symmetry-breaking for boolean satisfiability
Proceedings of the 40th annual Design Automation Conference
Exploiting structure in symmetry detection for CNF
Proceedings of the 41st annual Design Automation Conference
Faster symmetry discovery using sparsity of symmetries
Proceedings of the 45th annual Design Automation Conference
Dynamic Symmetry Breaking by Simulating Zykov Contraction
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Efficient symmetry breaking for boolean satisfiability
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Solving difficult instances of Boolean satisfiability in the presence of symmetry
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Conflict anticipation in the search for graph automorphisms
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
A semi-canonical form for sequential AIGs
Proceedings of the Conference on Design, Automation and Test in Europe
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The past few years have seen significant progress in algorithms and heuristics for both SAT and symmetry detection. Additionally, the thesis that some of SAT’s intractability can be explained by the presence of symmetry, and that it can be addressed by the introduction of symmetry-breaking constraints, was tested, albeit only to a rather limited extent. In this paper we explore further connections between symmetry and satisfiability and demonstrate the existence of intractable SAT instances that exhibit few or no symmetries. Specifically, we describe a highly scalable symmetry detection algorithm based on a decision tree that combines elements of group-theoretic computation and SAT-inspired backtracking search, and provide results of its application on the SAT 2009 competition benchmarks. For SAT instances with significant symmetry we also compare SAT runtimes with and without the addition of symmetry-breaking constraints.