Journal of the ACM (JACM)
Handbook of combinatorics (vol. 2)
A comparative study of two Boolean formulations of FPGA detailed routing constraints
Proceedings of the 2001 international symposium on Physical design
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Solving difficult SAT instances in the presence of symmetry
Proceedings of the 39th annual Design Automation Conference
BerkMin: A Fast and Robust Sat-Solver
Proceedings of the conference on Design, automation and test in Europe
Exploiting structure in symmetry detection for CNF
Proceedings of the 41st annual Design Automation Conference
ShatterPB: symmetry-breaking for pseudo-Boolean formulas
Proceedings of the 2004 Asia and South Pacific Design Automation Conference
Integration of supercubing and learning in a SAT solver
Proceedings of the 2005 Asia and South Pacific Design Automation Conference
Dynamic symmetry-breaking for improved Boolean optimization
Proceedings of the 2005 Asia and South Pacific Design Automation Conference
Propositional Satisfiability and Constraint Programming: A comparative survey
ACM Computing Surveys (CSUR)
Symmetry breaking for pseudo-Boolean formulas
Journal of Experimental Algorithmics (JEA)
Faster symmetry discovery using sparsity of symmetries
Proceedings of the 45th annual Design Automation Conference
SAT graph-based representation: A new perspective
Journal of Algorithms
SymChaff: a structure-aware satisfiability solver
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Symmetry-breaking answer set solving
AI Communications - Answer Set Programming
Symmetry breaking for distributed multi-context systems
LPNMR'11 Proceedings of the 11th international conference on Logic programming and nonmonotonic reasoning
Symmetry and satisfiability: an update
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Directed test generation for validation of multicore architectures
ACM Transactions on Design Automation of Electronic Systems (TODAES) - Special section on verification challenges in the concurrent world
Conflict anticipation in the search for graph automorphisms
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Diversely enumerating system-level architectures
Proceedings of the Eleventh ACM International Conference on Embedded Software
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Boolean satisfiability (SAT) solvers have experienced dramatic improvements in their performance and scalability over the last several years [5, 7] and are now routinely used in diverse EDA applications. Nevertheless, a number of practical SAT instances remain difficult to solve [9] and continue to defy even the best available SAT solvers [5, 7]. Recent work pointed out that symmetries in the Boolean search space are often to blame. A theoretical framework for detecting and breaking such symmetries was introduced in [2]. This framework was subsequently extended, refined, and empirically shown to yield significant speed-ups for a large number of benchmark classes in [1].Symmetries in the search space are broken by adding appropriate symmetry-breaking predicates (SBPs) to a SAT instance in conjunctive normal form (CNF). The SBPs prune the search space by acting as a filter that confines the search to non-symmetric regions of the space without affecting the satisfiability of the CNF formula. For symmetry breaking to be effective in practice, the computational overhead of generating and manipulating the SBPs must be significantly less than the run time savings they yield due to search space pruning. In this paper we present several new constructions of SBPs that improve on previous work. Specifically, we give a linear-sized CNF formula that selects lex-leaders (among others) for single permutations. We also show how that formula can be simplified by taking advantage of the sparsity of permutations. We test these improvements against earlier constructions and show that they yield smaller SBPs and lead to run time reductions on many benchmarks.