An effective SAT preprocessing technique is the construction of symmetry breaking formulas: auxiliary clauses that guide a SAT solver away from needless exploration of symmetric subproblems. However, during the past decade, state-of-the-art SAT solvers rarely incorporated symmetry breaking. This suggests that the reduction of the search space does not outweigh the overhead incurred by detecting symmetry and constructing symmetry breaking formulas. We present three methods to construct more effective symmetry breaking formulas. The first method simply improves the encoding of symmetry breaking formulas. The second detects special symmetry subgroups, for which complete symmetry breaking formulas exist. The third infers binary symmetry breaking clauses for a symmetry group as a whole rather than longer clauses for individual symmetries. We implement these methods as a symmetry breaking preprocessor, and verify their effectiveness on both hand-picked problems as well as the 2014 SAT competition benchmark set. Our experiments indicate that our symmetry breaking preprocessor improves the current state-of-the-art in static symmetry breaking for SAT and has a sufficiently low overhead to improve the performance of modern SAT solvers on hard combinatorial instances.

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Symmetry in combinatorial problems is an extensively studied topic. We continue this research in the context of model expansion problems, with the aim of automating the workflow of detecting and breaking symmetry. We focus on local domain symmetry, which is induced by permutations of domain elements, and which can be detected on a first-order level. As such, our work is a continuation of the symmetry exploitation techniques of model generation systems, while it differs from more recent symmetry breaking techniques in answer set programming which detect symmetry on ground programs. Our main contributions are sufficient conditions for symmetry of model expansion problems, the identification of local domain interchangeability, which can often be broken completely, and efficient symmetry detection algorithms for both local domain interchangeability as well as local domain symmetry in general. Our approach is implemented in the model expansion system IDP, and we present experimental results showcasing the strong and weak points of our approach compared to SBASS, a symmetry breaking technique for answer set programming.Under consideration for acceptance in TPLP.