Improved Static Symmetry Breaking for SAT

  • Jo DevriendtEmail author
  • Bart Bogaerts
  • Maurice Bruynooghe
  • Marc Denecker
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9710)


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 investigate 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 in 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.



This research was supported by the project GOA 13/010 Research Fund KU Leuven and projects G.0489.10, G.0357.12 and G.0922.13 of FWO (Research Foundation - Flanders). Bart Bogaerts is supported by the Finnish Center of Excellence in Computational Inference Research (COIN) funded by the Academy of Finland (grant #251170).


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Jo Devriendt
    • 1
    Email author
  • Bart Bogaerts
    • 1
    • 2
  • Maurice Bruynooghe
    • 1
  • Marc Denecker
    • 1
  1. 1.KU Leuven – University of LeuvenLeuvenBelgium
  2. 2.Helsinki Institute for Information Technology HIIT, Department of Computer ScienceAalto UniversityAaltoFinland

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