Symmetry-Breaking Predicates for Search Problems

Many reasoning and optimization problems exhibit symmetries. Previous work has shown how special purpose algorithms can make use of these symmetries to simplify reasoning. We present a general scheme whereby symmetries are exploited by adding \symmetry-breaking" predicates to the theory. Our approach can be used on any propo-sitional satissability problem, and can be used as a pre-processor to any (systematic or non-systematic) reasoning method. In the general case adding symmetry-breaking axioms appears to be intractable. We discuss methods for generating partial symmetry-breaking predicates, and show that in several speciic cases symmetries can be broken either fully are partially using a polynomial number of predicates. These ideas have been implemented and we include experimental results on two classes of constraint-satisfaction problems.