Symmetry-Breaking Formulas for Groups with Bounded Orbit Projections

This paper consider the problem of generating symmetry-breaking formulas for permutation groups acting on n points, where the projection of the group into each orbit is bounded by a polynomial in n. We show that the lex-leader formula, which is satisfied by the lexicographic leader of each set of symmetrical points in the search space, can be generated in polynomial time (and space). Our construction is based on writing a Boolean formula that captures the underlying logic of Sims’s methods to test membership in permutation groups, a classic result in computational group theory.