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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,… (More)

We announce an algebraic approach to the problem of assigning <italic>canonical forms</italic> to graphs. We compute canonical forms and the associated canonical labelings (or renumberings) in polynomial time for graphs of bounded valence, in moderately exponential, exp(n<supscrpt>½ + &ogr;(1)</supscrpt>),time for general graphs, in subexponential,… (More)

Suppose we are given a set of generators for a group G of permutations of a colored set A. The color automorphism problem for G involves finding generators for the subgroup of G which stabilizes the color classes. It is shown that testing isomorphism of graphs of bounded valance is polynomial-time reducible to the color automorphism problem for groups with… (More)

We present new algorithms for permutation group manipulation. Our methods result in an improvement of nearly an order of magnitude in the worst-case analysis for the fundamental problems of finding strong generating sets and testing membership. The normal structure of the group is brought into play even for such elementary issues. An essential element is… (More)

We introduce new Monte Carlo methods to speed up and greatly simplify the manipulation of permutation groups. The methods are of a combinatorial character and use elementary group theory only. We achieve a nearly optimal 0(n3 loge n) running time for membership testing, an improvement of two orders of magnitude compared to known elementary algorithms and… (More)

Giveng enerators for a group of permutations, it is shown that generators for the subgroups in a composition series can be found in polynomial time. The procedure also yields permutation representations of the composition factors.