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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)

- László Babai, Eugene M. Luks
- STOC
- 1983

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)

- Eugene M. Luks
- 21st Annual Symposium on Foundations of Computer…
- 1980

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. Testing isomorphism of graphs of valence ≤ t is polynomial-time reducible to the color automorphism problem for groups with small simple… (More)

- László Babai, Eugene M. Luks, Ákos Seress
- FOCS
- 1988

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)

- Merrick L. Furst, John E. Hopcroft, Eugene M. Luks
- 21st Annual Symposium on Foundations of Computer…
- 1980

A permutation group on n letters may always be represented by a small set of generators, even though its size may be exponential in n. We show that it is practical to use such a representation since many problems such as membership testing, equality testing, and inclusion testing are decidable in polynomial time. In addition, we demonstrate that the normal… (More)

- Eugene M. Luks
- Groups And Computation
- 1991

- László Babai, Eugene M. Luks, Ákos Seress
- SIAM J. Comput.
- 1997

- László Babai, William M. Kantor, Eugene M. Luks
- 24th Annual Symposium on Foundations of Computer…
- 1983

We address the graph isomorphism problem and related fundamental complexity problems of computational group theory. The main results are these: A1. A polynomial time algorithm to test simplicity and find composition factors of a given permutation group (COMP). A2. A polynomial time algorithm to find elements of given prime order p in a permutation group of… (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)

- Eugene M. Luks
- Combinatorica
- 1987

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.