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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)

- 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
- 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
- Groups And Computation
- 1991

- 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)

- 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)

- Eugene M. Luks
- 27th Annual Symposium on Foundations of Computer…
- 1986

We develop parallel techniques for dealing with permutation group problems. These are most effective on the class of groups with bounded non-abelian composition factors. For this class, we place in NC problems such as membership testing, finding the center and composition factors, and, of particular significance, finding pointwise-set-stabilisers. The last… (More)

- László Babai, Robert Beals, Jin-Yi Cai, Gábor Ivanyos, Eugene M. Luks
- SODA
- 1996

We consider the solvability of the equation k Y i=1Aixi = B and generalizations, where the Ai and B are given commuting matrices over an algebraic number eld F . In the semigroup membership problem, the variables xi are constrained to be nonnegative integers. While this problem is NP-complete for variable k, we give a polynomial time algorithm if k is xed.… (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)

- László Babai, Eugene M. Luks, Ákos Seress
- STOC
- 1987

We show that the basic problems of permutation group manipulation admit efficient parallel solutions. Given a permutation group G by a list of generators, we find a set of NC-efficient strong generators in NC. Using this, we show, that the following problems are in NC: membership in G; determining the order of G; finding the center of G; finding a… (More)