L. Babai, R. Beals, and D. Rockmore Deciding finiteness of matrix groups in deterministic polynomial time, Tech Rep, U. Chicago, 1992. Home/Search Document Not in Database Summary Related Articles Check |
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Algorithms for matrix groups and the Tits alternative - Beals (1995) (4 citations) Self-citation (Beals) (Correct)
.... the oldest papers dating back only 15 years [Ba79, FHL] As is the case with computational group theory, the area of permutation groups is particularly well studied [Ba91a, KLu, Lu93] Polynomial time algorithms for several classes of finite matrix groups have been obtained in the last few years [Lu92, BBR, BB]. Some important complexity results for these groups were obtained ten years ago [BSz, Ba85] For infinite matrix groups, polynomial time algorithms are known only for the class of abelian groups [KLi, Ge93a, Ge93b, CLZ, BBCIL] This research has benefited theoretical computer science in several ....
....for example, Lu92] In recent years, algorithms have been obtained for two important classes of groups: finite groups and abelian groups. For finite groups, Beals and Babai [BB] give Las Vegas algorithms for constructive membership and computing a presentation. Also, Babai, Beals, and Rockmore [BBR] have given a deterministic polynomial time algorithm to test finiteness. For abelian groups, Babai, Beals, Cai, Ivanyos, and Luks [BBCIL] give deterministic algorithms for both problems, building on work of Cai, Lipton, and Zalcstein [CLZ] and Ge [Ge93a, Ge93b] G. Ostheimer [Os] has developed ....
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L. Babai, R. Beals, D. Rockmore: Deciding finiteness of matrix groups in deterministic polynomial time, Israel J. Math., to appear.
Multiplicative equations over commuting matrices (Extended.. - Babai, al. (1994) (6 citations) Self-citation (Babai) (Correct)
....[Be] A non trivial byproduct of our main results is that this problem belongs to NP and is therefore NP complete (for variable k) We do not know the complexity status of this problem for variable k but bounded dimension. Finite matrix groups in characteristic zero are well understood [BB] [BBR]. The case of matrix groups over finite fields is of different nature [Lu] BB] While undecidability cannot occur, other obstacles do; the 1 Theta 1 case is identical with the discrete log problem. The introduction of [CLZ] provides additional history and further explanation of the number ....
L. Babai, R. Beals, D. Rockmore: Deciding finiteness of matrix groups in deterministic polynomial time, Israel J. Math., to appear.
Computing in Solvable Matrix Groups - Luks (1992) (13 citations) (Correct)
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L. Babai, R. Beals, and D. Rockmore Deciding finiteness of matrix groups in deterministic polynomial time, Tech Rep, U. Chicago, 1992.
Testing Membership in Unitriangular Matrix Groups - Ivanyos (1996) (Correct)
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L. Babai, R. Beals, D. Rockmore: Deciding finiteness of matrix groups in deterministic polynomial time, Israel J. Math., to appear.
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