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Probabilistic Solutions of Equations in the Braid Group | | D. Garber
; S. Kaplan
; M. Teicher
; B. Tsaban
; U. Vishne
; | | Date: |
5 Apr 2004 | | Subject: | Group Theory; Cryptography and Security; Geometric Topology | math.GR cs.CR math.GT | | Abstract: | Given a system of equations in a "random" finitely generated subgroup of the braid group, we show how to find a small ordered list of elements in the subgroup, which contains a solution to the equations with a significant probability. Moreover, with a significant probability, the solution will be the first in the list. This gives a probabilistic solution to: The conjugacy problem, the group membership problem, the shortest representation of an element, and other combinatorial group-theoretic problems in random subgroups of the braid group. We use a memory-based extension of the standard length-based approach, which in principle can be applied to any group admitting an efficient, reasonably behaving length function. | | Source: | arXiv, math.GR/0404076 | | Services: | Forum | Review | PDF | Favorites | |
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