2 citations · 5 across the 10 of their papers we have counts for
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On the palindromic and primitive widths of a free group
Valery Bardakov, Vladimir Shpilrain, Vladimir Tolstykh
Let G be a group and S a subset of G that generates G. For each x in G define the length l_S(x) of x relative to S to be the minimal k such that x is a product of k elements of S.…
Assessing security of some group based cryptosystems
Vladimir Shpilrain
One of the possible generalizations of the discrete logarithm problem to arbitrary groups is the so-called conjugacy search problem (sometimes erroneously called just the conjugacy…
Generic properties of Whitehead's Algorithm and isomorphism rigidity of random one-relator groups
Ilya Kapovich, Paul Schupp, Vladimir Shpilrain
We prove that Whitehead's algorithm for solving the automorphism problem in a fixed free group has strongly linear time generic-case complexity. This is done by showing that…
On the Andrews-Curtis equivalence
Alexei D. Myasnikov, Alexei G. Myasnikov, Vladimir Shpilrain
The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of ``elementary transformations" which a…