6 research outputs found
Compressed Decision Problems in Hyperbolic Groups
We prove that the compressed word problem and the compressed simultaneous conjugacy problem are solvable in polynomial time in hyperbolic groups. In such problems, group elements are input as words defined by straight-line programs defined over a finite generating set for the group. We prove also that, for any infinite hyperbolic group G, the compressed knapsack problem in G is NP-complete
The compressed conjugacy problem in relatively hyperbolic groups
We prove that the compressed conjugacy problem in a group that is hyperbolic relative to a collection of free abelian subgroups is solvable in polynomial time
Compressed decision problems in hyperbolic groups
We prove that the compressed word problem and the compressed simultaneous conjugacy problem are solvable in polynomial time in hyperbolic groups. In such problems, group elements are input as words defined by straight-line programs defined over a finite generating set for the group. We prove also that, for any infinite hyperbolic group G, the compressed knapsack problem in G is NP-complete