The word problem in Hanoi Towers groups - Bondarenko, I. (Algebra and Discrete Mathematics, 2014)
We prove that the elements of the Hanoi Towers groups Hm have depth bounded from above by a poly-logarithmic function O(logm⁻²n), where n is the length of an element. Therefore the word problem in groups Hm is solvable in subexponential time exp(O(logm⁻²n)).