Geodesic
The word problem in Hanoi Towers groups
Algebra and discrete mathematics, Tome 17 (2014) no. 2, pp. 248-255

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We prove that the elements of the Hanoi Towers groups $\mathcal{H}_m$ have depth bounded from above by a poly-logarithmic function $O(\log^{m-2} n)$, where $n$ is the length of an element. Therefore the word problem in groups $\mathcal{H}_m$ is solvable in subexponential time $exp(O(\log^{m-2} n))$.
Keywords: the Tower of Hanoi game, word problem, complexity.
Mots-clés : automaton group 
@article{ADM_2014_17_2_a5,
     author = {Ievgen Bondarenko},
     title = {The word problem in {Hanoi} {Towers} groups},
     journal = {Algebra and discrete mathematics},
     pages = {248--255},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2014_17_2_a5/}
}
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Ievgen Bondarenko. The word problem in Hanoi Towers groups. Algebra and discrete mathematics, Tome 17 (2014) no. 2, pp. 248-255. http://geodesic.mathdoc.fr/item/ADM_2014_17_2_a5/