Abstract
In this paper we prove that the conjugacy problem in the Grigorchuk group Γ has log-space complexity.
A Appendix
The proof of Proposition 5 follows that given in [10], but the goal in this case is to estimate the height of the tree and not its overall size.
Proof.
In order to estimate the height of the tree
Let
Observe that the reduced length,
It is easy to see that, for any two words
By choosing the specific values
(as combinations of the root of unity of the polynomial
Proposition 6 ([10]).
Let
Then the following statements hold:
if
if
Lemma 7 ([10]).
Let
Using these facts about the norm, we can now proceed to prove the proposition.
Consider an arbitrary branch
there exists an
there exists an
Moreover, since the size of
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