The Conjugacy Problem in the Grigorchuk Group is polynomial time decidable

TL;DR

This paper proves that the conjugacy problem in the Grigorchuk group can be decided efficiently within polynomial time, advancing understanding of computational problems in this complex algebraic structure.

Contribution

It establishes the polynomial time decidability of the conjugacy problem specifically for the Grigorchuk group, a significant result in computational group theory.

Findings

Conjugacy problem in the Grigorchuk group is polynomial time decidable.

Provides an algorithm with polynomial complexity for the conjugacy problem.

Enhances understanding of computational complexity in self-similar groups.

Abstract

In this paper we prove that the Conjugacy Problem in the Grigorchuk group $\Gamma$ has polynomial time complexity.