A fast algorithm for constructing Arf closure and a conjecture

In this article, we give a fast and an easily implementable algorithm for computing the Arf closure of an irreducible algebroid curve (or a branch). Moreover, we study the relation between the branches having the same Arf closure and their regularity indices. We give some results and a conjecture, which are steps towards the interpretation of Arf closure as a specific way of taming the singularity.