ABSTRACT
Until now, several braid recognition algorithms have been constructed. The first of them was contained in the original work of Artin [Art1] (and, in more detail, [Art2]). However, the approach proposed by Artin was not very clearly explained; both articles are quite difficult to read. There were other works on braid recognition (by Birman [Bir], Garside [Gar], Thurston, et al.) Here we are going to describe a geometrically explicit algorithm (proving the completeness of a slightly modified Artin invariant according to [GM], see also [BZ]) and the algebraic algorithm by Dehornoy.
