  Since the braid group was discovered by E. Artin, the question of its
conjugacy problem has been solved by Garside and Birman, Ko and Lee. However,
the solutions given thus far are difficult to compute with a computer, since
the number of operations needed is extremely large. Meanwhile, random
algorithms used to solve difficult problems such as primality of a number were
developed, and the random practical methods have become an important tool. We
give a random algorithm, along with a conjecture of how to improve its
convergence speed, in order to identify elements in the braid group, which are
conjugated to its generators for a given power. These elements of the braid
group, the half-twists, are important in themselves, as they are the key
players in some geometrical and algebraical methods, the building blocks of
quasipositive braids and they construct endless sets of generators for the
group.
