  A general result of Epstein and Thurston implies that all link groups are
automatic, but the proof provides no explicit automaton. Here we show that the
groups of all torus links are groups of fractions of so-called Garside monoids,
i.e., roughly speaking, monoids with a good theory of divisibility, which
allows us to reprove that those groups are automatic, but, in addition, gives a
completely explicit description of the involved automata, thus partially
answering a question of D.F.Holt.
