We show that any finitely-dependent invariant process on a transitive
amenable graph is a finitary factor of an i.i.d. process. With an additional
assumption on the geometry of the graph, namely that no two balls with
different centers are identical, we further show that the i.i.d. process may be
taken to have entropy arbitrarily close to that of the finitely-dependent
process. As an application, we give an affirmative answer to a question of
Holroyd.Comment: 28 pages, 1 figur