Hausdorff dimension of self-similar sets with overlaps

We provide a simple formula to compute the Hausdorff dimension of the attractor of an overlapping iterated function system of contractive similarities satisfying a certain collection of assumptions. This formula is obtained by associating a non-overlapping infinite iterated function system to an iterated function system satisfying our assumptions and using the results of Moran to compute the Hausdorff dimension of the attractor of this infinite iterated function system, thus showing that the Hausdorff dimension of the attractor of this infinite iterated function system agrees with that of the attractor of the original iterated function system. Our methods are applicable to some iterated function systems that do not satisfy the infinite type condition recently introduced by Ngai and Wang.