  Difference hierarchies were originally introduced by Hausdorff and they play
an important role in descriptive set theory. In this survey paper, we study
difference hierarchies of regular languages. The first sections describe
standard techniques on difference hierarchies, mostly due to Hausdorff. We
illustrate these techniques by giving decidability results on the difference
hierarchies based on shuffle ideals, strongly cyclic regular languages and the
polynomial closure of group languages.
