Star height problem

The star-height problem in [formal language theory]? is the question whether all regular languages be expressed using regular expressions with a limited nesting depth of Kleene stars? Specifically, is a nesting depth of more than 2 required? If so, can we determine how many are required? This theoretical problem remained open for 30 years, to be solved by [Kosaburo Hashiguchi]? in 1983. The answer is yes.

The generalized star height problem is the same problem for regular expressions that include the complement operator. This is still an open problem.