Open problems about regular languages, 35 years later

In December 1979, Janusz A. Brzozowski presented a selection of six open problems about regular languages and mentioned two other problems in the conclusion of his article. These problems have been the source of some of the greatest breakthroughs in automata theory over the past 35 years. This survey article summarizes the state of the art on these questions and the hopes for the next 35 years. Thirty-five years ago, at a conference in Santa Barbara in December 1979, Janusz A. Brzozowski [8] presented a selection of six open problems about regular languages and mentioned two other topics in the conclusion of his article. These six open problems were, in order, star height , restricted star height , group complexity , star removal , regularity of non-counting classes and optimality of prefix codes . The two other topics were the limitedness problem and the dot-depth hierarchy . These problems proved to be very influential in the development of automata theory and were the source of critical breakthroughs. The aim of this paper is to survey these results, to describe their impact on current research and to outline some hopes for the next thirty-five years. Due to the lack of space, the dot-depth hierarchy is treated in a separate article [ 61].