The Consequences of Imre Simon’s Work in the Theory of Automata, Languages, and Semigroups
In this lecture, I will show how influential has been the work of Imre in the theory of automata, languages and semigroups. I will mainly focus on two celebrated problems, the restricted star-height problem (solved) and the decidability of the dot-depth hierarchy (still open). These two problems lead to surprising developments and are currently the topic of very active research. I will present the prominent results of Imre on both topics, and demonstrate how these results have been the motor nerve of the research in this area for the last thirty years.