A Logical Approach to Decidability of Hierarchies of Regular Star-Free Languages

摘要

We propose a new, logical, approach to the decidability problem for the Straubing and Brzozowski hierarchies based on the preservation theorems from model theory, on a theorem of Higman, and on the Rabin tree theorem. In this way, we get purely logical, short proofs for some known facts on decidability, which might be of methodological interest. Our approach is also applicable to some other similar situations, say to "words" over dense orderings which is relevant to the continuous time and hybrid systems.