Bounds in w-Regularity

We consider an extension of omega-regular expressions where two new variants of the Kleene star L* are added: L^B and L^S . These exponents act as the standard star, but restrict the number of iterations to be bounded (for L^B) or to tend toward infinity (for L^S). These expressions can define languages that are not omega-regular. We develop a theory for these languages. We study the decidability and closure questions. We also define an equivalent automaton model, extending Buchi automata. This culminates with a - partial -complementation result