THE MISSING LINK FOR ω-RATIONAL SETS, AUTOMATA, AND SEMIGROUPS
J Duparc, Mariane Riss · International Journal of Algebra and Computation · 2006
In 1997, following the works of Klaus W. Wagner on ω-regular sets, Olivier Carton and Dominique Perrin introduced the notions of chains and superchains for ω-semigroups. There is a clear correspondence between the algebraic representation of each of these operations and the automata-theoretical one. Unfortunately, chains and superchains do not suffice to describe the whole Wagner hierarchy. We introduce a third notion that completes the task undertaken by these two authors.