Interval logics and ωb-regular languages

Abstract

In the recent years, interval temporal logics are emerging as a workable alternative to more standard point-based ones. In this paper, we establish an original connection between these logics and ωB-regular languages. First, we provide a logical characterization of regular (resp., ω-regular) languages in the interval logic of Allen's relations meets, begun by, and begins over finite linear orders (resp., ℕ). Then, we lift such a correspondence to ωB-regular languages by substituting for (is obtained from by adding a modality for Allen's relation met by). In addition, we show that new classes of extended (ω-)regular languages can be naturally defined in. © 2013 Springer-Verlag Berlin Heidelberg.