Parity automata for quantitative linear time logics

We initiate a study of automata-based model checking for previously proposed quantitative linear time logics interpreted over coalgebras. Our results include: (i) an automata-theoretic characterisation of the semantics of these logics, based on a notion of extent of a quantitative parity automaton, (ii) a study of the expressive power of Büchi variants of such automata, with implications on the expressiveness of fragments of the logics considered, and (iii) a naïve algorithm for computing extents, under additional assumptions on the domain of truth values