Title: On the trade-off between labels and weights in quantitative bisimulation,
Abstract: Reductions for transition systems have been recently introduced as a uniform
and principled method for comparing the expressiveness of system models with
respect to a range of properties, especially bisimulations. In this paper we
study the expressiveness (w.r.t. bisimulations) of models for quantitative
computations such as weighted labelled transition systems (WLTSs), uniform
labelled transition systems (ULTraSs), and state-to-function transition systems
(FuTSs). We prove that there is a trade-off between labels and weights: at one
extreme lays the class of (unlabelled) weighted transition systems where
information is presented using weights only; at the other lays the class of
labelled transition systems (LTSs) where information is shifted on labels.
These categories of systems cannot be further reduced in any significant way
and subsume all the aforementioned models.