This paper defines action-labelled quantitative transition systems as a general framework for combining qualitative and quantitative analysis. We define state-metrics as a natural extension of bisimulation from non-quantitative systems to quantitative ones. We then prove that any single state-metric corresponds to a bisimulation and that the greatest state-metric corresponds to bisimilarity. Furthermore, we provide two extended examples which show that our results apply to both probabilistic and weighted automata as special cases of action-labelled quantitative transition systems.
REF considered a more general framework, called action-labeled quantitative transition systems (AQTS).
Metrics for Action-labelled Quantitative Transition Systems
Electr. Notes Theor. Comput. Sci.
Computer Science