Generalized Quantitative Analysis of Metric Transition Systems

The formalism of metric transition systems, as introduced by de Alfaro, Faella and Stoelinga, is convenient for modeling systems and properties with quantitative information, such as probabilities or time. For a number of applications however, one needs other distances than the point-wise (and possibly discounted) linear and branching distances introduced by de Alfaro et.al. for analyzing quantitative behavior. In this paper, we show a vast generalization of the setting of de Alfaro et.al., to a framework where any of a large number of other useful distances can be applied. Concrete instantiations of our framework hence give e.g. limit-average, discounted-sum, or maximum-lead linear and branching distances; in each instantiation, properties similar to the ones of de Alfaro et.al. hold. In the end, we achieve a framework which is not only suitable for modeling different kinds of quantitative systems and properties, but also for analyzing these by using different application-determined ways of mea-suring quantitative behavior.