We study different behavioral metrics, such as those arising from both branching and linear-time semantics, in a coalgebraic setting. Given a coalgebra α : X → HX for a functor H : Set → Set, we define a framework for deriving pseudometrics on X which measure the behavioral distance of states. A crucial step is the lifting of the functor H on Set to a functor H' on the category PMet of pseudometric spaces. We present two different approaches which can be viewed as generalizations of the Kantorovich and Wasserstein pseudometrics for probability measures. We show that the pseudometrics provided by the two approaches coincide on several natural examples, but in general they differ. If H has a final coalgebra, every lifting H' yields in a canonical way a behavioral distance which is usually branching-time, i.e., it generalizes bisimilarity. In order to model linear-time metrics (generalizing trace equivalences), we show sufficient conditions for lifting distributive laws and monads. These results enable us to employ the generalized powerset construction.
Coalgebraic Behavioral Metrics
Paolo Baldan;
2018
Abstract
We study different behavioral metrics, such as those arising from both branching and linear-time semantics, in a coalgebraic setting. Given a coalgebra α : X → HX for a functor H : Set → Set, we define a framework for deriving pseudometrics on X which measure the behavioral distance of states. A crucial step is the lifting of the functor H on Set to a functor H' on the category PMet of pseudometric spaces. We present two different approaches which can be viewed as generalizations of the Kantorovich and Wasserstein pseudometrics for probability measures. We show that the pseudometrics provided by the two approaches coincide on several natural examples, but in general they differ. If H has a final coalgebra, every lifting H' yields in a canonical way a behavioral distance which is usually branching-time, i.e., it generalizes bisimilarity. In order to model linear-time metrics (generalizing trace equivalences), we show sufficient conditions for lifting distributive laws and monads. These results enable us to employ the generalized powerset construction.File | Dimensione | Formato | |
---|---|---|---|
LMCS-Probability-2018.pdf
accesso aperto
Descrizione: Copia PDF
Tipologia:
Published (publisher's version)
Licenza:
Accesso gratuito
Dimensione
717.92 kB
Formato
Adobe PDF
|
717.92 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.