2026-07-22T08:27:36Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25450 2026-03-19T13:28:43Z ddc:004 open_access

ε-Distance via Lévy-Prokhorov Lifting Desharnais, Josée Sokolova, Ana Lévy-Prokhorov metric behavioural distance epsilon-bisimulation reactive probabilistic transition systems discrete labelled Markov processes coalgebraic epsilon-(bi)simulation The most studied and accepted pseudometric for probabilistic processes is one based on the Kantorovich distance between distributions. It comes with many theoretical and motivating results, in particular it is the fixpoint of a given functional and defines a functor on (complete) pseudometric spaces. It is also the foundation for a categorical lifting of pseudometrics. Other notions of behavioural pseudometrics have also been proposed, one of them (ε-distance) based on ε-bisimulation. ε-Distance has the advantages that it is intuitively easy to understand, it relates systems that are conceptually close (for example, an imperfect implementation is close to its specification), and it comes equipped with a natural notion of ε-coupling. Finally, this distance is easy to compute. We show that ε-distance is also the greatest fixpoint of a functional and provides a functor. The latter is obtained by replacing the Kantorovich distance in the lifting functor with the Lévy-Prokhorov distance. In addition, we show that ε-couplings and ε-bisimulations have an appealing coalgebraic characterization. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Josée Desharnais and Ana Sokolova 2026 Is Part Of LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2026.26 urn:nbn:de:0030-drops-254506 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.26 eng https://creativecommons.org/licenses/by/4.0/legalcode