Logical Characterization of Bisimulation Metrics

• Main Authors: Valentina Castiglioni, Daniel Gebler, Simone Tini
• Format: Article
• Language: English
• Published: Open Publishing Association 2016-10-01
• Series: Electronic Proceedings in Theoretical Computer Science
• Online Access: http://arxiv.org/pdf/1610.08169v1

Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic variant of the Hennessy-Milner logic. Our approach is based on the novel notions of mimicking formulae and distance between formulae. The former are a weak version of the well known characteristic formulae and allow us to characterize also (ready) probabilistic simulation and probabilistic bisimilarity. The latter is a 1-bounded pseudometric on formulae that mirrors the Hausdorff and Kantorovich lifting the defining bisimilarity pseudometric. We show that the distance between two processes equals the distance between their own mimicking formulae.