Logical Characterization of Bisimulation Metrics

Valentina Castiglioni, Daniel Gebler, Simone Tini
2016 Electronic Proceedings in Theoretical Computer Science  
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
more » ... mulation 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.
doi:10.4204/eptcs.227.4 fatcat:k4h6kolaprgg3lfx724s4gbhzm