Logical Characterization of Bisimulation Metrics

TL;DR

This paper introduces a logical framework using a probabilistic variant of Hennessy-Milner logic to characterize bisimulation metrics, enabling precise behavioral comparisons of probabilistic processes.

Contribution

It presents a novel logical characterization of bisimulation metrics through mimicking formulae and a distance measure on formulae, extending the understanding of probabilistic process equivalences.

Findings

Distance between processes equals distance between their mimicking formulae

Characterizes probabilistic simulation and bisimilarity logically

Defines a 1-bounded pseudometric on formulae

Abstract

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.