Contextual Behavioural Metrics (Extended Version)

TL;DR

This paper introduces contextual behavioural metrics (CBMs) that measure process behavior discrepancies while considering environmental context, unifying various equivalence notions and analyzing compositional properties.

Contribution

The paper presents CBMs as a new framework that incorporates context into process metrics and explores their properties and relation to existing equivalences.

Findings

CBMs unify many known process equivalences.

CBMs are compositional with respect to key process algebra operators.

CBMs account for environmental factors in process behavior analysis.

Abstract

We introduce contextual behavioural metrics (CBMs) as a novel way of measuring the discrepancy in behaviour between processes, taking into account both quantitative aspects and contextual information. This way, process distances by construction take the environment into account: two (non-equivalent) processes may still exhibit very similar behaviour in some contexts, e.g., when certain actions are never performed. We first show how CBMs capture many well-known notions of equivalence and metric, including Larsen's environmental parametrized bisimulation. We then study compositional properties of CBMs with respect to some common process algebraic operators, namely prefixing, restriction, non-deterministic sum, parallel composition and replication.