Compositional bisimulation metric reasoning with Probabilistic Process Calculi

TL;DR

This paper investigates how standard operators in probabilistic process calculi support compositional reasoning using bisimulation metrics, enabling modular analysis of recursive and continuous processes for performance validation.

Contribution

It introduces a uniform continuity framework for compositional reasoning with bisimulation metrics in probabilistic process calculi, including recursive processes.

Findings

Characterizes distances between probabilistic processes with standard operators

Demonstrates compositional reasoning for recursive processes

Enables metric-based performance validation of systems

Abstract

We study which standard operators of probabilistic process calculi allow for compositional reasoning with respect to bisimulation metric semantics. We argue that uniform continuity (generalizing the earlier proposed property of non-expansiveness) captures the essential nature of compositional reasoning and allows now also to reason compositionally about recursive processes. We characterize the distance between probabilistic processes composed by standard process algebra operators. Combining these results, we demonstrate how compositional reasoning about systems specified by continuous process algebra operators allows for metric assume-guarantee like performance validation.