A New Branching Bisimulation for Probabilistic Processes

2026-07-18

AI Summary

Existing notions of probabilistic process equivalence suffer from insufficient discriminative power when abstracting away unobservable actions and struggle to accommodate dynamic constructs such as recursion. This work proposes a novel branching bisimulation relation tailored to characterize behavioral equivalence among probabilistic processes. Within a comprehensive probabilistic process calculus encompassing both static and dynamic operators—including recursion—the root variant of this relation is shown, for the first time, to satisfy congruence. Compared to prior approaches, the proposed relation offers a more refined abstraction of behavioral equivalence while simultaneously achieving greater discriminating capability and favorable algebraic properties.

Abstract

We introduce a new branching bisimulation for probabilistic processes, which induces a more refined equivalence relation than any known equivalence that abstracts from unobservable actions, with a rooted version that is a congruence for a language of probabilistic process with the usual static as well as dynamic constructs including recursion.

Problem

• probabilistic processes
• branching bisimulation
• unobservable actions
• equivalence relation
• congruence

Innovation

• branching bisimulation
• probabilistic processes
• congruence
• unobservable actions
• equivalence relation