Rooted branching bisimulation as a congruence for probabilistic transition systems

TL;DR

This paper introduces a new probabilistic transition system specification format ensuring that rooted branching bisimulation remains a congruence, extending existing theories to handle probability distributions.

Contribution

It extends the theory of transition system specifications to probabilistic settings and proves that rooted branching bisimulation is a congruence under the probabilistic RBB safe format.

Findings

Probabilistic RBB safe format guarantees congruence of rooted branching bisimulation.

Provides a scheduler-free characterization of probabilistic branching bisimulation.

Includes counterexamples to justify format conditions.

Abstract

We propose a probabilistic transition system specification format, referred to as probabilistic RBB safe, for which rooted branching bisimulation is a congruence. The congruence theorem is based on the approach of Fokkink for the qualitative case. For this to work, the theory of transition system specifications in the setting of labeled transition systems needs to be extended to deal with probability distributions, both syntactically and semantically. We provide a scheduler-free characterization of probabilistic branching bisimulation as adapted from work of Andova et al. for the alternating model. Counter examples are given to justify the various conditions required by the format.