Weighted and Branching Bisimilarities from Generalized Open Maps

TL;DR

This paper extends the open map approach to bisimilarity to include weighted, probabilistic, and branching bisimilarities, enabling the modeling of quantitative and history-preserving system equivalences.

Contribution

It generalizes open maps to handle weighted and probabilistic bisimilarity, and captures branching bisimilarity within this extended framework.

Findings

Open maps cannot model probabilistic bisimilarity.

The generalized framework captures weighted and probabilistic bisimilarity.

Branching bisimilarity is characterized as a restriction of weak bisimilarity.

Abstract

In the open map approach to bisimilarity, the paths and their runs in a given state-based system are the first-class citizens, and bisimilarity becomes a derived notion. While open maps were successfully used to model bisimilarity in non-deterministic systems, the approach fails to describe quantitative system equivalences such as probabilistic bisimilarity. In the present work, we see that this is indeed impossible and we thus generalize the notion of open maps to also accommodate weighted and probabilistic bisimilarity. Also, extending the notions of strong path and path bisimulations into this new framework, we show that branching bisimilarity can be captured by this extended theory and that it can be viewed as the history preserving restriction of weak bisimilarity.