# Robust Probabilistic Bisimilarity for Labelled Markov Chains

arXiv: https://arxiv.org/abs/2505.15290 · HTML: https://mlsanity.com/paper/2505.15290/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2025.

## Built on by (most cited first, 2 of 2)

- [Comparing Labeled Markov Chains: A Cantor-Kantorovich Approach](https://mlsanity.com/paper/2511.18103/) (2025)
- [Computing Fixpoints of Learned Functions: Chaotic Iteration and Simple Stochastic Games](https://mlsanity.com/paper/2601.16142/) (2026)

## Abstract (arXiv)

Despite its prevalence, probabilistic bisimilarity suffers from a lack of robustness under minuscule perturbations of the transition probabilities. This can lead to discontinuities in the probabilistic bisimilarity distance function, undermining its reliability in practical applications where transition probabilities are often approximations derived from experimental data. Motivated by this limitation, we introduce the notion of robust probabilistic bisimilarity for labelled Markov chains, which ensures the continuity of the probabilistic bisimilarity distance function. We also propose an efficient algorithm for computing robust probabilistic bisimilarity and show that it performs well in practice, as evidenced by our experimental results.