# A Spectrum of Approximate Probabilistic Bisimulations

arXiv: https://arxiv.org/abs/2407.07584 · HTML: https://mlsanity.com/paper/2407.07584/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2024.

## Built on by (most cited first, 1 of 1)

- [Approximate Homomorphisms and Convergent Representations in Transducers](https://mlsanity.com/paper/2608.20428/) (2026)

## Abstract (arXiv)

This paper studies various notions of approximate probabilistic bisimulation on labeled Markov chains (LMCs). We introduce approximate versions of weak and branching bisimulation, as well as a notion of varepsilon-perturbed bisimulation that relates LMCs that can be made (exactly) probabilistically bisimilar by small perturbations of their transition probabilities. We explore how the notions interrelate and establish their connections to other well-known notions like varepsilon-bisimulation.