# Distribution Bisimilarity via the Power of Convex Algebras

arXiv: https://arxiv.org/abs/1707.02344 · HTML: https://mlsanity.com/paper/1707.02344/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2017.

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

- [Interval POMDP Shielding for Imperfect-Perception Agents](https://mlsanity.com/paper/2604.20728/) (2026)

## Abstract (arXiv)

Probabilistic automata (PA), also known as probabilistic nondeterministic labelled transition systems, combine probability and nondeterminism. They can be given different semantics, like strong bisimilarity, convex bisimilarity, or (more recently) distribution bisimilarity. The latter is based on the view of PA as transformers of probability distributions, also called belief states, and promotes distributions to first-class citizens. We give a coalgebraic account of distribution bisimilarity, and explain the genesis of the belief-state transformer from a PA. To do so, we make explicit the convex algebraic structure present in PA and identify belief-state transformers as transition systems with state space that carries a convex algebra. As a consequence of our abstract approach, we can give a sound proof technique which we call bisimulation up-to convex hull.