Distribution Bisimilarity via the Power of Convex Algebras

TL;DR

This paper presents a coalgebraic framework for distribution bisimilarity in probabilistic automata, emphasizing the convex algebraic structure of belief states and introducing a sound bisimulation proof technique.

Contribution

It provides a novel coalgebraic account of distribution bisimilarity, highlighting the convex algebraic structure and introducing a bisimulation up-to convex hull method.

Findings

Coalgebraic characterization of distribution bisimilarity.

Explicit connection between belief states and convex algebraic structures.

Introduction of a bisimulation up-to convex hull proof technique.

Abstract

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.