# On path-based coalgebras and weak notions of bisimulation

## TL;DR

This paper develops a coalgebraic framework for understanding branching bisimulation in systems with silent actions, showing that recording execution paths up to stuttering suffices for behavioral equivalence.

## Contribution

It introduces a coalgebraic characterization of branching bisimulation for labelled transition and probabilistic systems, addressing silent actions.

## Key findings

- Recording execution paths characterizes branching bisimulation.
- Coalgebraic approach unifies different system types.
- Silent actions are effectively handled in the framework.

## Abstract

It is well known that the theory of coalgebras provides an abstract definition of behavioural equivalence that coincides with strong bisimulation across a wide variety of state-based systems. Unfortunately, the theory in the presence of so-called silent actions is not yet fully developed. In this paper, we give a coalgebraic characterisation of branching bisimulation in the context of labelled transition systems and fully probabilistic systems. It is shown that recording executions (up to a notion of stuttering), rather than the set of successor states, from a state is sufficient to characterise branching bisimulation in both cases.