Coalgebraic Weak Bisimulation from Recursive Equations over Monads

TL;DR

This paper develops a coalgebraic framework for weak bisimulation, extending the coalgebraic approach to encompass weak equivalences across various system types using order-enriched monads.

Contribution

It introduces a novel coalgebraic treatment of weak bisimulation using recursive equations over monads, unifying several existing notions.

Findings

Aligns with existing weak bisimulation notions for different systems

Uses least fixpoints of recursive equations to characterize weak equivalences

Provides a general coalgebraic framework for weak bisimulation

Abstract

Strong bisimulation for labelled transition systems is one of the most fundamental equivalences in process algebra, and has been generalised to numerous classes of systems that exhibit richer transition behaviour. Nearly all of the ensuing notions are instances of the more general notion of coalgebraic bisimulation. Weak bisimulation, however, has so far been much less amenable to a coalgebraic treatment. Here we attempt to close this gap by giving a coalgebraic treatment of (parametrized) weak equivalences, including weak bisimulation. Our analysis requires that the functor defining the transition type of the system is based on a suitable order-enriched monad, which allows us to capture weak equivalences by least fixpoints of recursive equations. Our notion is in agreement with existing notions of weak bisimulations for labelled transition systems, probabilistic and weighted systems, and simple Segala systems.