Folk Theorems on the Correspondence between State-Based and Event-Based Systems

TL;DR

This paper explores the deep connections between Kripke Structures and Labelled Transition Systems, demonstrating how embeddings can be used to translate various behavioral equivalences and facilitate minimization across models.

Contribution

It extends prior work by showing embeddings for multiple equivalences and enabling cross-domain minimization techniques.

Findings

Embeddings work for strong bisimilarity, simulation, and trace equivalence.

Translations allow minimization techniques to be applied across models.

The correspondence generalizes to various behavioral equivalences.

Abstract

Kripke Structures and Labelled Transition Systems are the two most prominent semantic models used in concurrency theory. Both models are commonly believed to be equi-expressive. One can find many ad-hoc embeddings of one of these models into the other. We build upon the seminal work of De Nicola and Vaandrager that firmly established the correspondence between stuttering equivalence in Kripke Structures and divergence-sensitive branching bisimulation in Labelled Transition Systems. We show that their embeddings can also be used for a range of other equivalences of interest, such as strong bisimilarity, simulation equivalence, and trace equivalence. Furthermore, we extend the results by De Nicola and Vaandrager by showing that there are additional translations that allow one to use minimisation techniques in one semantic domain to obtain minimal representatives in the other semantic domain for these equivalences.