A Comprehensive History of $μ$CRL and mCRL2

2026-07-16

AI Summary

This work addresses the challenge of correctly designing and verifying communication behaviors in complex interactive systems. It systematically traces the evolution of μCRL and its successor mCRL2, integrating process algebra, term rewriting systems, and modal μ-calculus to establish a formal modeling framework that combines rigorous mathematical foundations with practical engineering applicability. Building upon this foundation, the authors have developed a comprehensive mCRL2 toolset capable of modeling, automatically analyzing, and formally verifying the dynamic behavior of sophisticated computer-controlled systems. This integrated approach significantly enhances the scalability and usability of formal methods in real-world system design and validation.

Abstract

This article gives a historical overview of the background, motivation and development of μCRL and its successor mCRL2, from the inception to the present. Both mCRL2 and μCRL are similar, compact, but very expressive formalisms based on process algebra, term rewriting, and the modal mu-calculus. They are developed to model and analyse the behaviour of interacting systems, i.e., systems that communicate by exchange of messages, among each other and with the outside world. Every contemporary computer system can be viewed as such an interacting system and their communication schemes are difficult to design correctly. By sticking to the mathematical foundations, but being led by the desire to be practically relevant, the formalism has grown to become very versatile. In particular, mCRL2 does not only foster the development of theory and the formulation of correctness proofs, but it is also the basis of a large set of automatic tools that help to provide insight in the behaviour of complex computer controlled systems.

Problem

• interacting systems
• communication protocols
• formal modeling
• behavior analysis
• computer-controlled systems

Innovation

• process algebra
• term rewriting
• modal mu-calculus
• formal verification
• interactive systems