Formal Methods in System Design

, Volume 43, Issue 2, pp 191–232 | Cite as

A compositional modelling and analysis framework for stochastic hybrid systems

  • Ernst Moritz Hahn
  • Arnd HartmannsEmail author
  • Holger Hermanns
  • Joost-Pieter Katoen


The theory of hybrid systems is well-established as a model for real-world systems consisting of continuous behaviour and discrete control. In practice, the behaviour of such systems is also subject to uncertainties, such as measurement errors, or is controlled by randomised algorithms. These aspects can be modelled and analysed using stochastic hybrid systems. In this paper, we present HModest, an extension to the Modest modelling language—which is originally designed for stochastic timed systems without complex continuous aspects—that adds differential equations and inclusions as an expressive way to describe the continuous system evolution. Modest is a high-level language inspired by classical process algebras, thus compositional modelling is an integral feature. We define the syntax and semantics of HModest and show that it is a conservative extension of Modest that retains the compositional modelling approach. To allow the analysis of HModest models, we report on the implementation of a connection to recently developed tools for the safety verification of stochastic hybrid systems, and illustrate the language and the tool support with a set of small, but instructive case studies.


Stochastic hybrid automata Process calculus Modelling Analysis Abstraction 



The authors thank Pedro D’Argenio for discussions on the language design and Nicolás Wolovick (both from University of Cordoba, Argentina) for his support in the development of the concrete semantics.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Ernst Moritz Hahn
    • 1
  • Arnd Hartmanns
    • 1
    Email author
  • Holger Hermanns
    • 1
  • Joost-Pieter Katoen
    • 2
  1. 1.Saarland University – Computer ScienceSaarbrückenGermany
  2. 2.LS2: Software Modelling and VerificationRWTH Aachen UniversityAachenGermany

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