Abstract
We study the expressive power of two modelling formalisms, viz. hybrid automata and μCRL t . The automaton based language of hybrid automata is a popular formalism that is used for describing and analysing the behaviours of hybrid systems. The process algebraic language μCRL t is designed for specifying real-time and data-dependent systems and to reason about such systems. We show that every hybrid automaton can be translated to a μCRL t expression without loss of information, i.e. the translation is equivalence preserving. This proves that μCRL t is at least as expressive as the modelling language of hybrid automata. Subsequently, we extend the standard model of a hybrid automaton to deal with communications via shared continuous variables. We show that the resulting enhanced hybrid automata can also be embedded in μCRL t .
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alur, R., Henzinger, T.A., Ho, P.-H.: Automatic symbolic verification of embedded systems. IEEE Transactions on Software Engineering 22(3), 181–201 (1996)
Baeten, J.C.M., Middelburg, C.A.: Process Algebra with Timing. EATCS Monograph. Springer, Heidelberg (2002)
Bos, V., Kleijn, J.J.T.: Formal Specification and Analysis of Industrial Systems. PhD thesis, Eindhoven University of Technology (March 2002)
Corradini, F.: Absolute versus relative time in process algebras. In: Palamidessi, C., Parrow, J. (eds.) Proceedings of EXPRESS 1997. ENTCS, vol. 7, pp. 113–132. Elsevier, Amsterdam (1997)
Groote, J.F.: The syntax and semantics of timed μCRL. Software Engineering Report SEN-R9709, CWI (June 1997)
Groote, J.F., Ponse, A.: The syntax and semantics of μCRL. In: Ponse, A., Verhoef, C., van Vlijmen, S.F.M. (eds.) Algebra of Communicating Processes 1994. Workshops in Computing Series, pp. 26–62. Springer, Heidelberg (1995)
Groote, J.F., Reniers, M.A.: Algebraic process verification. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra, vol. ch. 17, pp. 1151–1208. Elsevier, North-Holland (2001)
Groote, J.F., van Wamel, J.J.: Analysis of three hybrid systems in timed μCRL. Journal of Logic and Algebraic Programming 39, 215–247 (2001)
Henzinger, T.A.: The theory of hybrid automata. In: The Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science (LICS 1996), pp. 278–292 (1996)
Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: HyTech: A model checker for hybrid systems. Software Tools for Technology Transfer 1, 110–122 (1997)
Reniers, M.A., Groote, J.F., van der Zwaag, M.B., van Wamel, J.: Completeness of timed μCRL. Fundamenta Informaticae 50(3-4), 361–402 (2002)
Willemse, T.A.C.: Semantics and Verification in Process Algebras with Data and Timing. PhD thesis, Eindhoven University of Technology (February 2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Willemse, T.A.C. (2004). Embeddings of Hybrid Automata in Process Algebra. In: Boiten, E.A., Derrick, J., Smith, G. (eds) Integrated Formal Methods. IFM 2004. Lecture Notes in Computer Science, vol 2999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24756-2_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-24756-2_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21377-2
Online ISBN: 978-3-540-24756-2
eBook Packages: Springer Book Archive