Approximate Bisimilarity

  • Mingsheng Ying
  • Martin Wirsing
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1816)


We introduce a notion of approximate bisimilarity in order to be able to reason about the approximate equivalence of processes. Approximate bisimilarity is based on the notion of bisimulation index for labelled transition systems. We establish some basic properties of bisimulation indexes and give a Hennessy-Milner logical characterization of approximate bisimilarity. As an application we show how to describe approximate correctness of real time systems by giving an example in real time ACP.


Process Algebra Bisimulation Real Time ACP 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Arnold and M. Nivat. Metric Interpretations of Infinite Trees and Semantics of Nondeterministic Recursive Programs. Theoretical Computer Science, 11:181–205, 1980.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    A. Arnold and M. Nivat. The Metric Space of Infinite Trees, Algebraic and Topological Properties. Fundamenta Informaticae, 4:445–476, 1980.MathSciNetGoogle Scholar
  3. [3]
    J. C. M. Baeten and J. Bergstra. Real-Time Process Algebra. Formal Aspects of Computing, 3:142–188, 1991.CrossRefGoogle Scholar
  4. [4]
    J. W. de Bakker and J. J. M. M. Rutten, editors. Ten Years of Concurrency Semantics, Selected Papers of the Amsterdam Concurreny Group. World Scientific, Singapore, 1992.Google Scholar
  5. [5]
    J. W. de Bakker and J. I. Zucker. Processes and the Denotational Semantics of Concurrency. Information and Control, 54:70–120, 1982.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    J. N. Kok and J. J. M. M. Rutten. Contractions in Comparing Concurrency Semantics. Theoretical Computer Science, 76:179–222, 1990.CrossRefzbMATHMathSciNetGoogle Scholar
  7. [7]
    R. Milner. A Calculus of Communicating Systems, volume 92 of Lecture Notes in Computer Science. Springer, Berlin, 1980.zbMATHGoogle Scholar
  8. [8]
    R. Milner. Communication and Concurrency. Prentice Hall, New York, 1989.zbMATHGoogle Scholar
  9. [9]
    F. van Breugel. Comparative Metric Semantics of Programming Languages: Nondeterminism and Recursion. Birkhäuser, Boston, 1998.zbMATHGoogle Scholar
  10. [10]
    R. J. van Glabbeek and J. J. M. M. Rutten. The Processes of de Bakker and Zucker Represent Bisimulation Equivalences Classes. In J. W. de Bakker, editor, 25 Jaar Semantik, Liber Amicorum, pages 243–246. CWI, Amsterdam, 1989.Google Scholar
  11. [11]
    Y. Wang. Real-Time Behaviour of Asynchronous Agents. In J. C. M. Baeten and J. W. Klop, editors, Proc. CONCUR’90, volume 458 of Lecture Notes in Computer Science, pages 502–520. Springer, Berlin, 1990.Google Scholar
  12. [12]
    M. S. Ying and M. Wirsing. Approximate Bisimilarity and Its Applications. Technical report 9906, Institut für Informatik, Ludwig-Maximilians-Universität München, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Mingsheng Ying
    • 1
  • Martin Wirsing
    • 2
  1. 1.State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and TechnologyTsinghua UniversityBeijingChina
  2. 2.Institut für InformatikLudwig-Maximilians-Universtät MünchenMünchenGermany

Personalised recommendations