Automatic Verification of Real-Time Systems with Discrete Probability Distributions

  • Marta Kwiatkowska
  • Gethin Norman
  • Roberto Segala
  • Jeremy Sproston
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1601)


We consider the timed automata model of [3], which allows the analysis of real-time systems expressed in terms of quantitative timing constraints. Traditional approaches to real-time system description express the model purely in terms of nondeterminism; however, we may wish to express the likelihood of the system making certain transitions. In this paper, we present a model for real-time systems augmented with discrete probability distributions. Furthermore, using the algorithm of [5] with fairness, we develop a model checking method for such models against temporal logic properties which can refer both to timing properties and probabilities, such as, “with probability 0.6 or greater, the clock x remains below 5 until clock y exceeds 2”


Model Check Atomic Formula Atomic Proposition Hybrid Automaton Region Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. Alur, C. Courcoubetis, and D. Dill. Model-checking for probabilistic real-time systems. In Automata, Languages and Programming: Proceedings of the 18th ICALP, Lecture Notes in Computer Science 510, pages 115–126, 1991.CrossRefGoogle Scholar
  2. [2]
    R. Alur, C. Courcoubetis, and D. Dill. Model-checking in dense real-time. Information and Computation, 104(1):2–34, 1993. Preliminary version appears in the Proc. of 5th LICS, 1990.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    R. Alur and D. Dill. A theory of timed automata. Theoretical Computer Science, 126:183–235, 1994. Preliminary version appears in Proc. 17th ICALP, 1990, LNCS 443.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    C. Baier. Personal communication, 1998.Google Scholar
  5. [5]
    C. Baier and M. Kwiatkowska. Model checking for a probabilistic branching time logic with fairness. Distributed Computing, 11:125–155, 1998.CrossRefGoogle Scholar
  6. [6]
    J. Bengtsson, K. Larsen, F. Larsson, P. Pettersson, W. Yi, and C. Weise. New generation of UPPAAL. In Proceedings of the International Workshop on Software Tools for Technology Transfer, Aalborg, Denmark, July 1998.Google Scholar
  7. [7]
    A. Bianco and L. de Alfaro. Model checking of probabilistic and nondeterministic systems. In Foundations of Software Technology and Theoretical Computer Science, volume 1026 of Lecture Notes in Computer Science, pages 499–513, 1995.CrossRefGoogle Scholar
  8. [8]
    M. Bozga, C. Daws, O. Maler, A. Olivero, S. Tripakis, and S. Yovine. Kronos: a model-checking tool for real-time systems. In Proc. of the 10th Conference on Computer-Aided Verification, Vancouver, Canada, 28 June — 2 July 1998. Springer Verlag.Google Scholar
  9. [9]
    P. D’Argenio, J.-P. Katoen, T. Ruys, and J. Tretmans. Modeling and verifying a bounded retransmission protocol. In Z. Brezocnik and T. Kapus, editors, Proc. of COST 247 International Workshop on Applied Formal Methods in System Design, Maribor, Slovenia, Technical Report. University of Maribor, 1996.Google Scholar
  10. [10]
    H. Gregersen and H. E. Jensen. Formal design of reliable real time systems. Master’s thesis, Department of Mathematics and Computer Science, Aalborg University, 1995.Google Scholar
  11. [11]
    H. Hansson and B. Jonsson. A logic for reasoning about time and reliability. Formal Aspects of Computing, 6(5):512–535, 1994.CrossRefzbMATHGoogle Scholar
  12. [12]
    T. Henzinger, P. Kopke, A. Puri, and P. Varaiya. What’s decidable about hybrid automata? Journal of Computer and System Sciences, 57(1):94–124, Aug. 1998.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    T. Henzinger and O. Kupferman. From quantity to quality. In O. Maler, editor, HART 97: Hybrid and Real-time Systems, Lecture Notes in Computer Science 1201, pages 48–62. Springer-Verlag, 1997.CrossRefGoogle Scholar
  14. [14]
    T. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine. Symbolic model checking for real-time systems. Information and Computation, 111(2):193–244, 1994. Special issue for LICS 92.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    G. Lafferriere, G. Pappas, and S. Yovine. Decidable hybrid systems. Technical Report UCB/ERL M98/39, University of California at Berkeley, June 1998.Google Scholar
  16. [16]
    S. Yovine. Model checking timed automata. In G. Rozenberg and F. Vaandrager, editors, Embedded Systems, volume 1494 of Lecture Notes in Computer Science. Springer, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Marta Kwiatkowska
    • 1
  • Gethin Norman
    • 1
  • Roberto Segala
    • 2
  • Jeremy Sproston
    • 1
  1. 1.University of BirminghamBirminghamUK
  2. 2.Università di BolognaBolognaItaly

Personalised recommendations