Skip to main content

Accurate Widenings and Boundedness Properties of Timed Systems

  • Conference paper
  • First Online:
Perspectives of System Informatics (PSI 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2244))

Abstract

We propose a symbolic model checking procedure for timed systems that is based on operations on constraints. To accelerate the termination of the model checking procedure, we define history-dependent widening operators, again in terms of constraint-based operations. We show that these widenings are accurate, i.e., they don’t lose precision even with respect to the test of boundedness properties.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Alur, C. Courcoubetis, D. Dill, N. Halbwachs, and H. Wong-Toi. Minimization of timed transition systems. In R. Cleaveland, editor, CONCUR: Concurrency Theory, volume 630 of LNCS, pages 340–354. Springer-Verlag, 1992.

    Google Scholar 

  2. R. Alur and D. Dill. A theory of timed automata. Theoretical Computer Science, 126(2):183–236, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  3. F. Balarin. Approximate reachability analysis of timed automata. In 17th IEEE Real-Time Systems Symposium, pages 52–61. IEEE Computer Society Press, 1996.

    Google Scholar 

  4. B. Boigelot, L. Bronne, and S. Rassart. An improved reachability analysis method for strongly linear hybrid systems. In O. Grumberg, editor, CAV’97: Computer Aided Verification, volume 1254 of LNCS, pages 167–178. Springer-Verlag, 1997.

    Google Scholar 

  5. B. Berard and L. Fribourg. Reachability analysis of (timed) petri nets using real arithmetic. In J. C. M. Baeten and S. Mauw, editors, CONCUR: Concurrency Theory, volume 1664 of LNCS, pages 178–193. Springer-Verlag, 1999.

    Chapter  Google Scholar 

  6. T. Bultan, R. Gerber, and W. Pugh. Symbolic model checking of infinite state systems using presburger arithmetics. In Orna Grumberg, editor, the 9th International Conference on Computer Aided Verification (CAV’97), LNCS 1254, pages 400–411. Springer, Haifa, Israel, July 1997.

    Google Scholar 

  7. T. Bultan, R. Gerber, and W. Pugh. Model Checking Concurrent Systems with Unbounded Integer Variables: Symbolic Representations, Approximations and Experimental Results, february 1998.

    Google Scholar 

  8. Johan Bengtsson, Kim. G. Larsen, Fredrik Larsson, Paul Petersson, and Wang Yi. Uppaal in 1995. In T. Margaria and B. Steffen, editors, TACAS, LNCS 1055, pages 431–434. Springer-Verlag, 1996.

    Google Scholar 

  9. Bernard Boigelot and Pierre Wolper. Symbolic verification with periodic sets. In David Dill, editor, 6th International Conference on Computer-Aided Verification, volume 818 of LNCS, pages 55–67. Springer-Verlag, June 1994.

    Google Scholar 

  10. Patrick Cousot and Radhia Cousot. Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In the 4th ACM Symposium on Principles of Programming Languages, 1977.

    Google Scholar 

  11. P. Cousot and N. Halbwachs. Automatic discovery of linear restraints among variables of a program. In the Fifth Annual ACM Symposium on Principles of Programming Languages. ACM Press, 1978.

    Google Scholar 

  12. C. Daws and S. Tripakis. Model checking of real-time reachability properties using abstractions. InBernhard Steffen, editor, TACAS98: Tools and Algorithms for the Construction of Systems, LNCS 1384, pages 313–329. Springer-Verlag, March/April 1998.

    Chapter  Google Scholar 

  13. N. Halbwachs. Delay analysis in synchronous programs. In C. Courcoubetis, editor, the International Conference on Computer-Aided-Verification, volume 697 of LNCS, pages 333–346. Springer-Verlag, 1993.

    Google Scholar 

  14. T. A. Henzinger and P.-H. Ho. A note on abstract-interpretation strategies for hybrid automata. In P. Antsaklis, A. Nerode, W. Kohn, and S. Sastry, editors, Hybrid Systems II, LNCS 999, pages 252–264. Springer-Verlag, 1995.

    Google Scholar 

  15. T. A. Henzinger, P.-H. Ho, and H. Wong-Toi. HyTech: a model checker for hybrid systems. In O. Grumberg, editor, CAV97: Computer-aided Verification, LNCS 1254, pages 460–463. Springer-Verlag, 1997.

    Google Scholar 

  16. Thomas. A. Henzinger and Orna Kupferman. From quantity to quality. In Oded Maler, editor, Hybrid and Real-Time Systems International Workshop,Hart’97, volume 1201 of LNCS, pages 48–62, Grenoble, France, March 1997. Springer-Verlag.

    Google Scholar 

  17. T. A. Henzinger, P. W. Kopke, A. Puri, and P. Varaiya. What’s decidable about hybrid automata? In the 27th Annual Symposium on Theory of Computing, pages 373–382. ACM Press, 1995.

    Google Scholar 

  18. T. A. Henzinger, O. Kupferman, and S. Qadeer. From pre-historic to post-modern symbolic model checking. In A. J. Hu and M. Y. Vardi, editors, CAV’98: Computeraided Verification, LNCS 1427, pages 195–206. Springer-Verlag, 1998.

    Chapter  Google Scholar 

  19. N. Halbwachs, Y-E. Proy, and P. Romanoff. Verification of real-time systems using linear relation analysis. Formal Methods in System Design, 11(2):157–185, 1997.

    Article  Google Scholar 

  20. Pei-Hsin Ho and Howard Wong-Toi. Automated analysis of an audio control protocol. In P. Wolper, editor, the Seventh Conference on Computer-Aided Verification, pages 381–394, Liege, Belgium, 1995. Springer-Verlag. LNCS 939.

    Google Scholar 

  21. J. Jaffar and M. J. Maher. Constraint logic programming: A survey. The Journal of Logic Programming, 19/20:503–582, May–July 1994.

    Article  MathSciNet  Google Scholar 

  22. K.G. Larsen, P. Pettersson, and W. Yi. Compositional and symbolic model checking of real-time systems. In Proceedings of the 16th Annual Real-time Systems Symposium, pages 76–87. IEEE Computer Society Press, 1995.

    Google Scholar 

  23. S. Mukhopadhyay and A. Podelski. Model checking for timed logic processes. In J. Lloyd, V. Dahl, U. Furbach, M. Kerber, K-K. Lau, C. Palamidessi, L. M. Pereira, Y. Sagiv, and P. J. Stuckey, editors, CL: Computational Logic, LNCS, pages 598–612. Springer, 2000. Available at http://www.mpi-sb.mpg.de/?supratik/.

    Chapter  Google Scholar 

  24. H. Wong-Toi. Symbolic Approximations for Verifying Real-Time Systems. PhD thesis, Stanford University, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mukhopadhyay, S., Podelski, A. (2001). Accurate Widenings and Boundedness Properties of Timed Systems. In: Bjørner, D., Broy, M., Zamulin, A.V. (eds) Perspectives of System Informatics. PSI 2001. Lecture Notes in Computer Science, vol 2244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45575-2_10

Download citation

  • DOI: https://doi.org/10.1007/3-540-45575-2_10

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43075-9

  • Online ISBN: 978-3-540-45575-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics