Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems

International Symposium of the CEC-Supported Working Group Provably Correct Systems

FTRTFT 1994, ProCoS 1994: Formal Techniques in Real-Time and Fault-Tolerant Systems pp 351–372Cite as

Verification methods for the divergent runs of clock systems

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 863))

Abstract

We present a methodology for proving temporal properties of the divergent runs of reactive systems with real-valued clocks. A run diverges if time advances beyond any bound. Since the divergent runs of a system may satisfy liveness properties that are not satisfied by some convergent runs, the standard proof rules are incomplete if only divergent runs are considered.

First, we develop a sound and complete proof calculus for divergence, which is based on translating clock systems into discrete systems. Then, we show that simpler proofs can be obtained for stronger divergence assumptions, such as unknown ε-divergence, which requires that all delays have a minimum duration of some unknown constant ε. We classify all real-time systems into an infinite hierarchy, according to how well they admit the translation of eventuality properties into equivalent safety properties.

Supported in part by the National Science Foundation under grant CCR-9200794, by the United States Air Force Office of Scientific Research under contract F49620-93-1-0056, and by the Defense Advanced Research Projects Agency under grant NAG2-892.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Alur, H. Attiya, and G. Taubenfeld. Time-adaptive algorithms for synchronization. In Proceedings of the 26th Annual Symposium on Theory of Computing. ACM Press, 1994.

    Google Scholar 

  2. R. Alur, C. Courcoubetis, and T.A. Henzinger. The observational power of clocks. In CONCUR 94: Theories of Concurrency, Lecture Notes in Computer Science. Springer-Verlag, 1994.

    Google Scholar 

  3. R. Alur and D.L. Dill. Automata for modeling real-time systems. In M.S. Paterson, editor, ICALP 90: Automata, Languages, and Programming, Lecture Notes in Computer Science 443, pages 322–335. Springer-Verlag, 1990.

    Google Scholar 

  4. R. Alur and T.A. Henzinger. Logics and models of real time: a survey. In J.W. de Bakker, K. Huizing, W.-P. de Roever, and G. Rozenberg, editors, Real Time: Theory in Practice, Lecture Notes in Computer Science 600, pages 74–106. Springer-Verlag, 1992.

    Google Scholar 

  5. R. Alur and T.A. Henzinger. Real-time system = discrete system + clock variables. In T. Rus, editor, Proceedings of the First AMAST Workshop on Real-time Systems, 1993.

    Google Scholar 

  6. R. Alur and T.A. Henzinger. Finitary fairness. In Proceedings of the Ninth Annual Symposium on Logic in Computer Science. IEEE Computer Society Press, 1994.

    Google Scholar 

  7. M. Abadi and L. Lamport. An old-fashioned recipe for real time. In J.W. de Bakker, K. Huizing, W.-P. de Roever, and G. Rozenberg, editors, Real Time: Theory in Practice, Lecture Notes in Computer Science 600, pages 1–27. Springer-Verlag, 1992.

    Google Scholar 

  8. R. Gawlick, R. Segala, J. SØgaard-Andersen, and N. Lynch. Liveness in timed and untimed systems. Technical Report 587, Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1993.

    Google Scholar 

  9. T.A. Henzinger. Sooner is safer than later. Information Processing Letters, 43:135–141, 1992.

    Google Scholar 

  10. T.A. Henzinger, Z. Manna, and A. Pnueli. Temporal proof methodologies for real-time systems. In Proceedings of the 18th Annual Symposium on Principles of Programming Languages, pages 353–366. ACM Press, 1991.

    Google Scholar 

  11. T.A. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine. Symbolic model checking for real-time systems. In Proceedings of the Seventh Annual Symposium on Logic in Computer Science, pages 394–406. IEEE Computer Society Press, 1992.

    Google Scholar 

  12. N. Lynch and F. Vaandrager. Forward and backward simulations for timing-based systems. In J.W. de Bakker, K. Huizing, W.-P. de Roever, and G. Rozenberg, editors, Real Time: Theory in Practice, Lecture Notes in Computer Science 600, pages 397–446. Springer-Verlag, 1992.

    Google Scholar 

  13. Z. Manna and A. Pnueli. Completing the temporal picture. In G. Ausiello, M. Dezani-Ciancaglini, and S. Ronchi Della Rocca, editors, ICALP 89: Automata, Languages, and Programming, Lecture Notes in Computer Science 372, pages 534–558. Springer-Verlag, 1989.

    Google Scholar 

  14. Z. Manna and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer-Verlag, 1992.

    Google Scholar 

  15. Z. Manna and A. Pnueli. Models for reactivity. Acta Informatica, 30:609–678, 1993.

    Google Scholar 

  16. F.B. Schneider. On Concurrent Programming. To Appear, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, Cornell University, 14853, Ithaca, NY

    Thomas A. Henzinger & Peter W. Kopke

Authors
  1. Thomas A. Henzinger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter W. Kopke
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hans Langmaack Willem-Paul de Roever Jan Vytopil

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Henzinger, T.A., Kopke, P.W. (1994). Verification methods for the divergent runs of clock systems. In: Langmaack, H., de Roever, WP., Vytopil, J. (eds) Formal Techniques in Real-Time and Fault-Tolerant Systems. FTRTFT ProCoS 1994 1994. Lecture Notes in Computer Science, vol 863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58468-4_173

Download citation

  • DOI: https://doi.org/10.1007/3-540-58468-4_173

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58468-1

  • Online ISBN: 978-3-540-48984-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation