Skip to main content

Expressiveness bounds for completeness in trace-based network proof systems

  • Parallelism And Concurrency
  • Conference paper
  • First Online:
CAAP '88 (CAAP 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 299))

Included in the following conference series:

  • 139 Accesses

Abstract

Network proof systems based on first-order specifications over channel traces are incomplete unless reasoning over the interleaving of communication events is permitted. Relatively complete trace-based proof systems using temporal logic have been described, but full temporal logic is more powerful than necessary. Using the interleaving approach, we isolate the expressiveness required of a relatively complete trace logic. A hierarchy of temporal logic subsets is then defined; a certain subset is shown to have necessary and sufficient expressive power for relative completeness.

This work was supported in part by the National Science Foundation under grants DCR-8320274 and DCR-8602072.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. Alpern and F.B. Schneider. Defining liveness. Information Processing Letters, 21(4):181–185, October 1985.

    Google Scholar 

  2. J.D. Brock and W.B. Ackerman. Scenarios: a model of non-determinate computation. In Formalization of Programming Concepts, Lecture Notes in Computer Science 107, pages 252–259, Springer-Verlag, Berlin, 1981.

    Google Scholar 

  3. S.D. Brookes. A semantics and proof system for communicating processes. In Logics of Programs, Lecture Notes in Computer Science 164, pages 68–85, Springer-Verlag, Berlin, 1984.

    Google Scholar 

  4. Z.C. Chen and C.A.R. Hoare. Partial correctness of communicating sequential processes. In Proceedings of the IEEE International Conference on Distributed Computing Systems, pages 1–12, Paris, April 1981.

    Google Scholar 

  5. S.A. Cook. Soundness and completeness of an axiom system for program verification. SIAM Journal on Computing, 7(1):70–90, February 1978.

    Google Scholar 

  6. E.C.R. Hehner and C.A.R. Hoare. A more complete model of communicating processes. Theoretical Computer Science, 26:105–120, September 1983.

    Google Scholar 

  7. C.A.R. Hoare. Communicating Sequential Processes. Prentice-Hall, Englewood Cliffs, New Jersey, 1985.

    Google Scholar 

  8. B. Jonsson. A model and proof system for asynchronous networks. In Proceedings of the Fourth ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pages 49–58, August 1985.

    Google Scholar 

  9. J. Misra and K.M. Chandy. Proofs of networks of processes. IEEE Transactions on Software Engineering, 7(7):417–426, July 1981.

    Google Scholar 

  10. Z. Manna and A. Pnueli. Verification of concurrent programs: the temporal framework. In R.S. Boyer and J.S. Moore, editors, The Correctness Problem in Computer Science, pages 215–273, International Lecture Series in Computer Science, Academic Press, London, 1981.

    Google Scholar 

  11. Z. Manna and A. Pnueli. Verification of concurrent programs: a temporal proof system. In Proceedings of the Fourth School on Advanced Programming, pages 163–255, Amsterdam, June 1982.

    Google Scholar 

  12. V. Nguyen, A. Demers, D. Gries, and S. Owicki. A model and temporal proof system for networks of processes. Distributed Computing, 1(1):7–25, January 1986.

    Google Scholar 

  13. V. Nguyen. The incompleteness of Misra and Chandy's proof systems. Information Processing Letters, 21:93–96, August 1985.

    Google Scholar 

  14. N. Rescher and A. Urquhart. Temporal Logic. Library of Exact Philosophy, Springer-Verlag, Vienna, 1971.

    Google Scholar 

  15. J.R. Schoenfield. Mathematical Logic. Addison-Wesley, Reading, Massachusetts, 1967.

    Google Scholar 

  16. J. Widom, D. Gries, and F.B. Schneider. Completeness and incompleteness of trace-based network proof systems. In Proceedings of the Fourteenth ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, pages 27–38, January 1987.

    Google Scholar 

  17. J. Widom. Trace-Based Network Proof Systems: Expressiveness and Completeness. PhD thesis, Cornell University, Ithaca, New York, May 1987.

    Google Scholar 

  18. P. Wolper. Temporal logic can be more expressive. In Proceedings of the 22nd Annual Symposium on Foundations of Computer Science, pages 340–348, October 1981.

    Google Scholar 

  19. J. Zwiers, W.P. de Roever, and P. van Emde Boas. Compositionality and concurrent networks: soundness and completeness of a proofsystem. In Proceedings of the 12th International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science 194, pages 509–519, Springer-Verlag, Berlin, 1985.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

M. Dauchet M. Nivat

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Widom, J., Panangaden, P. (1988). Expressiveness bounds for completeness in trace-based network proof systems. In: Dauchet, M., Nivat, M. (eds) CAAP '88. CAAP 1988. Lecture Notes in Computer Science, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0026105

Download citation

  • DOI: https://doi.org/10.1007/BFb0026105

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19021-9

  • Online ISBN: 978-3-540-38930-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics