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A Compared Study of Two Correctness Proofs for the Standardized Algorithm of ABR Conformance

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Abstract

The ABR conformance protocol is a real-time program that controls dataflow rates on ATM networks. A crucial part of this protocol is the dynamical computation of the expected rate of data cells. We present here a modelling of the corresponding program with its environment, using the notion of (parametric) timed automata. A fundamental property of the service provided by the protocol to the user is expressed in this framework and proved by two different methods. The first proof relies on inductive invariants, and was originally verified using theorem-proving assistant COQ. The second proof is based on reachability analysis, and was obtained using model-checker HYTECH. We explain and compare these two proofs in the unified framework of timed automata.

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References

  1. M. Abadi and L. Lamport, “The existence of refinement mappings,” Theoretical Computer Science, Vol. 82, No. 2, pp. 253–284, 1991.

    Google Scholar 

  2. R. Alur, C. Courcoubetis, N. Halbwachs, T.A. Henzinger, P.-H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine, “The algorithmic analysis of hybrid systems,” Theoretical Computer Science, Vol. 138, No. 3, pp. 3–34, 1995.

    Google Scholar 

  3. R. Alur, C. Courcoubetis, T.A. Henzinger, and P.-H. Ho, “Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems,” in Hybrid Systems I, LNCS, Vol. 736, 1993, pp. 209–229.

    Google Scholar 

  4. R. Alur and D. Dill, “Automata for modeling real-time systems,” in Proc. 17th ICALP, LNCS, Vol. 443, 1990, pp. 322–335.

    Google Scholar 

  5. R. Alur, T.A. Henzinger, and M. Vardi, “Parametric real-time reasoning,” in Proc. 25th Annual ACM Symp. on Theory of Computing (STOC), 1993, pp. 592–601.

  6. B. Barras, S. Boutin, C. Cornes, J. Courant, J.C. Filliâtre, E. Giménes, H. Herbelin, G. Huet, P. Manoury, C. Munõz, C. Murthy, C. Parent, C. Paulin-Mohring, A. Saïbi, and B. Werner, The Coq Proof Assistant User's Guide, version 6.1, INRIA Rocquencourt and CNRS-ENS Lyon, 1996.

  7. J. Bengtsson, K.G. Larsen, F. Larsson, P. Pettersson, and W. Yi, “UPPAAL—A Tool Suite for Automatic Verification of Real-Time Systems,” in Hybrid Systems III, LNCS, Vol. 1066, 1996, pp. 232–243.

    Google Scholar 

  8. B. Bérard and L. Fribourg, “Automated verification of a parametric real-time program: the ABR conformance protocol,” in Proc. 11th Int. Conf. Computer Aided Verification (CAV'99), LNCS,Vol. 1633, 1999, pp. 96–107. (Also available at http://www.lsv.ens-cachan.fr/Publis/).

    Google Scholar 

  9. P. Bouyer, C. Dufourd, E. Fleury, and A. Petit, “Are timed automata updatable?” in Proc. 12th Int. Conf. Computer Aided Verification (CAV'00), LNCS, Vol. 1855, 2000.

  10. P. Castéran and D. Rouillard, “Reasoning about parametrized automata,” in Proc. Internat. Conf. on Real Time Systems, 2000, pp. 107–119.

  11. C. Daws, A. Olivero, S. Tripakis, and S. Yovine, “The tool KRONOS,” in Hybrid Systems III, LNCS, Vol. 1066, 1996, pp. 208–219.

    Google Scholar 

  12. L. Fribourg, “A closed-form evaluation for extended timed automata,” Technical Report LSV–98–2, CNRS & Ecole Normale Supérieure de Cachan, 1998 (Available at http://www.lsv.ens-cachan.fr/Publis/).

  13. K. Havelund, A. Skou, K.G. Larsen, and K. Lund, “Formal modelling and analysis of an audio/video protocol: An industrial case study using UPPAAL,” in Proc. 18th IEEE Real-Time Systems Symposium. San Francisco, California, USA, 1997, pp. 2–13.

  14. T. Henzinger, P.-H. Ho, and H. Wong-Toi, “A user guide to HYTECH,” in Proc. TACAS'95, LNCS, Vol. 1019, 1995, pp. 41–71.

    Google Scholar 

  15. ITU-T Recommendation I.371.1, “Traffic control and congestion control in B-ISDN,” 1997.

  16. K.G. Larsen, P. Pettersson, and W. Yi, “Model-checking for real-time systems,” in Proc. 10th International Conference on Fundamentals of Computation Theory, LNCS, Vol. 965, 1995, pp. 62–88.

    Google Scholar 

  17. Z. Manna, “Beyond model checking,” in CAV'94, LNCS, Vol. 818, Springer-Verlag, Berlin, 1994, pp. 220–221.

    Google Scholar 

  18. J.F. Monin, “Proving a real time algorithm for ATM in Coq,” Types for Proofs and Programs, LNCS, Vol. 1512, 1998, pp. 277–293.

    Google Scholar 

  19. J.-F. Monin and F. Klay. “Correctness proof of the standardized algorithm for ABR conformance,” in Formal Methods 99, LNCS, Vol. 1708, Springer Verlag, Berlin, 1999, pp. 662–681.

    Google Scholar 

  20. X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine, “An approach to the description and analysis of hybrid systems,” in Hybrid Systems I, LNCS, Vol. 736, 1993, pp. 149–178.

    Google Scholar 

  21. A. Pnueli and E. Shahar, “A platform for combining deductive with algorithmic verification,” in CAV'96, LNCS, Vol. 1102, Springer-Verlag, Berlin, 1996, pp. 184–195.

    Google Scholar 

  22. C. Rabadan, L'ABR et sa conformité. NT DAC/ARP/034, CNET, 1997.

  23. S. Rajan, N. Shankar, and M.K. Srivas, “An integration of model checking with automated proof checking,” in CAV'95, LNCS, Vol. 939, Springer-Verlag, Berlin, 1995, pp. 84–97.

    Google Scholar 

  24. P.Z. Revesz, “A closed-form evaluation for datalog queries with integer (Gap)-order constraints,” Theoretical Computer Science, Vol. 116, pp. 117–149, 1993.

    Google Scholar 

  25. D. Rouillard, “Formalisation dans CClair de la preuve de conformité de l'algorithme β´” Unpublished Manuscript, February 2000, 15 pages.

  26. M. Rusinowitch, S. Stratulat, and F. Klay, “Mechanical verification of a generic incremental ABR conformance algorithm,” in Proc. 12th Int. Conf. Computer Aided Verification (CAV'00), LNCS, Vol. 1855, 2000.

  27. A.U. Shankar, “An introduction to assertional reasoning for concurrent systems,” ACM Computing Surveys, Vol. 25, No. 3, pp. 225–262, 1993.

    Google Scholar 

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Authors and Affiliations

  1. LSV, CNRS UMR 8643, ENS de Cachan, 61 av. du Prés. Wilson, 94235, Cachan Cedex, France

    Béatrice Bérard & Laurent Fribourg

  2. Technopole Anticipa, France Telecom CNET DTL/MSV, 2 av. Pierre Marzin, 22307, Lannion, France

    Francis Klay & Jean-François Monin

Authors
  1. Béatrice Bérard
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  2. Laurent Fribourg
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  3. Francis Klay
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  4. Jean-François Monin
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Bérard, B., Fribourg, L., Klay, F. et al. A Compared Study of Two Correctness Proofs for the Standardized Algorithm of ABR Conformance. Formal Methods in System Design 22, 59–86 (2003). https://doi.org/10.1023/A:1021704214464

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