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Theorem Proving for Verification

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Modeling and Verification of Parallel Processes (MOVEP 2000)

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Abstract

The challenges in using theorem proving for verification of parallel systems are to achieve adequate automation, and to allow human guidance to be expressed in terms of the system under examination rather than the mechanisms of the prover. This paper provides an overview of techniques that address these challenges.

This research was supported by DARPA through USAF Rome Laboratory Contract F30602-96-C-0204 and USAF Electronic Systems Center Contract F19628-96-C-0006.

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References

  1. Parosh Aziz Abdulla, Aurore Annichini, Saddek Bensalem, Ahmed Bouajjani, Peter Habermehl, and Yassine Lakhnech. Verification of infinite-state systems by combining abstraction and reachability analysis. In Halbwachs and Peled [13], pages 146–159.

    Google Scholar 

  2. Kai Baukus, Saddek Bensalem, Yassine Lakhnech, and Karsten Stahl. Abstracting WS1S systems to verify parameterized networks. In Susanne Graf and Michael Schwartzbach, editors, Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2000), pages 188–203, Berlin, Germany, March 2000.

    Google Scholar 

  3. Saddek Bensalem, Vijay Ganesh, Yassine Lakhnech, Cesar Muñoz, Sam Owre, Harald Rueß, John Rushby, Vlad Rusu, Hassen Saïdi, N. Shankar, Eli Singerman, and Ashish Tiwari. An overview of SAL. In C. Michael Holloway, editor, LFM 2000: Fifth NASA Langley Formal Methods Workshop, NASA Langley Research Center, Hampton, VA, June 2000. To appear.

    Google Scholar 

  4. Saddek Bensalem and Yassine Lakhnech. Automatic generation of invariants. Formal Methods in Systems Design, 15(1):75–92, July 1999.

    Article  Google Scholar 

  5. Saddek Bensalem, Yassine Lakhnech, and Sam Owre. Computing abstractions of infinite state systems compositionally and automatically. In Hu and Vardi [15], pages 319–331.

    Google Scholar 

  6. Saddek Bensalem, Yassine Lakhnech, and Sam Owre. InVeSt: A tool for the verification of invariants. In Hu and Vardi [15], pages 505–510.

    Google Scholar 

  7. Nikolaj Bjørner, I. Anca Browne, and Zohar Manna. Automatic generation of invariants and intermediate assertions. Theoretical Computer Science, 173(1):49–87, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  8. David Cyrluk, Patrick Lincoln, and N. Shankar. On Shostak’s decision procedure for combinations of theories. In M. A. McRobbie and J. K. Slaney, editors, Automated Deduction-CADE-13, volume 1104 of Springer-Verlag Lecture Notes in Artificial Intelligence, pages 463–477, New Brunswick, NJ, July/August 1996.

    Google Scholar 

  9. Satyaki Das, David L. Dill, and Seungjoon Park. Experience with predicate abstraction. In Halbwachs and Peled [13], pages 160–171.

    Google Scholar 

  10. M. Gordon, R. Milner, and C. Wadsworth. Edinburgh LCF: A Mechanized Logic of Computation, volume 78 of Lecture Notes in Computer Science. Springer-Verlag, 1979.

    Google Scholar 

  11. M. J. C. Gordon and T. F. Melham, editors. Introduction to HOL: A Theorem Proving Environment for Higher-Order Logic. Cambridge University Press, Cambridge, UK, 1993.

    MATH  Google Scholar 

  12. Jan Friso Groote and Joost P. Warners. The propositional formula checker Heer-Hugo. Journal of Automated Reasoning, 24(1-2):101–125, February 2000.

    Article  MATH  MathSciNet  Google Scholar 

  13. Nicolas Halbwachs and Doron Peled, editors. Computer-Aided Verification, CAV’ 99, volume 1633 of Springer-Verlag Lecture Notes in Computer Science, Trento, Italy, July 1999.

    Google Scholar 

  14. Klaus Havelund and N. Shankar. Experiments in theorem proving and model checking for protocol verification. In Formal Methods Europe FME’ 96, Volume 1051 of Springer-Verlag Lecture Notes in Computer Science, pages 662–681, Oxford, UK, March 1996.

    Google Scholar 

  15. Alan J. Hu and Moshe Y. Vardi, editors. Computer-Aided Verification, CAV’ 98, volume 1427 of Springer-Verlag Lecture Notes in Computer Science, Vancouver, Canada, June 1998.

    Google Scholar 

  16. Matt Kaufmann, Panagiotis Manolios, and J Strother Moore. Computer-Aided Reasoning: An Approach, volume 3 of Advances in Formal Methods. Kluwer, 2000.

    Google Scholar 

  17. Leslie Lamport. A new solution of Dijkstra’s concurrent programming problem. Communications of the ACM, 17(8):453–455, August 1974.

    Article  MATH  MathSciNet  Google Scholar 

  18. C. Loiseaux, S. Graf, J. Sifakis, A. Bouajjani, and S. Bensalem. Property preserving abstractions for the verification of concurrent systems. Formal Methods in System Design, 6:11–44, 1995.

    Article  MATH  Google Scholar 

  19. G. Nelson and D. C. Oppen. Simplification by cooperating decision procedures. ACM Transactions on Programming Languages and Systems, 1(2):245–257, 1979.

    Article  MATH  Google Scholar 

  20. Sam Owre, John Rushby, Natarajan Shankar, and Friedrich von Henke. Formal verification for fault-tolerant architectures: Prolegomena to the design of PVS. IEEE Transactions on Software Engineering, 21(2):107–125, February 1995.

    Article  Google Scholar 

  21. S. Rajan, N. Shankar, and M.K. Srivas. An integration of model-checking with automated proof checking. In Pierre Wolper, editor, Computer-Aided Verification, CAV’ 95, volume 939 of Springer-Verlag Lecture Notes in Computer Science, pages 84–97, Liege, Belgium, June 1995.

    Google Scholar 

  22. John Rushby, Sam Owre, and N. Shankar. Subtypes for specifications: Predicate subtyping in PVS. IEEE Transactions on Software Engineering, 24(9):709–720, September 1998.

    Article  Google Scholar 

  23. Hassen Saïdi and Susanne Graf. Construction of abstract state graphs with PVS. In Orna Grumberg, editor, Computer-Aided Verification, CAV’ 97, volume 1254 of Springer-Verlag Lecture Notes in Computer Science, pages 72–83, Haifa, Israel, June 1997.

    Google Scholar 

  24. Hassen Saïdi and N. Shankar. Abstract and model check while you prove. In Halbwachs and Peled [13], pages 443–454.

    Google Scholar 

  25. Robert E. Shostak. On the SUP-INF method for proving Presburger formulas. Journal of the ACM, 24(4):529–543, October 1977.

    Article  MATH  MathSciNet  Google Scholar 

  26. Robert E. Shostak. An algorithm for reasoning about equality. Communications of the ACM, 21(7):583–585, July 1978.

    Article  MATH  MathSciNet  Google Scholar 

  27. Robert E. Shostak. Deciding linear inequalities by computing loop residues. Journal of the ACM, 28(4):769–779, October 1981.

    Article  MATH  MathSciNet  Google Scholar 

  28. Robert E. Shostak. Deciding combinations of theories. Journal of the ACM, 31(1):1–12, January 1984.

    Article  MATH  MathSciNet  Google Scholar 

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Rushby, J. (2001). Theorem Proving for Verification. In: Cassez, F., Jard, C., Rozoy, B., Ryan, M.D. (eds) Modeling and Verification of Parallel Processes. MOVEP 2000. Lecture Notes in Computer Science, vol 2067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45510-8_2

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  • DOI: https://doi.org/10.1007/3-540-45510-8_2

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