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Solving Coverability Problem for Monotonic Counter Systems by Supercompilation

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Book cover Perspectives of Systems Informatics (PSI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7162))

Abstract

We put the program transformation method known as supercompilation in the context of works on counter systems, well-structured transition systems, Petri nets, etc. Two classic versions of the supercompilation algorithm are formulated for counter systems, using notions and notation adopted from the literature on transition systems.

A procedure to solve the coverability problem for a counter system by iterative application of a supercompiler to the system along with initial and target sets of states, is presented. Its correctness for monotonic counter systems provided the target set is upward-closed and the initial set has a certain form, is proved.

The fact that a supercompiler can solve the coverability problem for a lot of practically interesting counter systems has been discovered by A. Nemytykh and A. Lisitsa when they performed experiments on verification of cache-coherence protocols and other models by means of the Refal supercompiler SCP4, and since then theoretical explanation why this was so successful has been an open problem. Here the solution for the monotonic counter systems is given.

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References

  1. Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.-K.: General decidability theorems for infinite-state systems. In: Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science, New Brunswick, New Jersey, July 27-30, pp. 313–321. IEEE Computer Society (1996)

    Google Scholar 

  2. Bardin, S., Finkel, A., Leroux, J., Petrucci, L.: FAST: acceleration from theory to practice. International Journal on Software Tools for Technology Transfer 10(5), 401–424 (2008)

    Article  Google Scholar 

  3. Dufourd, C., Finkel, A., Schnoebelen, P.: Reset Nets Between Decidability and Undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 103–115. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  4. Finkel, A.: The Minimal Coverability Graph for Petri Nets. In: Rozenberg, G. (ed.) APN 1993. LNCS, vol. 674, pp. 210–243. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  5. Geeraerts, G.: Coverability and Expressiveness Properties of Well-Structured Transition Systems. PhD thesis, Université Libre de Bruxelles, Belgique (May 2007), http://www.ulb.ac.be/di/verif/ggeeraer/thesis.pdf

  6. Geeraerts, G., Raskin, J.-F., Van Begin, L.: Expand, Enlarge and Check: New algorithms for the coverability problem of WSTS. Journal of Computer and System Sciences 72(1), 180–203 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Geeraerts, G., Raskin, J.-F., Van Begin, L.: On the Efficient Computation of the Minimal Coverability Set for Petri Nets. In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds.) ATVA 2007. LNCS, vol. 4762, pp. 98–113. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Glück, R., Leuschel, M.: Abstraction-Based Partial Deduction for Solving Inverse Problems - A Transformational Approach to Software Verification. In: Bjorner, D., Broy, M., Zamulin, A.V. (eds.) PSI 1999. LNCS, vol. 1755, pp. 93–100. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  9. Karp, R.M., Miller, R.E.: Parallel program schemata. J. Comput. Syst. Sci. 3(2), 147–195 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  10. Klimov, And.V.: An approach to supercompilation for object-oriented languages: the Java Supercompiler case study. In: Nemytykh, A.P. (ed.) Proceedings of the First International Workshop on Metacomputation in Russia, Pereslavl-Zalessky, Russia, July 2-5, pp. 43–53. Ailamazyan University of Pereslavl, Pereslavl-Zalessky (2008)

    Google Scholar 

  11. Klimov, And.V.: JVer Project: Verification of Java programs by Java Supercompiler (2008), http://pat.keldysh.ru/jver/

  12. Klimov, And.V.: A Java Supercompiler and Its Application to Verification of Cache-Coherence Protocols. In: Pnueli, A., Virbitskaite, I., Voronkov, A. (eds.) PSI 2009. LNCS, vol. 5947, pp. 185–192. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  13. Klimov, And.V.: Yet another algorithm for solving coverability problem for monotonic counter systems. In: Nepomnyaschy, V., Sokolov, V. (eds.) Second Workshop on Program Semantics, Specification and Verification: Theory and Applications, PSSV 2011, St. Petersburg, Russia, June 12-13, pp. 59–67. Yaroslavl State University (2011)

    Google Scholar 

  14. Klyuchnikov, I.: Supercompiler HOSC 1.1: proof of termination. Preprint 21, Keldysh Institute of Applied Mathematics, Moscow (2010)

    Google Scholar 

  15. Klyuchnikov, I., Romanenko, S.: Multi-result Supercompilation as Branching Growth of the Penultimate Level in Metasystem Transitions. In: Clarke, E., Virbitskaite, I., Voronkov, A. (eds.) PSI 2011. LNCS, vol. 7162, pp. 210–226. Springer, Heidelberg (2012)

    Google Scholar 

  16. Leuschel, M., Lehmann, H.: Coverability of Reset Petri Nets and Other Well-Structured Transition Systems by Partial Deduction. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 101–115. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  17. Leuschel, M., Lehmann, H.: Solving coverability problems of Petri nets by partial deduction. In: Proceedings of the 2nd International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming, Montreal, Canada, September 20-23, pp. 268–279. ACM (2000)

    Google Scholar 

  18. Lisitsa, A.P., Nemytykh, A.P.: Solving coverability problems by supercompilation. Invited talk. In: The Second Workshop on Reachability Problems in Computational Models (RP 2008), Liverpool, UK, September 15-17 (2008)

    Google Scholar 

  19. Lisitsa, A.P., Nemytykh, A.P.: Towards verification via supercompilation. In: COMPSAC (2), pp. 9–10. IEEE Computer Society (2005)

    Google Scholar 

  20. Lisitsa, A.P., Nemytykh, A.P.: Experiments on verification via supercompilation (2007), http://refal.botik.ru/protocols/

  21. Lisitsa, A.P., Nemytykh, A.P.: Verification as a parameterized testing (experiments with the SCP4 supercompiler). Programming and Computer Software 33(1), 14–23 (2007)

    Article  MATH  Google Scholar 

  22. Lisitsa, A.P., Nemytykh, A.P.: Reachability analysis in verification via supercompilation. Int. J. Found. Comput. Sci. 19(4), 953–969 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. Luttge, K.: Zustandsgraphen von Petri-Netzen. Master’s thesis, Humboldt-Universität zu Berlin, Germany (1995)

    Google Scholar 

  24. Nemytykh, A.P.: The Supercompiler SCP4: General Structure. In: Broy, M., Zamulin, A.V. (eds.) PSI 2003. LNCS, vol. 2890, pp. 162–170. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  25. Sørensen, M.H., Glück, R.: An algorithm of generalization in positive supercompilation. In: Lloyd, J.W. (ed.) International Logic Programming Symposium, Portland, Oregon, December 4-7, pp. 465–479. MIT Press (1995)

    Google Scholar 

  26. Turchin, V.F.: The Use of Metasystem Transition in Theorem Proving and Program Optimization. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 645–657. Springer, Heidelberg (1980)

    Chapter  Google Scholar 

  27. Turchin, V.F.: The concept of a supercompiler. Transactions on Programming Languages and Systems 8(3), 292–325 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  28. Turchin, V.F.: The algorithm of generalization in the supercompiler. In: Bjørner, D., Ershov, A.P., Jones, N.D. (eds.) Partial Evaluation and Mixed Computation, pp. 531–549. North-Holland (1988)

    Google Scholar 

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 4 Miusskaya sq., Moscow, 125047, Russia

    Andrei V. Klimov

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  1. Andrei V. Klimov
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Editors and Affiliations

  1. Computer Science Department, Carnegie Mellon University, 5000 Forbes Avenue, 15213-3891, Pittsburgh, PA, USA

    Edmund Clarke

  2. A.P. Ershov Institute of Informatics Systems Siberian Branch of the Russian Academy of Sciences, 6, Acad. Lavrentiev ave, Novosibirsk, 630090, Russia

    Irina Virbitskaite

  3. The University of Manchester, Oxford Road, M13 9PL, Manchester, UK

    Andrei Voronkov

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Klimov, A.V. (2012). Solving Coverability Problem for Monotonic Counter Systems by Supercompilation. In: Clarke, E., Virbitskaite, I., Voronkov, A. (eds) Perspectives of Systems Informatics. PSI 2011. Lecture Notes in Computer Science, vol 7162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29709-0_18

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  • DOI: https://doi.org/10.1007/978-3-642-29709-0_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29708-3

  • Online ISBN: 978-3-642-29709-0

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