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On Stubborn Sets in the Verification of Linear Time Temporal Properties

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Application and Theory of Petri Nets 1998 (ICATPN 1998)

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Abstract

The stubborn set method is one of the methods that try to relieve the state space explosion problem that occurs in state space generation. This paper is concentrated on the verification of nexttime-less LTL (linear time temporal logic) formulas with the aid of the stubborn set method. The contribution of the paper is a theorem that gives us a way to utilize the structure of the formula when the stubborn set method is used and there is no fairness assumption. Connections to already known results are drawn by modifying the theorem to concern verification under fairness assumptions.

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References

  1. Bause, F.: Analysis of Petri Nets with a Dynamic Priority Method. Azéma, P., and Balbo, G. (Eds.), Proceedings of PN’ 97, Toulouse. LNCS 1248, Springer-Verlag 1997, pp. 215–234.

    Google Scholar 

  2. Courcoubetis, C. (Ed.): Proceedings of CAV’ 93, Elounda, Greece. LNCS 697, Springer-Verlag 1993, 504 p.

    Google Scholar 

  3. Dembiński, P., and Średniawa, M. (Eds.): Proceedings of PSTV’ 95, Warsaw. Chapman & Hall 1996, 453 p.

    Google Scholar 

  4. Emerson, E.A.: Temporal and Modal Logic. van Leeuwen, J. (Ed.), Handbook of Theoretical Computer Science, Vol. B. Elsevier 1990, pp. 995–1072.

    Google Scholar 

  5. Francez, N.: Fairness. Springer-Verlag 1986, 295 p.

    Google Scholar 

  6. Gerth, R., Kuiper, R., Peled, D., and Penczek, W.: A Partial Order Approach to Branching Time Logic Model Checking. Proceedings of the 3rd Israel Symposium on Theory of Computing and Systems, Tel Aviv 1995. IEEE Computer Society Press, Los Alamitos CA 1995, pp. 130–140.

    Chapter  Google Scholar 

  7. Gerth, R., Peled, D., Vardi, M.Y., and Wolper, P.: Simple On-the-Fly Automatic Verification of Linear Temporal Logic. In Średniawa, M. (Eds.): Proceedings of PSTV’ 95, Warsaw. Chapman & Hall 1996 [3], pp. 3–18.

    Google Scholar 

  8. Godefroid, P.: Partial-Order Methods for the Verification of Concurrent Systems — An Approach to the State-Explosion Problem. LNCS 1032, Springer-Verlag 1996, 143 p.

    Google Scholar 

  9. Godefroid, P., and Pirottin, D.: Refining Dependencies Improves Partial-Order Verification Methods. In [2], pp. 438–449.

    Google Scholar 

  10. Janicki, R., and Koutny, M.: Using Optimal Simulations to Reduce Reachability Graphs. Clarke, E.M., and Kurshan, R.P. (Eds.), Proceedings of CAV’ 90, New Brunswick NJ. LNCS 531, Springer-Verlag 1991, pp. 166–175.

    Google Scholar 

  11. Kaivola, R.: Equivalence, Preorders and Compositional Verification for Linear Time Temporal Logic and Concurrent Systems. Doctoral thesis, University of Helsinki, Department of Computer Science, Report A-1996-1, 1996, 185 p.

    Google Scholar 

  12. Katz, S., and Peled, D.: Verification of Distributed Programs Using Representative Interleaving Sequences. Distributed Computing 6 (1992) 2, pp. 107–120.

    Article  MATH  MathSciNet  Google Scholar 

  13. Kokkarinen, I., Peled, D., and Valmari, A.: Relaxed Visibility Enhances Partial Order Reduction. Grumberg, O. (Ed.), Proceedings of CAV’ 97, Haifa. LNCS 1254, Springer-Verlag 1997, pp. 328–339.

    Google Scholar 

  14. Koutny, M., and Pietkiewicz-Koutny, M.: On the Sleep Sets Method for Partial Order Verification of Concurrent Systems. University of Newcastle upon Tyne, Department of Computing Science, Technical Report 495, Newcastle upon Tyne 1994.

    Google Scholar 

  15. Overman, W.T.: Verification of Concurrent Systems: Function and Timing. PhD thesis, University of California at Los Angeles 1981, 174 p.

    Google Scholar 

  16. Peled, D.: All from One, One for All: on Model Checking Using Representatives. In [2], pp. 409–423.

    Google Scholar 

  17. Peled, D.: Combining Partial Order Reductions with On-the-Fly Model-Checking. Formal Methods in System Design 8 (1996) 1, pp. 39–64.

    Article  Google Scholar 

  18. Peled, D., and Penczek, W.: Using Asynchronous Büchi Automata for Efficient Automatic Verification of Concurrent Systems. In Średniawa, M. (Eds.): Proceedings of PSTV’ 95, Warsaw. Chapman & Hall 1996 [3], pp. 115–130.

    Google Scholar 

  19. Ramakrishna, Y.S., and Smolka, S.A.: Partial-Order Reduction in the Weak Modal Mu-Calculus. Mazurkiewicz, A., and Winkowski, J. (Eds.), Proceedings of CONCUR’ 97, Warsaw. LNCS 1243, Springer-Verlag 1997, pp. 5–24.

    Google Scholar 

  20. Rauhamaa, M.: A Comparative Study of Methods for Efficient Reachability Analysis. Helsinki University of Technology, Digital Systems Laboratory Report A 14, 1990, 61 p.

    Google Scholar 

  21. Reisig, W.: Petri Nets: An Introduction. EATCS Monographs on Theoretical Computer Science 4, Springer-Verlag 1985, 161 p.

    Google Scholar 

  22. Sloan, R.H., and Buy, U.: Stubborn Sets for Real-Time Petri Nets. Formal Methods in System Design 11 (1997) 1, pp. 23–40.

    Article  Google Scholar 

  23. Valmari, A.: A Stubborn Attack on State Explosion. Formal Methods in System Design 1 (1992) 4, pp. 297–322.

    Article  MATH  Google Scholar 

  24. Valmari, A.: Stubborn Sets of Coloured Petri Nets. Proceedings of PN’ 91, Gjern, Denmark, pp. 102–121.

    Google Scholar 

  25. Valmari, A.: Alleviating State Explosion during Verification of Behavioural Equivalence. University of Helsinki, Department of Computer Science, Report A-1992-4, 1992, 57 p.

    Google Scholar 

  26. Valmari, A.: On-the-Fly Verification with Stubborn Sets. In [2], pp. 397–408.

    Google Scholar 

  27. Varpaaniemi, K.: On Combining the Stubborn Set Method with the Sleep Set Method. Valette, R. (Ed.), Proceedings of PN’ 94, Zaragoza. LNCS 815, Springer-Verlag 1994, pp. 548–567.

    Google Scholar 

  28. Vernadat, F., Azéma, P., and Michel, F.: Covering Step Graph. Billington, J., and Reisig, W. (Eds.): Proceedings of PN’ 96, Osaka. LNCS 1091, Springer-Verlag 1996, pp. 516–535.

    Google Scholar 

  29. Yoneda, T., Shibayama, A., Schlingloff, B.-H., and Clarke, E.M.: Efficient Verification of Parallel Real-Time Systems. In [2], pp. 321–332.

    Google Scholar 

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Varpaaniemi, K. (1998). On Stubborn Sets in the Verification of Linear Time Temporal Properties. In: Desel, J., Silva, M. (eds) Application and Theory of Petri Nets 1998. ICATPN 1998. Lecture Notes in Computer Science, vol 1420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69108-1_8

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  • DOI: https://doi.org/10.1007/3-540-69108-1_8

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  • Online ISBN: 978-3-540-69108-2

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