Bounded Verification of Past LTL

  • Alessandro Cimatti
  • Marco Roveri
  • Daniel Sheridan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3312)


Temporal logics with past operators are gaining increasing importance in several areas of formal verification for their ability to concisely express useful properties. In this paper we propose a new approach to bounded verification of PLTL, the linear time temporal logic extended with past temporal operators. Our approach is based on the transformation of PLTL into Separated Normal Form, which in turn is amenable for reduction to propositional satisfiability. An experimental evaluation shows that our approach induces encodings which are significantly smaller and more easily solved than previous approaches, in the cases of both model checking and satisfiability problems.


Model Check Temporal Logic Past Operator Linear Temporal Logic Propositional Variable 
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  1. 1.
    Accellera. Accelera Property Specification Language: Reference Manual – Version 1.0Google Scholar
  2. 2.
    Bacchus, F., Kabanza, F.: Control strategies in planning. In: Proceedings of the AAAI Spring Symposium Series on Extending Theories of Action: Formal Theory and Practical Applications, Stanford University, CA, USA, March 1995, pp. 5–10. AAAI Press, Menlo Park (1995)Google Scholar
  3. 3.
    Benedetti, M., Cimatti, A.: Bounded model checking for past LTL. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 18–33. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Biere, A., Cimatti, A., Clarke, E.M., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Castro, J., Kolp, M., Mylopoulos, J.: A requirements-driven development methodology. In: Proceedings of the 13th International Conference on Advanced Information Systems Engineering (2001)Google Scholar
  6. 6.
    Cimatti, A., Clarke, E.M., Giunchiglia, F., Roveri, M.: NuSMV: a new Symbolic Model Verifier. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 495–499. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  7. 7.
    Fisher, M.: A resolution method for temporal logic. In: Proceedings of the Twelfth International Joint Conference on Artificial Intelligence (IJCAI), August 1991, Morgan Kaufmann, San Francisco (1991)Google Scholar
  8. 8.
    Fisher, M., Noël, P.: Transformation and synthesis in MetateM Part I: Propositional MetateM. Technical Report UMCS-92-2-1, Department of Computer Science, University of Manchester, Manchester M13 9PL, England (February 1992)Google Scholar
  9. 9.
    Frisch, A., Sheridan, D., Walsh, T.: A fixpoint based encoding for bounded model checking. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 238–254. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Fuxman, A., Liu, L., Pistore, M., Roveri, M., Mylopoulos, J.: Specifying and analyzing early requirements in Tropos: Some experimental results. In: Proceedings of the 11th IEEE International Requirements Engineering Conference, California, USA, September 2003, ACM-Press, Monterey Bay (2003)Google Scholar
  11. 11.
    Gabbay, D.: The declarative past and imperative future. In: Banieqbal, B., Pnueli, A., Barringer, H. (eds.) Temporal Logic in Specification. LNCS, vol. 398, Springer-Verlag, Heidelberg (1989)Google Scholar
  12. 12.
    Gnesi, S., Latella, D., Lenzini, G.: Formal verification of cryptographic protocols using history dependent automata. In: Proceedings of the of the 4th Workshop on Sistemi Distribuiti: Algoritmi, Architetture e Linguaggi (1999)Google Scholar
  13. 13.
    Kupferman, O., Piterman, N., Vardi, M.: Extended temporal logic revisited. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 519–534. Springer Verlag, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Laroussinie, F., Markey, N.: Ph. Schnoebelen. Temporal logic with forgettable past. In: Proceedings of the 17th IEEE Symp. Logic in Computer Science (LICS 2002), Denmark,, July 2002, pp. 383–392. IEEE Comp. Soc. Press, Copenhagen (2002)CrossRefGoogle Scholar
  15. 15.
    Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: 39th Design Automation Conference, Las Vegas (June 2001)Google Scholar
  16. 16.
    Sheridan, D.: The optimality of a fast CNF conversion and its use with SAT. Technical Report APES-82-2002, APES Research Group (March 2004), Available from
  17. 17.
    van Lamsweerde, A.: Goal-oriented requirements engineering: A guided tour. In: Proceedings of the 5th IEEE International Symposium on Requirements Engineering, pp. 249–263 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Alessandro Cimatti
    • 1
  • Marco Roveri
    • 1
  • Daniel Sheridan
    • 2
  1. 1.Istituto per la Ricerca Scientifica e Tecnologica (IRST)Povo, TrentoItaly
  2. 2.School of InformaticsThe University of EdinburghEdinburghUK

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