Skip to main content
SpringerLink
Log in

Reachability results for timed automata with unbounded data structures

  • Original Article
  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract

Systems of Data Management Timed Automata (SDMTAs) are networks of communicating timed automata with structures to store messages and functions to manipulate them. We prove the decidability of the reachability problem for a subclass of SDMTAs which assumes an unbounded knowledge, and we analyze the expressiveness of the model and the considered subclass. In particular, while SDMTAs can simulate a Turing machine, and hence the reachability problem is in general undecidable, the subclass for which reachability is decidable, when endowed with a concept of recognized language, accepts languages that are not regular. As an application, we model and analyze a variation of the Yahalom protocol.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abadi, M., Gordon, A.D.: A calculus for cryptographic protocols: The Spi calculus. In: 4th ACM Conference on Computer and Communications Security, pp. 36–47. ACM Press (1997)

  2. Abdullah, P.A., Jonsson, B.: Verifying networks of timed processes. In: Proceedings of TACAS’ 98, of LNCS, vol. 1384, pp. 298–312. Springer (1998)

  3. Alur R., Dill D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Behrmann G., David A., Larsen K.G.: A tutorial on uppaal. Springer LNCS 3185, 200–236 (2004)

    Google Scholar 

  5. Berthomieu B., Diaz M.: Modeling and verification of time dependent systems using time petri nets. IEEE Trans. Softw. Eng. 17(3), 259–273 (1991)

    Article  MathSciNet  Google Scholar 

  6. Bouajjani, A., Echahed, R., Robbana, R.: On the automatic verification of systems with continuous variables and unbounded discrete data structures. In: Proceedings Hybrid System II, Springer LNCS, vol. 999, pp. 64–85 (1995)

  7. Burrows, M., Abadi, M., Needham, R.: A logic for authentication. Technical Report 39, Digital Systems Research Center, Feb (1989)

  8. Corin, R., Etalle, S., Hartel, P.H., Mader, A.: Timed analysis of security protocols. Journal of Computer Security. A preliminary report appeared as CTIT Technichal Report TR–CTIT–05–14, University of Twente, The Netherlands (2005) (to appear)

  9. Cremers, C.J.F., Mauw, S., de Vink, E.P.: Defining authentication in a trace model. In: 1st International Workshop on Formal Aspects in Security and Trust (Fast 2003), pp. 131–145, Pisa, IITT-CNR technical report (2003)

  10. Dang Z.: Pushdown time automata: a binary reachability characterization and safety verification. Theor. Comp. Sci. 302, 93–121 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dolev D., Yao A.C.-C.: On the security of public key protocols. IEEE Trans. Inf. Theory 29(2), 198–207 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  12. Focardi, R., Gorrieri, R., Martinelli, F.: Non interference for the analysis of cryptographic protocols. In: International Conference on Automata, Languages and Programming (ICALP’00) of LNCS, vol. 1853, pp. 354–372. Springer (2000)

  13. Hoenicke J., Olderog E.R.: CSP-OZ-DC: a combination of specification techniques for processes, data and time. Nord. J. Comput. 9(4), 301–334 (2002)

    MATH  MathSciNet  Google Scholar 

  14. Ibarra O.H., Su J.: Augmenting the discrete timed automaton with other data structures. Theor. Comput. Sci. 289, 191–204 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kosaraju, S.R.: Decidability of reachability in vector addition systems. In: 14th Annual ACM Symposium on Theory of Computing, pp. 267–281. ACM Press (1982)

  16. Krcal, P., Yi, W.: Communicating Timed Automata: The More Synchronous, the More Difficult to Verify. CAV’06 of LNCS, vol. 4144, pp. 249–262, Springer (2006)

  17. Lanotte, R.: Expressive power of hybrid systems with real variables, integer variables and arrays. J of Automata, Languages and Combinatorics, (accepted for publication)

  18. Lanotte, R., Maggiolo-Schettini, A., Troina, A.: Timed automata with data structures for distributed systems design and analysis. In: 3nd International Conference on Software Engineering and Formal Methods (SEFM’05), pp. 44–53. IEEE Computer Society Press (2005)

  19. Lowe, G.: A hierarchy of authentication specifications. In: 10th International Computer Security Foundations Workshop (CSFW’97), pp. 31–44. IEEE Computer Society Press (1997)

  20. Napoli M., Parente M., Peron A.: Specification and verification of protocols with time constraints. Electronic Notes Theor. Comput. Sci. 99, 205–227 (2004)

    Article  Google Scholar 

  21. Paulson L.C.: Relations between secrets: two formal analyses of the Yahalom protocol. J. Comput. Secur. 9(3), 197–216 (2001)

    MathSciNet  Google Scholar 

  22. The Object-Z specification language. Kluwer Academic Publishers, Norwell (1999)

  23. Valero Ruiz, V., Cuartero Gomez, F., de Frutos-Escrig, D.: On non-decidability of reachability for timed-arc Petri nets. In: Proceedings 8th International Work. Petri Nets and Performance Models (PNPM’03) IEEE Computer Society Press, pp. 188–196 (1999)

  24. Wang J.: Timed Petri Nets: Theory and Application. Kluwer Academic Publishers, Dordrecht (1998)

    MATH  Google Scholar 

  25. Yovine S.: Kronos: a verification tool for real-time systems. Int. J. Softw. Tools Technol. Transf. 1, 123–133 (1997)

    Article  MATH  Google Scholar 

  26. Zhou C., Hoare C.A.R., Ravn A.P.: A calculus of durations. Inf. Process. Lett. 40(5), 269–276 (1991)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Comunicazione, Università dell’Insubria, Via Carloni 78, 22100, Como, Italy

    Ruggero Lanotte

  2. Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy

    Andrea Maggiolo-Schettini

  3. Dipartimento di Informatica, Università di Torino, Corso Svizzera 185, 10149, Torino, Italy

    Angelo Troina

Authors
  1. Ruggero Lanotte
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Maggiolo-Schettini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Angelo Troina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ruggero Lanotte.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lanotte, R., Maggiolo-Schettini, A. & Troina, A. Reachability results for timed automata with unbounded data structures. Acta Informatica 47, 279–311 (2010). https://doi.org/10.1007/s00236-010-0121-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00236-010-0121-8

Keywords

Search

Navigation