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On the Power of Cliques in the Parameterized Verification of Ad Hoc Networks

  • Giorgio Delzanno
  • Arnaud Sangnier
  • Gianluigi Zavattaro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6604)

Abstract

We study decision problems for parameterized verification of protocols for ad hoc networks. The problem we consider is control state reachability for networks of arbitrary size. We restrict our analysis to topologies that approximate the notion of bounded diameter often used in ad hoc networks for optimizing broadcast communication. We show that restricting to graphs with bounded diameter is not sufficient to make control state reachability decidable, but the problem turns out to be decidable when considering an additionally restricted class of graphs that still includes cliques. Although decidable, the problem is already Ackermann-hard over clique graphs.

References

  1. 1.
    Abdulla, P.A., Čerāns, C., Jonsson, B., Tsay, Y.-K.: General decidability theorems for infinite-state systems. In: LICS 1996, pp. 313–321. IEEE Computer Society, Los Alamitos (1996)Google Scholar
  2. 2.
    Abdulla, P.A., Čerāns, C., Jonsson, B., Tsay, Y.-K.: Algorithmic analysis of programs with well quasi-ordered domains. Inf. Comput. 160(1-2), 109–127 (2000)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Delzanno, G., Sangnier, A., Zavattaro, G.: Parameterized Verification of Ad Hoc Networks. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 313–327. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Delzanno, G., Sangnier, A., Zavattaro, G.: On the Power of Cliques in the Parameterized Verification of Ad Hoc Networks. Technical Report DISI-TR-11-01, DISI-University of Genova (2011)Google Scholar
  5. 5.
    Ding, G.: Subgraphs and well quasi ordering. J. of Graph Theory 16(5), 489–502 (1992)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Emerson, E.A., Namjoshi, K.S.: On model checking for non-deterministic infinite-state systems. In: LICS 1998, pp. 70–80. IEEE Computer Society, Los Alamitos (1998)Google Scholar
  7. 7.
    Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: LICS 1999, pp. 352–359. IEEE Computer Society, Los Alamitos (1999)Google Scholar
  8. 8.
    Fehnker, A., van Hoesel, L., Mader, A.: Modelling and verification of the LMAC protocol for wireless sensor networks. In: Davies, J., Gibbons, J. (eds.) IFM 2007. LNCS, vol. 4591, pp. 253–272. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Fernandess, Y., Malkhi, D.: K-clustering in wireless ad hoc networks. In: POMC 2002, pp. 31–37. ACM, New York (2002)Google Scholar
  10. 10.
    Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theoret. Comp. Sci. 256(1-2), 63–92 (2001)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Hoffman, A., Singleton, R.: On Moore graphs with diameter 2 and 3. IBM J. Res. Develop. 4, 497–504 (1960)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Meyer, R.: On boundedness in depth in the pi-calculus. In: Ausiello, G., Karhumäki, J., Mauri, G., Ong, L. (eds.) IFIP TCS 2008. IFIP, vol. 273, pp. 477–489. Springer, Heidelberg (2008)Google Scholar
  13. 13.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  14. 14.
    Minsky, M.: Computation: finite and infinite machines. Prentice-Hall, Englewood Cliffs (1967)zbMATHGoogle Scholar
  15. 15.
    Rackoff, C.: The covering and boundedness problems for vector addition systems. Theoret. Comp. Sci. 6, 223–231 (1978)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Rosa-Velardo, F.: Depth boundedness in multiset rewriting systems with name binding. In: Kučera, A., Potapov, I. (eds.) RP 2010. LNCS, vol. 6227, pp. 161–175. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Saksena, M., Wibling, O., Jonsson, B.: Graph Grammar Modeling and Verification of Ad Hoc Routing Protocols. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 18–32. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Schnoebelen, P.: Revisiting Ackermann-Hardness for Lossy Counter Machines and Reset Petri Nets. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 616–628. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  19. 19.
    Singh, A., Ramakrishnan, C.R., Smolka, S.A.: Query-Based Model Checking of Ad Hoc Network Protocols. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 603–619. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Wies, T., Zufferey, D., Henzinger, T.A.: Forward analysis of depth-bounded processes. In: Ong, L. (ed.) FOSSACS 2010. LNCS, vol. 6014, pp. 94–108. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Giorgio Delzanno
    • 1
  • Arnaud Sangnier
    • 2
  • Gianluigi Zavattaro
    • 3
  1. 1.University of GenovaItaly
  2. 2.LIAFAUniversity Paris 7, CNRSFrance
  3. 3.INRIA Focus TeamUniversity of BolognaItaly

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