Fast Acceleration of Ultimately Periodic Relations

  • Marius Bozga
  • Radu Iosif
  • Filip Konečný
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6174)

Abstract

Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we describe an efficient algorithm for computing the transitive closures of difference bounds, octagonal and finite monoid affine relations. On the theoretical side, this framework provides a common solution to the acceleration problem, for all these three classes of relations. In practice, according to our experiments, the new method performs up to four orders of magnitude better than the previous ones, making it a promising approach for the verification of integer programs.

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References

  1. 1.
    Annichini, A., Asarin, E., Bouajjani, A.: Symbolic techniques for parametric reasoning about counter and clock systems. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 419–434. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Annichini, A., Bouajjani, A., Sighireanu, M.: Trex: A tool for reachability analysis of complex systems. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 368–372. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Bagnara, R., Hill, P.M., Zaffanella, E.: An improved tight closure algorithm for integer octagonal constraints. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 8–21. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Bardin, S., Leroux, J., Point, G.: Fast extended release. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 63–66. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Boigelot, B.: Symbolic Methods for Exploring Infinite State Spaces, volume PhD Thesis, Vol. 189. Collection des Publications de l’Université de Liège (1999)Google Scholar
  6. 6.
    Bozga, M., Gîrlea, C., Iosif, R.: Iterating octagons. In: TACAS ’09, pp. 337–351. Springer, Heidelberg (2009)Google Scholar
  7. 7.
    Bozga, M., Iosif, R., Konečńy, F.: Fast Acceleration of Ultimately Periodic Relations. Technical Report TR-2010-3, Verimag, Grenoble, France (2010)Google Scholar
  8. 8.
    Bozga, M., Iosif, R., Lakhnech, Y.: Flat parametric counter automata. Fundamenta Informaticae 91, 275–303 (2009)MATHMathSciNetGoogle Scholar
  9. 9.
    Comon, H., Jurski, Y.: Multiple Counters Automata, Safety Analysis and Presburger Arithmetic. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 268–279. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  10. 10.
    Finkel, A., Leroux, J.: How to compose presburger-accelerations: Applications to broadcast protocols. In: Agrawal, M., Seth, A.K. (eds.) FSTTCS 2002. LNCS, vol. 2556, pp. 145–156. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
  12. 12.
    Miné, A.: The octagon abstract domain. Higher-Order and Symbolic Computation 19(1), 31–100 (2006)MATHCrossRefGoogle Scholar
  13. 13.
    De Schutter, B.: On the ultimate behavior of the sequence of consecutive powers of a matrix in the max-plus algebra. Linear Algebra and its Applications 307, 103–117 (2000)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Wolper, P., Boigelot, B.: Verifying systems with infinite but regular state spaces. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 88–97. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marius Bozga
    • 1
  • Radu Iosif
    • 1
  • Filip Konečný
    • 1
    • 2
  1. 1.VERIMAG, CNRSGièresFrance
  2. 2.FIT BUTBrnoCzech Republic

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