A Complete Abstract Interpretation Framework for Coverability Properties of WSTS

  • Pierre Ganty
  • Jean-François Raskin
  • Laurent Van Begin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3855)


We present an abstract interpretation based approach to solve the coverability problem of well-structured transition systems. Our approach distinguishes from other attempts in that (1) we solve this problem for the whole class of well-structured transition systems using a forward algorithm. So, our algorithm has to deal with possibly infinite downward closed sets. (2) Whereas other approaches have a non generic representation for downward closed sets of states, which turns out to be hard to devise in practice, we introduce a generic representation requiring no additional effort of implementation.


Coverability Problem Abstract Interpretation Reachable State Hybrid Automaton Abstract Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–236 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Henzinger, T.A.: The theory of hybrid automata. In: Proceedings of LICS, pp. 278–292. IEEE Computer Society Press, Los Alamitos (1996)Google Scholar
  3. 3.
    Abdulla, P.A., Jonsson, B.: Verifying programs with unreliable channels. Inf. Comput. 127, 91–101 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Abdulla, P., Annichini, A., Bouajjani, A.: Symbolic verification of lossy channel systems: Application to the bounded retransmission protocol. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 208–222. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Delzanno, G., Raskin, J.F., Van Begin, L.: Towards the automated verification of multithreaded java programs. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 173–187. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Bardin, S., Finkel, A., Leroux, J., Petrucci, L.: FAST: Fast acceleration of symbolic transition systems. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 118–121. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: Proceedings of LICS, pp. 352–359. IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
  8. 8.
    Reisig, W.: Petri Nets. An introduction. Springer, Heidelberg (1986)Google Scholar
  9. 9.
    Ciardo, G.: Petri nets with marking-dependent arc multiplicity: properties and analysis. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol. 815, pp. 179–198. Springer, Heidelberg (1994)Google Scholar
  10. 10.
    Dufourd, C., Finkel, A., Schnoebelen, P.: Reset nets between decidability and undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 103–115. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. 11.
    Raskin, J.F., Van Begin, L.: Petri nets with non-blocking arcs are difficult to analyse. In: Proceedings of INFINITY. ENTCS, vol. 96. Elsevier, Amsterdam (2003)Google Scholar
  12. 12.
    Emerson, E.A., Namjoshi, K.S.: On model checking for non-deterministic infinite-state systems. In: Proc. of LICS, pp. 70–80. IEEE Computer Society Press, Los Alamitos (1998)Google Scholar
  13. 13.
    Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2(3), 326–336 (1952)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Geeraerts, G., Raskin, J.F., Van Begin, L.: Expand, Enlarge and Check: new algorithms for the coverability problem of WSTS. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 287–298. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Abdulla, P., Deneux, J., Mahata, P., Nylen, A.: Forward reachability analysis of timed petri nets. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, pp. 343–362. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Ganty, P., Raskin, J.F., Van Begin, L.: A complete abstract interpretation framework for coverability properties of WSTS. Technical Report 2005.57, Centre Fédéré en Vérification, CFV (2005)Google Scholar
  17. 17.
    Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.K.: General decidability theorems for infinite-state systems. In: Proceedings of LICS, pp. 313–321. IEEE Computer Society Press, Los Alamitos (1996)Google Scholar
  18. 18.
    Delzanno, G., Raskin, J.F., Begin, L.V.: Covering sharing trees: a compact data structure for parameterized verification. Software Tools for Technology Transfer (STTT) 5, 268–297 (2004)CrossRefGoogle Scholar
  19. 19.
    Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theoretical Computer Science 256, 63–92 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Finkel, A.: Reduction and covering of infinite reachability trees. Inf. Comput. 89, 144–179 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Esparza, J., Ganty, P., Schwoon, S.: Locality-based abstractions. In: Hankin, C., Siveroni, I. (eds.) SAS 2005. LNCS, vol. 3672, pp. 118–134. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  22. 22.
    Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Computers 35, 677–691 (1986)zbMATHCrossRefGoogle Scholar
  23. 23.
    Van Begin, L.: Efficient Verification of Counting Abstractions for Parametric Systems. PhD thesis, Université Libre de Bruxelles (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Pierre Ganty
    • 1
  • Jean-François Raskin
    • 1
  • Laurent Van Begin
    • 2
  1. 1.Département d’InformatiqueUniversité Libre de Bruxelles 
  2. 2.LIAFA, Université Paris 7 

Personalised recommendations