[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

A Complete Abstract Interpretation Framework for Coverability Properties of WSTS

  • Conference paper
Verification, Model Checking, and Abstract Interpretation (VMCAI 2006)

Abstract

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.

Supported by the FRFC project “Centre Fédéré en Vérification” funded by the Belgian National Science Foundation (FNRS) under grant nr 2.4530.02.

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

Access this chapter

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
GBP 19.95
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
GBP 35.99
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
GBP 44.99
Price includes VAT (United Kingdom)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–236 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  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. Abdulla, P.A., Jonsson, B.: Verifying programs with unreliable channels. Inf. Comput. 127, 91–101 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Reisig, W.: Petri Nets. An introduction. Springer, Heidelberg (1986)

    Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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. 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. Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2(3), 326–336 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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. 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)

    Article  Google Scholar 

  19. Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theoretical Computer Science 256, 63–92 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  20. Finkel, A.: Reduction and covering of infinite reachability trees. Inf. Comput. 89, 144–179 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  22. Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Computers 35, 677–691 (1986)

    Article  MATH  Google Scholar 

  23. Van Begin, L.: Efficient Verification of Counting Abstractions for Parametric Systems. PhD thesis, Université Libre de Bruxelles (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ganty, P., Raskin, JF., Van Begin, L. (2005). A Complete Abstract Interpretation Framework for Coverability Properties of WSTS . In: Emerson, E.A., Namjoshi, K.S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2006. Lecture Notes in Computer Science, vol 3855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11609773_4

Download citation

  • DOI: https://doi.org/10.1007/11609773_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31139-3

  • Online ISBN: 978-3-540-31622-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics