Advertisement

Towards the Verification of Attributed Graph Transformation Systems

  • Barbara König
  • Vitali Kozioura
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5214)

Abstract

We describe an approach for the verification of attributed graph transformation systems (AGTS). AGTSs are graph transformation systems where graphs are labelled over an algebra. We base our verification procedure on so-called approximated unfoldings combined with counterexample-guided abstraction refinement. Both techniques were originally developed for non-attributed systems. With respect to refinement we focus especially on detecting whether the spurious counterexample is caused by structural over-approximation or by an abstraction of the attributes which is too coarse. The technique is implemented in the verification tool Augur 2 and a leader election protocol has been successfully verified.

Keywords

Graph Transformation Galois Connection Predicate Abstraction Graph Transformation System Spurious Counterexample 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aziz Abdulla, P., Jonsson, B., Kindahl, M., Peled, D.: A general approach to partial order reductions in symbolic verification. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 379–390. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  2. 2.
    Baldan, P., Corradini, A., Esparza, J., Heindel, T., König, B., Kozioura, V.: Verifying red-black trees. In: Proc. of COSMICAH 2005, Proceedings available as report RR-05-04 (Queen Mary, University of London) (2005)Google Scholar
  3. 3.
    Baldan, P., Corradini, A., König, B.: A static analysis technique for graph transformation systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 381–395. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Bauer, J., Wilhelm, R.: Static analysis of dynamic communication systems by partner abstraction. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 249–264. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Cousot, P.: Abstract Interpretation. ACM Computing Surveys (1996)Google Scholar
  6. 6.
    Dotti, F.L., Foss, L., Ribeiro, L., Marchi Santos, O.: Verification of distributed object-based systems. In: Najm, E., Nestmann, U., Stevens, P. (eds.) FMOODS 2003. LNCS, vol. 2884, pp. 261–275. Springer, Heidelberg (2003)Google Scholar
  7. 7.
    Dotti, F.L., König, B., Marchi Santos, O., Ribeiro, L.: A case study: Verifying a mutual exclusion protocol with process creation using graph transformation systems. Technical Report 08/2004, Universität Stuttgart (2004)Google Scholar
  8. 8.
    Ehrig, H., Padberg, J., Ribeiro, L.: Algebraic high-level nets: Petri nets revisited. In: Ehrig, H., Orejas, F. (eds.) Abstract Data Types 1992 and COMPASS 1992. LNCS, vol. 785, pp. 188–206. Springer, Heidelberg (1994)Google Scholar
  9. 9.
    Ehrig, H., Prange, U., Taentzer, G.: Fundamental theory for typed attributed graph transformation. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 161–177. Springer, Heidelberg (2004)Google Scholar
  10. 10.
    Graf, S., Saïdi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)Google Scholar
  11. 11.
    Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from proofs. In: Proc. of POPL 2004, pp. 232–244. ACM Press, New York (2004)CrossRefGoogle Scholar
  12. 12.
    Jensen, K.: Coloured Petri nets: Status and outlook. In: van der Aalst, W.M.P., Best, E. (eds.) ICATPN 2003. LNCS, vol. 2679, pp. 1–2. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Kastenberg, H.: Towards attributed graphs in GROOVE. In: Proceedings of Workshop on Graph Transformation for Verification and Concurrency, volume 05-34 of CTIT Technical Report, pp. 91–98 (2005)Google Scholar
  14. 14.
    König, B., Kozioura, V.: Augur 2—a new version of a tool for the analysis of graph transformation systems. In: Proc. of GT-VMT 2006 (Workshop on Graph Transformation and Visual Modeling Techniques). ENTCS, vol. 211, pp. 201–210. Elsevier, Amsterdam (2008)Google Scholar
  15. 15.
    König, B., Kozioura, V.: Counterexample-guided abstraction refinement for the analysis of graph transformation systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 197–211. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Kozioura, V.: Verification of random graph transformation systems. In: Proc. of GT-VC 2006 (Graph Transformation for Verification and Concurrency. ENTCS, vol. 175.4 (2006)Google Scholar
  17. 17.
    Kozyura, V.: Abstraction and Abstraction Refinement in the Verification of Graph Transformation Systems. PhD thesis, Universität Duisburg-Essen, forthcomingGoogle Scholar
  18. 18.
    Löwe, M., Korff, M., Wagner, A.: An algebraic framework for the transformation of attributed graphs. In: Term graph rewriting: theory and practice, pp. 185–199. John Wiley and Sons Ltd, Chichester (1993)Google Scholar
  19. 19.
    Reisig, W.: Petri Nets: An Introduction. EATCS Monographs on Theoretical Computer ScienceGermany. Springer, Berlin (1985)zbMATHGoogle Scholar
  20. 20.
    Rensink, A., Distefano, D.: Abstract graph transformation. In: Proc. of SVV 2005 (3rd International Workshop on Software Verification and Validation). ENTCS, vol. 157.1, pp. 39–59 (2005)Google Scholar
  21. 21.
    Varró, D.: Towards symbolic analysis of visual modeling languages. In: Workshop on Graph Transformation and Visual Modeling Techniques 2002. ENTCS, vol. 72, Elsevier, Amsterdam (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Barbara König
    • 1
  • Vitali Kozioura
    • 1
  1. 1.Abteilung für Informatik und Angewandte KognitionswissenschaftUniversität Duisburg-EssenGermany

Personalised recommendations