Pattern-Based Graph Abstraction

  • Arend Rensink
  • Eduardo Zambon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7562)


We present a new abstraction technique for the exploration of graph transformation systems with infinite state spaces. This technique is based on patterns, simple graphs describing structures of interest that should be preserved by the abstraction. Patterns are collected into pattern graphs, layered graphs that capture the hierarchical composition of smaller patterns into larger ones. Pattern graphs are then abstracted to a finite universe of pattern shapes by collapsing equivalent patterns. This paper shows how the application of production rules can be lifted to pattern shapes, resulting in an over-approximation of the original system behaviour and thus enabling verification on the abstract level.


Simple Graph Graph Transformation Pattern Graph Rule Application Pattern Shape 
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.


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  1. 1.
    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
  2. 2.
    Bauer, J.: Analysis of Communication Topologies by Partner Abstraction. PhD thesis, Universität des Saarlandes (2006)Google Scholar
  3. 3.
    Bauer, J., Boneva, I., Kurban, M., Rensink, A.: A modal-logic based graph abstraction. In: [7]Google 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.
    Becker, B., Beyer, D., Giese, H., Klein, F., Schilling, D.: Symbolic invariant verification for systems with dynamic structural adaptation. In: ICSE. ACM (2006)Google Scholar
  6. 6.
    de Lara, J., Varro, D. (eds.): GraBaTs. ECEASST, vol. 32. EASST (2010)Google Scholar
  7. 7.
    Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds.): ICGT 2008. LNCS, vol. 5214. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  8. 8.
    Ghamarian, A.H., de Mol, M., Rensink, A., Zambon, E., Zimakova, M.: Modelling and analysis using groove. STTT 14(1) (2012)Google Scholar
  9. 9.
    Ghamarian, A.H., Rensink, A., Jalali, A.: Incremental pattern matching in graph-based state space exploration. In: [6]Google Scholar
  10. 10.
    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
  11. 11.
    König, B., Kozioura, V.: Augur 2 - a new version of a tool for the analysis of graph transformation systems. ENTCS 211 (2008)Google Scholar
  12. 12.
    Rensink, A.: The GROOVE Simulator: A Tool for State Space Generation. In: Pfaltz, J.L., Nagl, M., Böhlen, B. (eds.) AGTIVE 2003. LNCS, vol. 3062, pp. 479–485. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Rensink, A.: Canonical Graph Shapes. In: Schmidt, D. (ed.) ESOP 2004. LNCS, vol. 2986, pp. 401–415. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Rensink, A., Distefano, D.: Abstract graph transformation. In: Workshop on Software Verification and Validation (SVV). ENTCS, vol. 157 (2006)Google Scholar
  15. 15.
    Rensink, A., Zambon, E.: Neighbourhood abstraction in groove. In: [6]Google Scholar
  16. 16.
    Rensink, A., Zambon, E.: Pattern-based graph abstraction (extended version). Technical report, University of Twente, Enschede, The Netherlands (2012)Google Scholar
  17. 17.
    Rieger, S., Noll, T.: Abstracting complex data structures by hyperedge replacement. In: [7]Google Scholar
  18. 18.
    Sagiv, S., Reps, T.W., Wilhelm, R.: Parametric shape analysis via 3-valued logic. ToPLaS 24(3) (2002)Google Scholar
  19. 19.
    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
  20. 20.
    Zambon, E., Rensink, A.: Graph subsumption in abstract state space exploration. In: GRAPHITE (Pre-proceedings) (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Arend Rensink
    • 1
  • Eduardo Zambon
    • 1
  1. 1.Formal Methods and Tools Group, Computer Science DepartmentUniversity of TwenteEnschedeThe Netherlands

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