Conflict Detection for Graph Transformation with Negative Application Conditions

  • Leen Lambers
  • Hartmut Ehrig
  • Fernando Orejas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4178)


This paper introduces a new theory needed for the purpose of conflict detection for graph transformation with negative application conditions (NACs). Main results are the formulation of a conflict notion for graph transformation with NACs and a conflict characterization derived from it. A critical pair definition is introduced and completeness of the set of all critical pairs is shown. This means that for each conflict, occuring in a graph transformation system with NACs, there exists a critical pair expressing the same conflict in a minimal context. Moreover a necessary and sufficient condition is presented for parallel independence of graph transformation systems with NACs. In order to facilitate the implementation of the critical pair construction for a graph transformation system with NACs a correct construction is formulated. Finally, it is discussed how to continue with the development of conflict detection and analysis techniques in the near future.


Model Transformation Graph Transformation Critical Pair Graph Grammar Direct Transformation 
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.
    Hausmann, J., Heckel, R., Taentzer, G.: Detection of Conflicting Functional Requirements in a Use Case-Driven Approach. In: Proc. of Int. Conference on Software Engineering 2002, Orlando, USA (2002)Google Scholar
  2. 2.
    Mens, T., Taentzer, G., Runge, O.: Detecting Structural Refactoring Conflicts using Critical Pair Analysis. In: Heckel, R., Mens, T. (eds.) Proc. Workshop on Software Evolution through Transformations: Model-based vs. Implementation-level Solutions (SETra 2004), Satellite Event of ICGT 2004), Rome, Italy, ENTCS (2004)Google Scholar
  3. 3.
    Taentzer, G., Ehrig, K., Guerra, E., de Lara, J., Lengyel, L., Levendovsky, T., Prange, U., Varro, D., Varro-Gyapay, S.: Model Transformation by Graph Transformation: A Comparative Study. In: Proc. Workshop Model Transformation in Practice, Montego Bay, Jamaica (2005)Google Scholar
  4. 4.
    Bottoni, P., Schürr, A., Taentzer, G.: Efficient Parsing of Visual Languages based on Critical Pair Analysis and Contextual Layered Graph Transformation. In: Proc. IEEE Symposium on Visual Languages (2000) (Long version available as technical report SI-2000-06, University of Rom)Google Scholar
  5. 5.
    Koch, M., Mancini, L.V., Parisi-Presicce, F.: Graph-based Specification of Acces Control Policies. In: JCSS 71, pp. 1–33 (2005)Google Scholar
  6. 6.
    Huet, G.: Confluent reductions: Abstract properties and applications to term rewriting systems. JACM 27(4), 797–821 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Plump, D.: Hypergraph Rewriting: Critical Pairs and Undecidability of Confluence. In: Sleep, M., Plasmeijer, M., van Eekelen, M.C. (eds.) Term Graph Rewriting, pp. 201–214. Wiley, Chichester, UK (1993)Google Scholar
  8. 8.
    Plump, D.: Confluence of graph transformation revisited. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity. LNCS, vol. 3838, pp. 280–308. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. EATCS Monographs in Theoretical Computer Science. Springer, Heidelberg (2006)Google Scholar
  10. 10.
    Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic approaches to graph transformation I: Basic Concepts and Double Pushout Approach. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation, Foundations, vol. 1, pp. 163–245. World Scientific, Singapore (1997)CrossRefGoogle Scholar
  11. 11.
    Annegret Habel, R.H., Taentzer, G.: Graph grammars with negative application conditions. Fundamenta Informaticae 26, 287–313 (1996)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Lambers, L., Ehrig, H., Orejas, F.: Efficient detection of conflicts in graph-based model transformation. In: Proc. International Workshop on Graph and Model Transformation (GraMoT 2005), Tallinn, Estonia. Electronic Notes in Theoretical Computer Science. Elsevier, Amsterdam (2005)Google Scholar
  13. 13.
    Schultzke, T.: Entwicklung und implementierung eines parsers für visuelle sprachen basierend auf kritischer paaranalyse. Master’s thesis, Technische Universität Berlin (2001)Google Scholar
  14. 14.
    Taentzer, G.: AGG: A Graph Transformation Environment for Modeling and Validation of Software. In: Pfaltz, J.L., Nagl, M., Böhlen, B. (eds.) AGTIVE 2003. LNCS, vol. 3062, pp. 446–453. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Lambers, L., Ehrig, H., Orejas, F.: Efficient conflict detection in graph transformation systems by essential critical pairs. In: Proc. Workshop GTVMT (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Leen Lambers
    • 1
  • Hartmut Ehrig
    • 1
  • Fernando Orejas
    • 2
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTechnische Universität BerlinGermany
  2. 2.Dept. L.S.I.Technical University CataloniaBarcelonaSpain

Personalised recommendations