Matrix Approach to Graph Transformation: Matching and Sequences

  • Pedro Pablo Pérez Velasco
  • Juan de Lara
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4178)


In this work we present our approach to (simple di-)graph transformation based on an algebra of boolean matrices. Rules are represented as boolean matrices for nodes and edges and derivations can be efficiently characterized with boolean operations only. Our objective is to analyze properties inherent to rules themselves (without considering an initial graph), so this information can be calculated at specification time. We present basic results concerning well-formedness of rules and derivations (compatibility), as well as concatenation of rules, the conditions under which they are applicable (coherence) and permutations. We introduce the match, which permits the identification of a grammar rule left hand side inside a graph. We follow a similar approach to the single pushout approach (SPO), where dangling edges are deleted, but we first adapt the rule in order to take into account any deleted edge. To this end, a notation borrowed from functional analysis is used. We study the conditions under which the calculated data at specification time can be used when the match is considered.


Graph Transformation Outgoing Edge Matrix Approach Graph Grammar Grammar Rule 
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.
  2. 2.
    Courcelle, B.: Graph Rewriting: An Algebraic and Logic Approach. In: Handbook of Theoretical Computer Science, vol. B, pp. 193–242 (1990)Google Scholar
  3. 3.
    Ehrig, H.: Introduction to the Algebraic Theory of Graph Grammars. In: Ng, E.W., Ehrig, H., Rozenberg, G. (eds.) Graph Grammars 1978. LNCS, vol. 73, pp. 1–69. Springer, Heidelberg (1979)CrossRefGoogle Scholar
  4. 4.
    Ehrig, H., Heckel, R., Korff, M., Löwe, M., Ribeiro, L., Wagner, A., Corradini, A.: Algebraic Approaches to Graph Transformation - Part II: Single Pushout Approach and Comparison with Double Pushout Approach. In: [11], vol. 1, pp. 247–312 (1999)Google Scholar
  5. 5.
    Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  6. 6.
    Heckel, R., Küster, J.M., Taentzer, G.: Confluence of Typed Attributed Graph Transformation Systems. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 161–176. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Kahl, W.: A Relational Algebraic Approach to Graph Structure Transformation. Tech.Rep. 2002-03. Universität der Bundeswehr München (2002)Google Scholar
  8. 8.
    Lambers, L., Ehrig, H., Orejas, F.: Efficient Conflict Detection in Graph Transformation Systems by Essential Critical Pairs. In: Proc. GT-VMT 2006, ENTCS (Elsevier) (to appear, 2006)Google Scholar
  9. 9.
    Mizoguchi, Y., Kuwahara, Y.: Relational Graph Rewritings. Theoretical Computer Science 141, 311–328 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Pérez Velasco, P.P., de Lara, J.: Towards a New Algebraic Approach to Graph Transformation: Long Version. Tech. Rep. of the School of Comp. Sci., Univ. Autónoma Madrid (2006),
  11. 11.
    Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation, vol. 1, (Foundations); vol. 2, (Applications, Languages and Tools); vol. 3, (Concurrency, Parallelism and Distribution). World Scientific, Singapore (1999)Google Scholar
  12. 12.
    Schürr, A.: Programmed Graph Replacement Systems. In: [11], vol. 1, pp. 479–546Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Pedro Pablo Pérez Velasco
    • 1
  • Juan de Lara
    • 1
  1. 1.Escuela Politécnica SuperiorUniversidad Autónoma de Madrid 

Personalised recommendations