Double-Pushout Rewriting in Context

  • Michael LöweEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11176)


Double-pushout rewriting (DPO) is the most popular algebraic approach to graph transformation. Most of its theory has been developed for linear rules, which allow deletion, preservation, and addition of vertices and edges only. Deletion takes place in a careful and circumspect way: a double pushout derivation does never delete vertices or edges which are not in the image of the applied match. Due to these restrictions, every DPO-rewrite is invertible. In this paper, we extend the DPO-approach to non-linear and still invertible rules. Some model transformation examples show that the extension is worthwhile from the practical point of view. And there is a good chance for the extension of the existing theory. In this paper, we investigate parallel independence.


  1. 1.
    Corradini, A., Duval, D., Echahed, R., Prost, F., Ribeiro, L.: AGREE – algebraic graph rewriting with controlled embedding. In: Parisi-Presicce, F., Westfechtel, B. (eds.) ICGT 2015. LNCS, vol. 9151, pp. 35–51. Springer, Cham (2015). Scholar
  2. 2.
    Danos, V., Heindel, T., Honorato-Zimmer, R., Stucki, S.: Reversible sesqui-pushout rewriting. In: Giese, H., König, B. (eds.) ICGT 2014. LNCS, vol. 8571, pp. 161–176. Springer, Cham (2014). Scholar
  3. 3.
    Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. MTCSAES. Springer, Heidelberg (2006). Scholar
  4. 4.
    Ehrig, H., Ermel, C., Golas, U., Hermann, F.: Graph and Model Transformation - General Framework and Applications. MTCSAES. Springer, Heidelberg (2015). Scholar
  5. 5.
    Ehrig, H., Rensink, A., Rozenberg, G., Schürr, A. (eds.): ICGT 2010. LNCS, vol. 6372. Springer, Heidelberg (2010). Scholar
  6. 6.
    Gamma, E., et al.: Design Patterns: Elements of Reusable Object-Oriented Software. Addison-Wesley, Boston (1994)Google Scholar
  7. 7.
    Fowler, M.: Refactoring - Improving the Design of Existing Code. Addison Wesley Object Technology Series. Addison-Wesley, Boston (1999)zbMATHGoogle Scholar
  8. 8.
    Habel, A., Heckel, R., Taentzer, G.: Graph grammars with negative application conditions. Fundam. Inform. 26(3/4), 287–313 (1996)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Habel, A., Müller, J., Plump, D.: Double-pushout graph transformation revisited. Math. Struct. Comput. Sci. 11(5), 637–688 (2001)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Heindel, T.: Hereditary pushouts reconsidered. In: Ehrig et al. [5], pp. 250–265 (2010)Google Scholar
  11. 11.
    Lack, S., Sobocinski, P.: Adhesive and quasiadhesive categories. ITA 39(3), 511–545 (2005)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Löwe, M.: Graph rewriting in span-categories. In: Ehrig et al. [5], pp. 218–233 (2010)Google Scholar
  13. 13.
    Löwe, M.: Refactoring information systems: association folding and unfolding. ACM SIGSOFT Softw. Eng. Notes 36(4), 1–7 (2011)CrossRefGoogle Scholar
  14. 14.
    Löwe, M.: Double pushout rewriting in context. Technical report 2018/02, Fachhochschule für die. Wirtschaft, Hannover (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.FHDW HannoverHannoverGermany

Personalised recommendations