Sesqui-Pushout Rewriting with Type Refinements

  • Michael LöweEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9761)


Sesqui-pushout rewriting is an algebraic graph transformation approach that provides mechanisms for vertex cloning. If a vertex gets cloned, the original and the copy obtain the same context, i.e. all incoming and outgoing edges of the original are copied as well. This behaviour is not satisfactory in practical examples which require more control over the context cloning process. In this paper, we provide such a control mechanism by allowing each transformation rule to refine the underlying type graph. We discuss the relation to the existing approaches to controlled sesqui-pushout vertex cloning, elaborate a basic theoretical framework, and demonstrate its applicability by a practical example.


  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, Heidelberg (2015)CrossRefGoogle Scholar
  2. 2.
    Corradini, A., Heindel, T., Hermann, F., König, B.: Sesqui-pushout rewriting. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 30–45. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Duval, D., Echahed, R., Prost, F.: Graph transformation with focus on incident edges. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2012. LNCS, vol. 7562, pp. 156–171. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  5. 5.
    Ehrig, H., Pfender, M., Schneider, H.J., Graph-grammars: an algebraic approach. In: FOCS, pp. 167–180. IEEE (1973)Google Scholar
  6. 6.
    Kennaway, R.: Graph rewriting in some categories of partial morphisms. In: Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) Graph-Grammars and Their Application to Computer Science. LNCS, vol. 532, pp. 490–504. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  7. 7.
    Lack, S., Sobocinski, P.: Adhesive and quasiadhesive categories. ITA 39(3), 511–545 (2005)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Löwe, M.: Algebraic approach to single-pushout graph transformation. Theor. Comput. Sci. 109(1&2), 181–224 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Löwe, M.: Graph rewriting in span-categories. Technical report 2010/02, FHDW-Hannover (2010)Google Scholar
  10. 10.
    Löwe, M.: A unifying framework for algebraic graph transformation. Technical report 2012/03, FHDW-Hannover (2012)Google Scholar
  11. 11.
    Löwe, M.: Polymorphic sesqui-pushout graph rewriting. Technical report 2014/02, FHDW-Hannover (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.FHDW HannoverHannoverGermany

Personalised recommendations