Advertisement

AGREE – Algebraic Graph Rewriting with Controlled Embedding

  • Andrea Corradini
  • Dominique Duval
  • Rachid Echahed
  • Frederic Prost
  • Leila RibeiroEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9151)

Abstract

The several algebraic approaches to graph transformation proposed in the literature all ensure that if an item is preserved by a rule, so are its connections with the context graph where it is embedded. But there are applications in which it is desirable to specify different embeddings. For example when cloning an item, there may be a need to handle the original and the copy in different ways. We propose a conservative extension of classical algebraic approaches to graph transformation, for the case of monic matches, where rules allow one to specify how the embedding of preserved items should be carried out.

Keywords

Algebraic Approach Graph Transformation Type Graph Black Node Grey Node 
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.

Notes

Acknowledgments

We are grateful to the anonymous reviewers of former versions of this paper for the insightful and constructive criticisms.

References

  1. 1.
    Bauderon, M., Jacquet, H.: Pullback as a generic graph rewriting mechanism. Appl. Categorical Struct. 9(1), 65–82 (2001)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cockett, J., Lack, S.: Restriction categories I: categories of partial maps. Theor. Comput. Sci. 270(12), 223–259 (2002)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cockett, J., Lack, S.: Restriction categories II: partial map classification. Theor. Comput. Sci. 294(12), 61–102 (2003)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Corradini, A., Duval, D., Echahed, R., Prost, F., Ribeiro, L.: AGREE - algebraic graph rewriting with controlled embedding. CoRR abs/1411.4597 (2014). http://arxiv.org/abs/1411.4597
  5. 5.
    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
  6. 6.
    Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic approaches to graph transformation - part I: basic concepts and double pushout approach. In: Rozenberg [19], pp. 163–246Google Scholar
  7. 7.
    Drewes, F., Hoffmann, B., Janssens, D., Minas, M.: Adaptive star grammars and their languages. Theor. Comput. Sci. 411(34–36), 3090–3109 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Duval, D., Echahed, R., Prost, F.: Graph rewriting with polarized cloning. CoRR abs/0911.3786 (2009). http://arxiv.org/abs/0911.3786
  9. 9.
    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
  10. 10.
    Duval, D., Echahed, R., Prost, F., Ribeiro, L.: Transformation of attributed structures with cloning. In: Gnesi, S., Rensink, A. (eds.) FASE 2014 (ETAPS). LNCS, vol. 8411, pp. 310–324. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  11. 11.
    Echahed, R.: Inductively sequential term-graph rewrite systems. In: Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds.) ICGT 2008. LNCS, vol. 5214, pp. 84–98. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  12. 12.
    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: Rozenberg [19], pp. 247–312Google Scholar
  13. 13.
    Ehrig, H., Pfender, M., Schneider, H.J.: Graph-grammars: an algebraic approach. In: 14th Annual Symposium on Switching and Automata Theory, Iowa City, Iowa, USA, October 15–17 1973, pp. 167–180. IEEE Computer Society (1973)Google Scholar
  14. 14.
    Engelfriet, J., Rozenberg, G.: Node replacement graph grammars. In: Rozenberg [19], pp. 1–94Google Scholar
  15. 15.
    Hay, M., Miklau, G., Jensen, D., Towsley, D.F., Li, C.: Resisting structural re-identification in anonymized social networks. VLDB J. 19(6), 797–823 (2010)CrossRefGoogle Scholar
  16. 16.
    Löwe, M.: Algebraic approach to single-pushout graph transformation. Theor. Comput. Sci. 109(1&2), 181–224 (1993)CrossRefGoogle Scholar
  17. 17.
    Löwe, M.: Graph rewriting in span-categories. In: Ehrig, H., Rensink, A., Rozenberg, G., Schürr, A. (eds.) ICGT 2010. LNCS, vol. 6372, pp. 218–233. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  18. 18.
    Mitchell, M., Oldham, J., Samuel, A.: Advanced Linux Programming. Landmark Series. Landmark, New Riders (2001) Google Scholar
  19. 19.
    Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformations. Foundations, vol. 1. World Scientific, Singapore (1997) Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Andrea Corradini
    • 1
  • Dominique Duval
    • 2
  • Rachid Echahed
    • 3
  • Frederic Prost
    • 3
  • Leila Ribeiro
    • 4
    Email author
  1. 1.Dipartimento di InformaticaUniversità di PisaPisaItaly
  2. 2.LJK - Université de Grenoble Alpes and CNRSGrenobleFrance
  3. 3.LIG - Université de Grenoble Alpes and CNRSGrenobleFrance
  4. 4.INF - Universidade Federal do Rio Grande do SulPorto AlegreBrazil

Personalised recommendations