Sesqui-Pushout Rewriting

  • Andrea Corradini
  • Tobias Heindel
  • Frank Hermann
  • Barbara König
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4178)


Sesqui-pushout (SqPO) rewriting—“sesqui” means “one and a half” in Latin—is a new algebraic approach to abstract rewriting in any category. SqPO rewriting is a deterministic and conservative extension of double-pushout (dpo) rewriting, which allows to model “deletion in unknown context”, a typical feature of single-pushout (spo) rewriting, as well as cloning.

After illustrating the expressiveness of the proposed approach through a case study modelling an access control system, we discuss sufficient conditions for the existence of final pullback complements and we analyze the relationship between SqPO and the classical dpo and spo approaches.


Algebraic Approach Graph Transformation Graph Grammar Access Control Model Primitive Operation 
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.


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  1. 1.
    Bauderon, M.: A uniform approach to graph rewriting: The pullback approach. In: Nagl, M. (ed.) WG 1995. LNCS, vol. 1017, pp. 101–115. Springer, Heidelberg (1995)Google Scholar
  2. 2.
    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, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation, Foundations, ch. 3, vol. 1. World Scientific, Singapore (1997)Google Scholar
  3. 3.
    Dyckhoff, R., Tholen, W.: Exponentiable morphisms, partial products and pullback complements. Journal of Pure and Applied Algebra 49(1-2), 103–116 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Ehrig, H., Habel, A., Kreowski, H.-J., Parisi-Presicce, F.: Parallelism and concurrency in high level replacement systems. Mathematical Structures in Computer Science 1, 361–404 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    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, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation, Foundations, ch. 4, vol. 1. World Scientific, Singapore (1997)Google Scholar
  6. 6.
    Ehrig, H., Löwe, M.: Categorical principles, techniques and results for high-level-replacement systems in computer science. Applied Categorical Structures 1, 21–50 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Ehrig, H., Pfender, M., Schneider, H.-J.: Graph grammars: An algebraic approach. In: Proc. 14th IEEE Symp. on Switching and Automata Theory, pp. 167–180 (1973)Google Scholar
  8. 8.
    Ferriolo, D.F., Kuhn, D.R., Chandramouli, R.: Role-Based Access Control. Artech House computer security series. Artech House (2003), ISBN: 1-580-53370-1Google Scholar
  9. 9.
    Goldblatt, R.: Topoi: The Categorial Analysis of Logic. Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Company, Amsterdam, The Netherlands (1984)zbMATHGoogle Scholar
  10. 10.
    Habel, A., Müller, J., Plump, D.: Double-pushout graph transformation revisited. Mathematical Structures in Computer Science 11(5), 637–688 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Harrison, M.A., Ruzzo, W.L., Ullman, J.D.: Protection in operating systems. Commun. ACM 19(8), 461–471 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Heckel, R., Ehrig, H., Wolter, U., Corradini, A.: Double-pullback transitions and coalgebraic loose semantics for graph transformation systems. Applied Categorical Structures 9(1) (2001)Google Scholar
  13. 13.
    Kahl, W.: A fibred approach to rewriting — how the duality between adding and deleting cooperates with the difference between matching and rewriting. Technical Report 9702, Fakultät für Informatik, Universität der Bundeswehr München (May 1997)Google Scholar
  14. 14.
    Kennaway, R.: Graph Rewriting in Some Categories of Partial Morphisms. In: Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) Graph Grammars 1990. LNCS, vol. 532, pp. 490–504. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  15. 15.
    Koch, M., Mancini, L.V., Parisi-Presicce, F.: A formal model for role-based access control using graph transformation. In: Cuppens, F., Deswarte, Y., Gollmann, D., Waidner, M. (eds.) ESORICS 2000. LNCS, vol. 1895, pp. 122–139. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  16. 16.
    Lack, S., Sobociński, P.: Adhesive and quasiadhesive categories. Theoretical Informatics and Applications 39(2), 511–546 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Löwe, M.: Algebraic approach to single-pushout graph transformation. Theoretical Computer Science 109, 181–224 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Monserrat, M., Rosselló, F., Torrens, J., Valiente, G.: Single pushout rewriting in categories of spans I: The general setting. Technical Report LSI-97-23-R, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya (1997)Google Scholar
  19. 19.
    Robinson, E., Rosolini, G.: Categories of partial maps. Information and Computation 79(2), 95–130 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Sandhu, R.S., Coyne, E.J., Feinstein, H.L., Youman, C.E.: Role-based access control models. IEEE Computer 29(2), 38–47 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andrea Corradini
    • 1
  • Tobias Heindel
    • 1
  • Frank Hermann
    • 2
  • Barbara König
    • 3
  1. 1.Dipartimento di InformaticaUniversità di PisaItaly
  2. 2.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany
  3. 3.Institut für Informatik und interaktive SystemeUniv. Duisburg-EssenGermany

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