Composition and Decomposition of DPO Transformations with Borrowed Context

  • Paolo Baldan
  • Hartmut Ehrig
  • Barbara König
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4178)


Double-pushout (DPO) transformations with borrowed context extend the standard DPO approach by allowing part of the graph needed in a transformation to be borrowed from the environment. The bisimilarity based on the observation of borrowed contexts is a congruence, thus facilitating system analysis. In this paper, focusing on the situation in which the states of a global system are built out of local components, we show that DPO transformations with borrowed context defined on a global system state can be decomposed into corresponding transformations on the local states and vice versa. Such composition and decomposition theorems, developed in the framework of adhesive categories, can be seen as a first step towards an inductive definition, in sos style, of the labelled transition system associated to a graph transformation system. As a special case we show how an ordinary DPO transformation on a global system state can be decomposed into local DPO transformations with borrowed context using the same production.


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  1. 1.
    Baldan, P., Ehrig, H., König, B.: Composition and decomposition of DPO transformations with borrowed contexts. Technical report, Universität Duisburg-Essen (2006)Google Scholar
  2. 2.
    Barendregt, H.P.: The Lambda Calculus—its Syntax and Semantics. Studies in Logic and Foundations of Mathematics, vol. 103. North-Holland, Amsterdam (1984)zbMATHGoogle Scholar
  3. 3.
    Bonchi, F., Gadducci, F., König, B.: Process bisimulation via a graphical encoding. In: Corradini, A., et al. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 168–183. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Cardelli, L., Gordon, A.D.: Mobile ambients. In: Nivat, M. (ed.) ETAPS 1998 and FOSSACS 1998. LNCS, vol. 1378, pp. 140–155. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. 5.
    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, ch. 3. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation, Foundations, vol. 1. World Scientific, Singapore (1997)Google Scholar
  6. 6.
    Ehrig, H., König, B.: Deriving bisimulation congruences in the DPO approach to graph rewriting. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 151–166. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Ehrig, H., Kreowski, H.-J., Montanari, U., Rozenberg, G. (eds.): Handbook of Graph Grammars and Computing by Graph Transformation, vol. 3: Concurrency, Parallellism, and Distribution. World Scientific, Singapore (1999)Google Scholar
  8. 8.
    Jensen, O.H., Milner, R.: Bigraphs and transitions. In: Proc. of POPL 2003, pp. 38–49. ACM Press, New York (2003)CrossRefGoogle Scholar
  9. 9.
    Lack, S., Sobociński, P.: Adhesive and quasiadhesive categories. RAIRO – Theoretical Informatics and Applications 39(3) (2005)Google Scholar
  10. 10.
    Leifer, J.J., Milner, R.: Deriving bisimulation congruences for reactive systems. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, p. 243. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  11. 11.
    Milner, R.: The polyadic π-calculus: a tutorial. In: Logic and Algebra of Specification. Springer, Heidelberg (1993)Google Scholar
  12. 12.
    Sassone, V., Sobociński, P.: Reactive systems over cospans. In: Proc. of LICS 2005, pp. 311–320. IEEE, Los Alamitos (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Paolo Baldan
    • 1
  • Hartmut Ehrig
    • 2
  • Barbara König
    • 3
  1. 1.Dipartimento di InformaticaUniversità Ca’ Foscari di VeneziaItaly
  2. 2.Institut für Softwaretechnik und Theoretische InformatikTechnische Universität  BerlinGermany
  3. 3.Institut für Informatik und interaktive SystemeUniversität Duisburg-EssenGermany

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