Abstract
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.
Research partially supported by the EC RTN 2-2001-00346 Project SegraVis, the MIUR Project ART, the DFG project SANDS and CRUI/DAAD Vigoni “Models based on Graph Transformation Systems: Analysis and Verification”.
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Baldan, P., Ehrig, H., König, B.: Composition and decomposition of DPO transformations with borrowed contexts. Technical report, Universität Duisburg-Essen (2006)
Barendregt, H.P.: The Lambda Calculus—its Syntax and Semantics. Studies in Logic and Foundations of Mathematics, vol. 103. North-Holland, Amsterdam (1984)
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)
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)
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)
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)
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)
Jensen, O.H., Milner, R.: Bigraphs and transitions. In: Proc. of POPL 2003, pp. 38–49. ACM Press, New York (2003)
Lack, S., Sobociński, P.: Adhesive and quasiadhesive categories. RAIRO – Theoretical Informatics and Applications 39(3) (2005)
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)
Milner, R.: The polyadic π-calculus: a tutorial. In: Logic and Algebra of Specification. Springer, Heidelberg (1993)
Sassone, V., Sobociński, P.: Reactive systems over cospans. In: Proc. of LICS 2005, pp. 311–320. IEEE, Los Alamitos (2005)
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Baldan, P., Ehrig, H., König, B. (2006). Composition and Decomposition of DPO Transformations with Borrowed Context. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds) Graph Transformations. ICGT 2006. Lecture Notes in Computer Science, vol 4178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841883_12
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