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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References
Baldan, P., Ehrig, H., König, B.: Composition and decomposition of DPO transformations with borrowed contexts. Technical report, Universität Duisburg-Essen (2006)
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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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