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See detailCategorical Frameworks for Graph Transformation and HLR Systems based on the DPO Approach
Ehrig, Hartmut; Golas, Ulrike; Hermann, Frank UL

in Bulletin of the EATCS (2010), 102

Several variants of high-level replacement (HLR) and adhesive categories have been introduced in the literature as categorical frameworks for graph transformation and HLR systems based on the double ... [more ▼]

Several variants of high-level replacement (HLR) and adhesive categories have been introduced in the literature as categorical frameworks for graph transformation and HLR systems based on the double pushout (DPO) approach. In addition to HLR, adhesive, and adhesive HLR categories several weak variants, especially weak adhesive HLR with horizontal and vertical variants, as well as partial variants, including partial map adhesive and partial VK square adhesive categories are reviewed and related to each other. We propose as weakest version the class of vertical weak adhesive HLR categories, short $\mathcalM$-adhesive categories, which are still sufficient to obtain most of the main results for graph transformation and HLR systems. The results in this paper are summarized in Fig.~f:hierarchy showing a hierarchy of all these variants of adhesive, adhesive HLR, and $\mathcalM$-adhesive categories, which can be considered as different categorical frameworks for graph transformation and HLR systems. [less ▲]

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See detailBehaviour Simulation and Equivalence of Systems Modelled by Graph Transformation
Ehrig, Hartmut; Ermel, Claudia; Hermann, Frank UL et al

in Bulletin of the EATCS (2009), 97

Our new project "Behaviour Simulation and Equivalence of Systems Modelled by Graph Transformation" funded by the German Research Council (DFG) has started in May 2008. In this contribution we present the ... [more ▼]

Our new project "Behaviour Simulation and Equivalence of Systems Modelled by Graph Transformation" funded by the German Research Council (DFG) has started in May 2008. In this contribution we present the main goals of the project and first results. [less ▲]

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See detailCospan DPO Approach: An Alternative for DPO Graph Transformations
Ehrig, Hartmut; Hermann, Frank UL; Prange, Ulrike

in Bulletin of the EATCS (2009)

The DPO approach for graph transformations is based on productions and direct transformations defined by two pushouts, where, roughly spoken, in the first pushout all items in L without K are deleted and ... [more ▼]

The DPO approach for graph transformations is based on productions and direct transformations defined by two pushouts, where, roughly spoken, in the first pushout all items in L without K are deleted and in the second one all items R without K are added, while those items in K are preserved. Intuitively, K is the intersection of L and R and, formally, p is a span of graph morphisms. In this paper we consider productions which are cospans of graph morphisms, and K corresponds to the union of L and R. As before, direct transformations are defined by double pushouts, but now the first pushout adds all items in KnL and the second one deletes KnR. This basic idea can be extended to an alternative graph transformation approach, called cospan DPO approach. Key notions of the classical DPO approach can be reformulated in the cospan DPO approach and our main result shows in which way corresponding concepts and results are equivalent. [less ▲]

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See detailProcess Definition using Subobject Transformation Systems
Hermann, Frank UL; Ehrig, Hartmut

in Bulletin of the EATCS (2008), 95

Process definition on the basis of graph transformation systems was introduced by the concept of occurrence grammars, which are a generalization of Petri net processes given by occurrence nets. Recently ... [more ▼]

Process definition on the basis of graph transformation systems was introduced by the concept of occurrence grammars, which are a generalization of Petri net processes given by occurrence nets. Recently, subobject transformation systems were proposed as abstract framework for occurrence grammars in adhesive categories, but they are still restricted to injective matches for graph transformation steps. In this paper we review the construction of STSs as processes for plain graph grammars and discuss an extension to attributed graph grammars with non-injective matches. This is the basis for a forthcoming formal treatment in the framework of adhesive categories. [less ▲]

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