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Adhesive Subcategories of Functor Categories with Instantiation to Partial Triple Graphs

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Graph Transformation (ICGT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11629))

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Abstract

Synchronization and integration processes of correlated models that are formally based on triple graph grammars often suffer from the fact that elements are unnecessarily deleted and recreated losing information in the process. It has been shown that this undesirable loss of information can be softened by allowing partial correspondence morphisms in triple graphs. We provide a formal framework for this new synchronization process by introducing the category \(\mathbf {PTrG}\) of partial triple graphs and proving it to be adhesive. This allows for ordinary double pushout rewriting of partial triple graphs. To exhibit \(\mathbf {PTrG}\) as an adhesive category, we present a fundamental construction of subcategories of functor categories and show that these are adhesive HLR if the base category already is. Secondly, we consider an instantiation of this framework by triple graphs to illustrate its practical relevance and to have a concrete example at hand.

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Notes

  1. 1.

    We do not depict identities of \(\mathcal {X}\) and mark the morphisms from the designated set S by a hooked arrow.

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Acknowledgments

We would like to thank the anonymous reviewers for their valuable feedback. This work was partially funded by the German Research Foundation (DFG), project “Triple Graph Grammars (TGG) 2.0”.

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Authors and Affiliations

  1. Philipps-Universität Marburg, Marburg, Germany

    Jens Kosiol & Gabriele Taentzer

  2. TU Darmstadt, Darmstadt, Germany

    Lars Fritsche & Andy Schürr

Authors
  1. Jens Kosiol
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  2. Lars Fritsche
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  4. Gabriele Taentzer
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Correspondence to Jens Kosiol .

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Editors and Affiliations

  1. Universidad Autónoma de Madrid, Madrid, Spain

    Esther Guerra

  2. Universitat Politècnica de Catalunya, Barcelona, Spain

    Fernando Orejas

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Kosiol, J., Fritsche, L., Schürr, A., Taentzer, G. (2019). Adhesive Subcategories of Functor Categories with Instantiation to Partial Triple Graphs. In: Guerra, E., Orejas, F. (eds) Graph Transformation. ICGT 2019. Lecture Notes in Computer Science(), vol 11629. Springer, Cham. https://doi.org/10.1007/978-3-030-23611-3_3

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  • DOI: https://doi.org/10.1007/978-3-030-23611-3_3

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