Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach

A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, M. Löwe, in: Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations, World Scientific, Singapore, 1997, pp. 163–245.

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Abstract
The algebraic approaches to graph transformation are based on the concept of gluing of graphs, modelled by pushouts in suitable categories of graphs and graph morphisms. This allows one not only to give an explicit algebraic or set theoretical description of the constructions, but also to use concepts and results from category theory in order to build up a rich theory and to give elegant proofs even in complex situations. In this chapter we start with an overwiev of the basic notions common to the two algebraic approaches, the double-pushout (DPO) approach and the singlepushout (SPO) approach; next we present the classical theory and some recent development of the double-pushout approach. The next chapter is devoted instead to the single-pushout approach, and it is closed by a comparison between the two approaches.
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Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations
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163-245
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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. In: Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations. Singapore: World Scientific; 1997:163-245.
Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., & Löwe, M. (1997). Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach. In Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations (pp. 163–245). Singapore: World Scientific.
@inbook{Corradini_Montanari_Rossi_Ehrig_Heckel_Löwe_1997, place={Singapore}, title={Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach}, booktitle={Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations}, publisher={World Scientific}, author={Corradini, Andrea and Montanari, Ugo and Rossi, Francesca and Ehrig, Hartmut and Heckel, Reiko and Löwe, Michael}, year={1997}, pages={163–245} }
Corradini, Andrea, Ugo Montanari, Francesca Rossi, Hartmut Ehrig, Reiko Heckel, and Michael Löwe. “Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach.” In Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations, 163–245. Singapore: World Scientific, 1997.
A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Löwe, “Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach,” in Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations, Singapore: World Scientific, 1997, pp. 163–245.
Corradini, Andrea, et al. “Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach.” Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations, World Scientific, 1997, pp. 163–245.

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