Abstract
We present an approach for the rule-based transformation of hierarchically structured (hyper)graphs. In these graphs, distinguished hyperedges contain graphs that can be hierarchical again. Our framework extends the double-pushout approach from flat to hierarchical graphs. In particular, we show how to construct recursively pushouts and pushout complements of hierarchical graphs and graph morphisms. To further enhance the expressiveness of the approach, we also introduce rule schemata with variables which allow to copy and to remove hierarchical subgraphs.
This work has been partially supported by the ESPRIT Working Group Applications of Graph Transformation (Appligraph) and by the TMR Research Network Getgrats through the University of Bremen.
On leave from Universität Bremen.
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References
J. Adámek, H. Herrlich, and G. Strecker. Abstract and Concrete Categories. John Wiley, New York, 1990.
M. Andries, G. Engels, A. Habel, B. Hoffmann, H.-J. Kreowski, S. Kuske, D. Plump, A. Schürr, and G. Taentzer. Graph transformation for specification and programming. Science of Computer Programming, 34:1–54, 1999.
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 G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation, volume 1, chapter 3, pages 163–245. World Scientific, 1997.
F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation, volume 1, chapter 2, pages 95–162. World Scientific, Singapore, 1997.
H. Ehrig. Introduction to the algebraic theory of graph grammars. In Proc. Graph-Grammars and Their Application to Computer Science and Biology, volume 73 of Lecture Notes in Computer Science, pages 1–69. Springer-Verlag, 1979.
G. Engels and A. Schürr. Encapsulated hierachical graphs, graph types, and meta types. In A. Corradini and U. Montanari, editors, Proc. Joint COMPUGRAPH/SEMAGRAPH Workshop on Graph Rewriting and Computation, volume 2 of Electronic Notes in Theoretical Computer Science. Elsevier, 1995.
C. Ermel, M. Rudolf, and G. Taentzer. The AGG approach: Language and environment. In H. Ehrig, G. Engels, H.-J. Kreowski, and G. Rozenberg, editors, Handbook of Graph Grammars and Computing by Graph Transformation, volume 2, pages 551–603. World Scientific, 1999.
P. Fradet and D. L. Métayer. Structured Gamma. Science of Computer Programming, 31(2/3):263–289, 1998.
A. Habel. Hyperedge Replacement: Grammars and Languages, volume 643 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1992.
R. Heckel, H. Ehrig, and G. Taentzer. Classification and comparison of module concepts for graph transformation systems. In H. Ehrig, G. Engels, H.-J. Kreowski, and G. Rozenberg, editors, Handbook of Graph Grammars and Computing by Graph Transformation, volume 2, chapter 17, pages 669–689. World Scientific, 1999.
B. Hoffmann. From graph transformation to rule-based programming with diagrams. In M. Nagl and A. Schürr, editors, Proc. Int’l Workshop on Applications of Graph Transformations with Industrial Relevance (Agtive’99), Lecture Notes in Computer Science, 1999. To appear.
M. Löwe and M. Beyer. AGG — an implementation of algebraic graph rewriting. In C. Kirchner, editor, Proc. Rewriting Techniques and Applications, volume 690 of Lecture Notes in Computer Science, pages 451–456, 1993.
F. Parisi-Presicce and G. Piersanti. Multi-level graph grammars. In E. W. Mayr, G. Schmidt, and G. Tinhofer, editors, Graph-Theoretical Concepts in Computer Science (WG’ 94), volume 903 of Lecture Notes in Computer Science, pages 51–64, 1995.
D. Plump and A. Habel. Graph unification and matching. In Proc. Graph Grammars and Their Application to Computer Science, volume 1073 of Lecture Notes in Computer Science, pages 75–89. Springer-Verlag, 1996.
T. W. Pratt. Pair grammars, graph languages and string-to-graph translations. Journal of Computer and System Sciences, 5:560–595, 1971.
H.-J. Schneider. On categorical graph grammars integrating structural transformations and operations on labels. Theoretical Computer Science, 109:257–274, 1993.
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Drewes, F., Hoffmann, B., Plump, D. (2000). Hierarchical Graph Transformation. In: Tiuryn, J. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2000. Lecture Notes in Computer Science, vol 1784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46432-8_7
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