Abstract
The categorical framework of \(\mathcal M\)-adhesive transformation systems does not cover graph transformation with relabelling. Rules that relabel nodes are natural for computing with graphs, however, and are commonly used in graph transformation languages. In this paper, we generalise \(\mathcal M\)-adhesive transformation systems to \(\mathcal M,\mathcal N\)-adhesive transformation systems, where \(\mathcal N\) is a class of morphisms containing the vertical morphisms in double-pushouts. We show that the category of partially labelled graphs is \(\mathcal M,\mathcal N\)-adhesive, where \(\mathcal M\) and \(\mathcal N\) are the classes of injective and injective, undefinedness-preserving graph morphisms, respectively. We obtain the Local Church-Rosser Theorem and the Parallelism Theorem for graph transformation with relabelling and application conditions as instances of results which we prove at the abstract level of \(\mathcal M,\mathcal N\)-adhesive systems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Baldan, P., Gadducci, F., Sobociński, P.: Adhesivity Is Not Enough: Local Church-Rosser Revisited. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 48–59. Springer, Heidelberg (2011)
Corradini, A., Gadducci, F.: On term graphs as an adhesive category. In: Fernández, M. (ed.) Proc. International Workshop on Term Graph Rewriting (TERMGRAPH 2004). Electronic Notes in Theoretical Computer Science, vol. 127(5), pp. 43–56 (2005)
Ehrig, H.: Introduction to the Algebraic Theory of Graph Grammars. In: Claus, V., Ehrig, H., Rozenberg, G. (eds.) Graph Grammars 1978. LNCS, vol. 73, pp. 1–69. Springer, Heidelberg (1979)
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Monographs in Theoretical Computer Science. Springer (2006)
Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.): Handbook of Graph Grammars and Computing by Graph Transformation. Applications, Languages, and Tools, vol. 2. World Scientific (1999)
Ehrig, H., Golas, U., Habel, A., Lambers, L., Orejas, F.: \(\mathcal{M}\)-adhesive transformation systems with nested application conditions. Part 1: Parallelism, concurrency and amalgamation. Mathematical Structures in Computer Science (to appear, 2012)
Ehrig, H., Golas, U., Habel, A., Lambers, L., Orejas, F.: \(\mathcal{M}\)-adhesive transformation systems with nested application conditions. Part 2: Embedding, critical pairs and local confluence. Fundamenta Informaticae 118, 35–63 (2012)
Ehrig, H., Golas, U., Hermann, F.: Categorical frameworks for graph transformation and HLR systems based on the DPO approach. Bulletin of the EATCS 102, 111–121 (2010)
Ehrig, H., Habel, A., Kreowski, H.-J., Parisi-Presicce, F.: Parallelism and concurrency in high-level replacement systems. Mathematical Structures in Computer Science 1, 361–404 (1991)
Ehrig, H., Kreowski, H.-J., Montanari, U., Rozenberg, G. (eds.): Handbook of Graph Grammars and Computing by Graph Transformation. Concurrency, Parallelism, and Distribution, vol. 3. World Scientific (1999)
Golas, U.: A General Attribution Concept for Models in M-Adhesive Transformation Systems. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2012. LNCS, vol. 7562, pp. 187–202. Springer, Heidelberg (2012)
Habel, A., Müller, J., Plump, D.: Double-pushout graph transformation revisited. Mathematical Structures in Computer Science 11(5), 637–688 (2001)
Habel, A., Pennemann, K.-H.: Correctness of high-level transformation systems relative to nested conditions. Mathematical Structures in Computer Science 19(2), 245–296 (2009)
Habel, A., Plump, D.: Relabelling in Graph Transformation. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 135–147. Springer, Heidelberg (2002)
Habel, A., Plump, D.: \(\mathcal{M,N}\)-adhesive transformation systems (long version) (2012), http://formale-sprachen.informatik.uni-oldenburg.de/pub/index.html
Heindel, T.: Hereditary Pushouts Reconsidered. In: Ehrig, H., Rensink, A., Rozenberg, G., Schürr, A. (eds.) ICGT 2010. LNCS, vol. 6372, pp. 250–265. Springer, Heidelberg (2010)
Lack, S., Sobociński, P.: Adhesive and quasiadhesive categories. Informatique Théorique et Applications 39(3), 511–545 (2005)
Plump, D.: The Graph Programming Language GP. In: Bozapalidis, S., Rahonis, G. (eds.) CAI 2009. LNCS, vol. 5725, pp. 99–122. Springer, Heidelberg (2009)
Plump, D.: The design of GP 2. In: Escobar, S. (ed.) Proc. International Workshop on Reduction Strategies in Rewriting and Programming (WRS 2011). Electronic Proceedings in Theoretical Computer Science, vol. 82, pp. 1–16 (2012)
Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation. Foundations, vol. 1. World Scientific (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Habel, A., Plump, D. (2012). \(\mathcal M, \mathcal N\)-Adhesive Transformation Systems. In: Ehrig, H., Engels, G., Kreowski, HJ., Rozenberg, G. (eds) Graph Transformations. ICGT 2012. Lecture Notes in Computer Science, vol 7562. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33654-6_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-33654-6_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33653-9
Online ISBN: 978-3-642-33654-6
eBook Packages: Computer ScienceComputer Science (R0)