Abstract
There are three major algebraic approaches to graph transformation, namely the double-pushout (DPO), single-pushout (SPO), and sesqui-pushout approach (SqPO). In this paper, we present a framework that generalises all three approaches. The central issue is a gluing construction, which is a generalisation of the construction introduced in [14]. It has pushout-like properties wrt. composition and decomposition, which allow to reestablish major parts of the theory for the algebraic approaches on a general level. We investigate parallel independence here.
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
Bauderon, M., Jacquet, H.: Pullback as a generic graph rewriting mechanism. Applied Categorical Structures 9(1), 65–82 (2001)
Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.): ICGT 2006. LNCS, vol. 4178. Springer, Heidelberg (2006)
Corradini, A., Heindel, T., Hermann, F., König, B.: Sesqui-pushout rewriting. In: Corradini, et al. (eds.) [2], pp. 30–45
Drewes, F., Hoffmann, B., Janssens, D., Minas, M., Van Eetvelde, N.: Adaptive star grammars. In: Corradini, et al. (eds.) [2], pp. 77–91
Duval, D., Echahed, R., Prost, F.: Graph rewriting with polarized cloning. CoRR, abs/0911.3786 (2009)
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Springer (2006)
Ehrig, H., Rensink, A., Rozenberg, G., Schürr, A. (eds.): ICGT 2010. LNCS, vol. 6372. Springer, Heidelberg (2010)
Golas, U., Ehrig, H., Habel, A.: Multi-amalgamation in adhesive categories. In: Ehrig, et al. (eds.) [7], pp. 346–361
Heindel, T.: Hereditary pushouts reconsidered. In: Ehrig, et al. (eds.) [7], pp. 250–265
Kahl, W.: A relation-algebraic approach to graph structure transformation. Habil. Thesis 2002-03, Fakultät für Informatik, Univ. der Bundeswehr München (2001)
Kahl, W.: Amalgamating pushout and pullback graph transformation in collagories. In: Ehrig, et al. (eds.) [7], pp. 362–378
Kennaway, R.: Graph Rewriting in Some Categories of Partial Morphisms. In: Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) Graph Grammars 1990. LNCS, vol. 532, pp. 490–504. Springer, Heidelberg (1991)
Löwe, M.: Algebraic approach to single-pushout graph transformation. Theor. Comput. Sci. 109(1&2), 181–224 (1993)
Löwe, M.: Graph rewriting in span-categories. In: Ehrig, et al. (eds.) [7], pp. 218–233
Löwe, M.: A unifying framework for algebraic graph transformation. Technical Report 2012/03, FHDW-Hannover (2012)
McLarty, C.: Elementary Categories, Elementary Toposes. Oxford Science Publications, Clarendon Press, Oxford (1992)
Monserrat, M., Rossello, F., Torrens, J., Valiente, G.: Single pushout rewriting in categories of spans i: The general setting. Technical Report LSI-97-23-R, Department de Llenguatges i Sistemes Informtics, Universitat Politcnica de Catalunya (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
Löwe, M. (2012). Refined Graph Rewriting in Span-Categories. 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_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-33654-6_8
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)