Abstract
Adhesive high-level replacement (HLR) categories and systems are introduced as a new categorical framework for graph transformation in a broad sense, which combines the well-known concept of HLR systems with the new concept of adhesive categories introduced by Lack and SobociĆski.
In this paper we show that most of the HLR properties, which had been introduced ad hoc to generalize some basic results from the category of graphs to high-level structures, are valid already in adhesive HLR categories. As a main new result in a categorical framework we show the Critical Pair Lemma for local confluence of transformations. Moreover we present a new version of embeddings and extensions for transformations in our framework of adhesive HLR systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ehrig, H., Habel, A., Kreowski, H.J., Parisi-Presicce, F.: Parallelism and Concurrency in High-Level Replacement Systems. Math. Struct. in Comp. Science 1, 361â404 (1991)
Ehrig, H.: Introduction to the Algebraic Theory of Graph Grammars (A Survey). In: Ng, E.W., Ehrig, H., Rozenberg, G. (eds.) Graph Grammars 1978. LNCS, vol. 73, pp. 1â69. Springer, Heidelberg (1979)
Lack, S., SobociĆski, P.: Adhesive Categories. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 273â288. Springer, Heidelberg (2004)
Brown, R., Janelidze, G.: Van Kampen Theorems for Categories of Covering Morphisms in Lextensive Categories. Journal of Pure and Applied Algebra 119, 255â263 (1997)
Corradini, A., Ehrig, H., Heckel, R., Löwe, M., Montanari, U., Rossi, F.: Algebraic Approaches to Graph Transformation I: Basic Concepts and Double Pushout Approach. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation. Foundations, vol. 1, World Scientific, Singapore (1997)
Padberg, J., Ehrig, H., Ribeiro, L.: Algebraic High-Level Net Transformation Systems. In: Mathematical Structures in Computer Science, vol. 2, pp. 217â256 (1995)
Ehrig, H., Gajewsky, M., Parisi-Presicce, F.: High-Level Replacement Systems with Applications to Algebraic Specifications and Petri Nets. In: Rozenberg, G., Montanari, U., Ehrig, H., Kreowski, H.J. (eds.) Handbook of Graph Grammars and Computing by Graph Transformations. Concurrency, Parallelism, and Distribution, vol. 3, pp. 341â400. World Scientific, Singapore (1999)
Löwe, M., Korff, M., Wagner, A.: An Algebraic Framework for the Transformation of Attributed Graphs. In: Term Graph Rewriting: Theory and Practice, pp. 185â199. John Wiley and Sons Ltd., Chichester (1993)
Heckel, R., KĂŒster, J., Taentzer, G.: Confluence of Typed Attributed Graph Transformation with Constraints. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 161â176. Springer, Heidelberg (2002)
Padberg, J., Taentzer, G.: Embedding of Derivations in High-Level Replacement Systems. Technical Report 1993/9, TU Berlin (1993)
Ehrig, H., Orejas, F., Braatz, B., Klein, M., Piirainen, M.: A Component Framework for System Modeling Based on High-Level Replacement Systems. In: Software and Systems Modeling, vol. 3(2), pp. 114â135. Springer, Heidelberg (2004)
Plump, D.: Hypergraph Rewriting: Critical Pairs and Undecidability of Confluence. In: Sleep, M., Plasmeijer, M., van Eekelen, M. (eds.) Term Graph Rewriting: Theory and Practice, pp. 201â213. John Wiley & Sons Ltd, Chichester (1993)
Ehrig, H., Habel, A., Padberg, J., Prange, U.: Adhesive High-Level Replacement Categories and Systems: Long Version. Technical Report TU Berlin (2004)
Ehrig, H., Prange, U., Taentzer, G.: Fundamental Theory for Typed Attributed Graph Transformation. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 161â177. Springer, Heidelberg (2004)
Ehrig, H., Orejas, F., Braatz, B., Klein, M., Piirainen, M.: A Generic Component Concept for System Modeling. In: Kutsche, R.-D., Weber, H. (eds.) FASE 2002. LNCS, vol. 2306, pp. 33â48. Springer, Heidelberg (2002)
Ehrig, H., Ehrig, K., Habel, A., Pennemann, K.: Constraints and Application Conditions: From Graphs to High-Level Structures. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 287â303. Springer, Heidelberg (2004)
Leifer, J., Milner, R.: Deriving Bisimulation Congruences for Reactive Systems. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 243â258. Springer, Heidelberg (2000)
Sassone, V., SobociĆski, P.: Deriving Bisimulation Congruences: 2-Categories vs Precategories. In: Gordon, A.D. (ed.) FOSSACS 2003. LNCS, vol. 2620, pp. 409â424. Springer, Heidelberg (2003)
Ehrig, H., König, B.: Deriving bisimulation congruences in the DPO approach to graph rewriting. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 151â166. Springer, Heidelberg (2004)
Lambek, J., Scott, P.: Introduction to Higher Order Categorical Logic. Cambridge University Press, Cambridge (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ehrig, H., Habel, A., Padberg, J., Prange, U. (2004). Adhesive High-Level Replacement Categories and Systems. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds) Graph Transformations. ICGT 2004. Lecture Notes in Computer Science, vol 3256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30203-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-30203-2_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23207-0
Online ISBN: 978-3-540-30203-2
eBook Packages: Springer Book Archive