Initial Conflicts and Dependencies: Critical Pairs Revisited
Considering a graph transformation system, a critical pair represents a pair of conflicting transformations in a minimal context. A conflict between two direct transformations of the same structure occurs if one of the transformations cannot be performed in the same way after the other one has taken place. Critical pairs allow for static conflict and dependency detection since there exists a critical pair for each conflict representing this conflict in a minimal context. Moreover it is sufficient to check each critical pair for strict confluence to conclude that the whole transformation system is locally confluent. Since these results were shown in the general categorical framework of M-adhesive systems, they can be instantiated for a variety of systems transforming e.g. (typed attributed) graphs, hypergraphs, and Petri nets.
In this paper, we take a more declarative view on the minimality of conflicts and dependencies leading to the notions of initial conflicts and initial dependencies. Initial conflicts have the important new characteristic that for each given conflict a unique initial conflict exists representing it. We introduce initial conflicts for M-adhesive systems and show that the Completeness Theorem and the Local Confluence Theorem still hold. Moreover, we characterize initial conflicts for typed graph transformation systems and show that the set of initial conflicts is indeed smaller than the set of essential critical pairs (a first approach to reduce the set of critical pairs to the important ones). Dual results hold for initial dependencies.
Many thanks to Leila Ribeiro and Jonas Santos Bezerra for providing us with support to CPA of our running example in Verigraph .
This work was partially funded by the German Research Foundation, Priority Program SPP 1593 “Design for Future – Managed Software Evolution”. This research was partially supported by the research project Visual Privacy Management in User Centric Open Environments (supported by the EU’s Horizon 2020 programme, Proposal number: 653642).
- 3.Heckel, R., Küster, J.M., Taentzer, G.: Confluence of typed attributed graph transformation systems. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 161–176. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45832-8_14 CrossRefGoogle Scholar
- 4.Ehrig, H., Habel, A., Padberg, J., Prange, U.: Adhesive high-level replacement categories and systems. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 144–160. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30203-2_12 CrossRefGoogle Scholar
- 5.Hausmann, J.H., Heckel, R., Taentzer, G.: Detection of conflicting functional requirements in a use case-driven approach: a static analysis technique based on graph transformation. In: 22rd International Conference on Software Engineering (ICSE), pp. 105–115. ACM (2002)Google Scholar
- 6.Jayaraman, P., Whittle, J., Elkhodary, A.M., Gomaa, H.: Model composition in product lines and feature interaction detection using critical pair analysis. In: Engels, G., Opdyke, B., Schmidt, D.C., Weil, F. (eds.) MODELS 2007. LNCS, vol. 4735, pp. 151–165. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75209-7_11 CrossRefGoogle Scholar
- 8.Lambers, L.: Certifying rule-based models using graph transformation. Ph.D thesis. Berlin Institute of Technology (2010)Google Scholar
- 11.Verigraph: Verigraph. https://github.com/Verites/verigraph
- 14.Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: 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, Volume 1: Foundations, pp. 163–245. World Scientific, Singapore (1997)CrossRefGoogle Scholar
- 15.Arendt, T., Biermann, E., Jurack, S., Krause, C., Taentzer, G.: Henshin: advanced concepts and tools for in-place EMF model transformations. In: Petriu, D.C., Rouquette, N., Haugen, Ø. (eds.) MODELS 2010. LNCS, vol. 6394, pp. 121–135. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16145-2_9. http://www.eclipse.org/henshin/ CrossRefGoogle Scholar