ICGT 2012: Graph Transformations pp 66-80 | Cite as
Pattern-Based Graph Abstraction
Abstract
We present a new abstraction technique for the exploration of graph transformation systems with infinite state spaces. This technique is based on patterns, simple graphs describing structures of interest that should be preserved by the abstraction. Patterns are collected into pattern graphs, layered graphs that capture the hierarchical composition of smaller patterns into larger ones. Pattern graphs are then abstracted to a finite universe of pattern shapes by collapsing equivalent patterns. This paper shows how the application of production rules can be lifted to pattern shapes, resulting in an over-approximation of the original system behaviour and thus enabling verification on the abstract level.
Keywords
Simple Graph Graph Transformation Pattern Graph Rule Application Pattern ShapePreview
Unable to display preview. Download preview PDF.
References
- 1.Baldan, P., Corradini, A., König, B.: A Static Analysis Technique for Graph Transformation Systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 381–395. Springer, Heidelberg (2001)CrossRefGoogle Scholar
- 2.Bauer, J.: Analysis of Communication Topologies by Partner Abstraction. PhD thesis, Universität des Saarlandes (2006)Google Scholar
- 3.Bauer, J., Boneva, I., Kurban, M., Rensink, A.: A modal-logic based graph abstraction. In: [7]Google Scholar
- 4.Bauer, J., Wilhelm, R.: Static Analysis of Dynamic Communication Systems by Partner Abstraction. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 249–264. Springer, Heidelberg (2007)CrossRefGoogle Scholar
- 5.Becker, B., Beyer, D., Giese, H., Klein, F., Schilling, D.: Symbolic invariant verification for systems with dynamic structural adaptation. In: ICSE. ACM (2006)Google Scholar
- 6.de Lara, J., Varro, D. (eds.): GraBaTs. ECEASST, vol. 32. EASST (2010)Google Scholar
- 7.Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds.): ICGT 2008. LNCS, vol. 5214. Springer, Heidelberg (2008)MATHGoogle Scholar
- 8.Ghamarian, A.H., de Mol, M., Rensink, A., Zambon, E., Zimakova, M.: Modelling and analysis using groove. STTT 14(1) (2012)Google Scholar
- 9.Ghamarian, A.H., Rensink, A., Jalali, A.: Incremental pattern matching in graph-based state space exploration. In: [6]Google Scholar
- 10.König, B., Kozioura, V.: Counterexample-Guided Abstraction Refinement for the Analysis of Graph Transformation Systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 197–211. Springer, Heidelberg (2006)CrossRefGoogle Scholar
- 11.König, B., Kozioura, V.: Augur 2 - a new version of a tool for the analysis of graph transformation systems. ENTCS 211 (2008)Google Scholar
- 12.Rensink, A.: The GROOVE Simulator: A Tool for State Space Generation. In: Pfaltz, J.L., Nagl, M., Böhlen, B. (eds.) AGTIVE 2003. LNCS, vol. 3062, pp. 479–485. Springer, Heidelberg (2004)CrossRefGoogle Scholar
- 13.Rensink, A.: Canonical Graph Shapes. In: Schmidt, D. (ed.) ESOP 2004. LNCS, vol. 2986, pp. 401–415. Springer, Heidelberg (2004)CrossRefGoogle Scholar
- 14.Rensink, A., Distefano, D.: Abstract graph transformation. In: Workshop on Software Verification and Validation (SVV). ENTCS, vol. 157 (2006)Google Scholar
- 15.Rensink, A., Zambon, E.: Neighbourhood abstraction in groove. In: [6]Google Scholar
- 16.Rensink, A., Zambon, E.: Pattern-based graph abstraction (extended version). Technical report, University of Twente, Enschede, The Netherlands (2012)Google Scholar
- 17.Rieger, S., Noll, T.: Abstracting complex data structures by hyperedge replacement. In: [7]Google Scholar
- 18.Sagiv, S., Reps, T.W., Wilhelm, R.: Parametric shape analysis via 3-valued logic. ToPLaS 24(3) (2002)Google Scholar
- 19.Saksena, M., Wibling, O., Jonsson, B.: Graph Grammar Modeling and Verification of Ad Hoc Routing Protocols. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 18–32. Springer, Heidelberg (2008)CrossRefGoogle Scholar
- 20.Zambon, E., Rensink, A.: Graph subsumption in abstract state space exploration. In: GRAPHITE (Pre-proceedings) (2012)Google Scholar