Abstract
While offering significant expressive power, graph transformation systems often come with rather limited capabilities for automated analysis, particularly if systems with many possible initial graphs and large or infinite state spaces are concerned. One approach that tries to overcome these limitations is inductive invariant checking. However, the verification of inductive invariants often requires extensive knowledge about the system in question and faces the approach-inherent challenges of locality and lack of context.
To address that, this paper discusses k-inductive invariant checking for graph transformation systems as a generalization of inductive invariants. The additional context acquired by taking multiple (k) steps into account is the key difference to inductive invariant checking and is often enough to establish the desired invariants without requiring the iterative development of additional properties.
To analyze possibly infinite systems in a finite fashion, we introduce a symbolic encoding for transformation traces using a restricted form of nested application conditions. As its central contribution, this paper then presents a formal approach and algorithm to verify graph constraints as k-inductive invariants. We prove the approach’s correctness and demonstrate its applicability by means of several examples evaluated with a prototypical implementation of our algorithm.
This work was partially developed in the course of the project Correct Model Transformations II (GI 765/1-2), which is funded by the Deutsche Forschungsgemeinschaft.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
To allow verification without forward propagation, Theorem 21 can be modified by considering all \( seq \in {\text {Seq}}_k(\mathcal {R}, \mathcal {F})\) instead of all \({\text {prop}}( seq ) \in {\text {Seq}}_k(\mathcal {R}, \mathcal {F})\).
- 2.
Setup: 64-bit system, two cores at 2.8 GHz, 8 GB main memory, Eclipse 4.5.1, Java 8, Windows 7. Java heap space limit was set to 1 GB, with the exception of variant 4 with forward propagation and \(k = 6\), which required 4 GB.
References
Becker, B., Beyer, D., Giese, H., Klein, F., Schilling, D.: Symbolic invariant verification for systems with dynamic structural adaptation. In: Proceedings of the 28th International Conference on Software Engineering (ICSE). ACM, New York (2006)
Blume, C., Bruggink, H.J.S., Engelke, D., König, B.: Efficient symbolic implementation of graph automata with applications to invariant checking. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2012. LNCS, vol. 7562, pp. 264–278. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33654-6_18
Boneva, I.B., Kreiker, J., Kurban, M.E., Rensink, A., Zambon, E.: Graph abstraction and abstract graph transformations (amended version). Technical report TR-CTIT-12-26, University of Twente, Enschede (2012)
Donaldson, A.F., Haller, L., Kroening, D., Rümmer, P.: Software verification using k-induction. In: Yahav, E. (ed.) SAS 2011. LNCS, vol. 6887, pp. 351–368. Springer, Heidelberg (2011). doi:10.1007/978-3-642-23702-7_26
Dyck, J., Giese, H.: Inductive invariant checking with partial negative application conditions. In: Parisi-Presicce, F., Westfechtel, B. (eds.) ICGT 2015. LNCS, vol. 9151, pp. 237–253. Springer, Cham (2015). doi:10.1007/978-3-319-21145-9_15
Dyck, J., Giese, H.: k-Inductive Invariant Checking for Graph Transformation Systems. Technical report, University of Potsdam (2017)
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Springer, Secaucus (2006)
Ehrig, H., Golas, U., Habel, A., Lambers, L., Orejas, F.: \(\cal{M}\)-adhesive transformation systems with nested application conditions. part 1: parallelism, concurrency and amalgamation. Math. Struct. Comput. Sci. 24, 1–48 (2014)
Ghamarian, A.H., de Mol, M.J., Rensink, A., Zambon, E., Zimakova, M.V.: Modelling and analysis using GROOVE. Int. J. Softw. Tools Technol. Transf. 14(1), 15–40 (2012)
Habel, A., Pennemann, K.-H.: Correctness of high-level transformation systems relative to nested conditions. Math. Struct. Comput. Sci. 19, 1–52 (2009)
König, B., Kozioura, V.: Augur 2 - a new version of a tool for the analysis of graph transformation systems. Electron. Notes Theoret. Comput. Sci. 211, 201–210 (2008)
König, B., Stückrath, J.: A general framework for well-structured graph transformation systems. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 467–481. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44584-6_32
Pennemann, K.-H.: Development of correct graph transformation systems. Ph.D. thesis, University of Oldenburg (2009)
Schmidt, Á., Varró, D.: CheckVML: a tool for model checking visual modeling languages. In: Stevens, P., Whittle, J., Booch, G. (eds.) UML 2003. LNCS, vol. 2863, pp. 92–95. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45221-8_8
Sheeran, M., Singh, S., Stålmarck, G.: Checking safety properties using induction and a SAT-solver. In: Hunt, W.A., Johnson, S.D. (eds.) FMCAD 2000. LNCS, vol. 1954, pp. 127–144. Springer, Heidelberg (2000). doi:10.1007/3-540-40922-X_8
Steenken, D.: Verification of infinite-state graph transformation systems via abstraction. Ph.D. thesis, University of Paderborn (2015)
Acknowledgments
We would like to thank Leen Lambers for her comprehensive feedback on a draft version of this paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Dyck, J., Giese, H. (2017). k-Inductive Invariant Checking for Graph Transformation Systems. In: de Lara, J., Plump, D. (eds) Graph Transformation. ICGT 2017. Lecture Notes in Computer Science(), vol 10373. Springer, Cham. https://doi.org/10.1007/978-3-319-61470-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-61470-0_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-61469-4
Online ISBN: 978-3-319-61470-0
eBook Packages: Computer ScienceComputer Science (R0)