Abstract
This paper explores how to reason locally about global properties of graph transformations, in particular properties involving transitive closure of the edge relations of the graph. We show under which conditions we can soundly reduce reasoning about all nodes in the graph to reasoning about a finite set of nodes. We then give an effective procedure to turn this reduced problem into a Boolean satisfiability problem.
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Asztalos, M., Lengyel, L., Levendovszky, T.: Towards automated, formal verification of model transformations. In: Proc. of the 3rd International Conference on Software Testing, Verification, and Validation, pp. 15–24. IEEE Computer Society, Los Alamitos (2010)
Baldan, P., Corradini, A., Esparza, J., Heindel, T., König, B., Kozioura, V.: Verifying red-black trees. In: Proc. of Concurrent Systems with Dynamic Allocated Heaps, COSMICAH 2005 (2005); Proceedings available as report RR-05-04 (Queen Mary, University of London)
Baldan, P., Corradini, A., König, B.: A framework for the verification of infinite-state graph transformation systems. Information and Computation 206(7), 869–907 (2008)
Berdine, J., Calcagno, C., O’Hearn, P.: A decidable fragment of separation logic. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 97–109. Springer, Heidelberg (2004)
Caferra, R., Echahed, R., Peltier, N.: A term-graph clausal logic: Completeness and incompleteness results. Journal of Applied Non-classical Logics 18(4), 373–411 (2008)
da Costa, S.A., Ribeiro, L.: Formal verification of graph grammars using mathematical induction. In: Proc. of the 11th Brazilian Symposium on Formal Methods (SBMF 2008). ENTCS, vol. 240, pp. 43–60. Elsevier (2009)
Dodds, M.: Graph Transformation and Pointer Structures. Ph.D. thesis, University of York (2008)
Ghamarian, A.H., de Mol, M.J., Rensink, A., Zambon, E., Zimakova, M.V.: Modelling and analysis using GROOVE. Tech. Rep. TR-CTIT-10-18, Centre for Telematics and Information Technology, University of Twente, Enschede (2010)
Habel, A., Pennemann, K.H.: Correctness of high-level transformation systems relative to nested conditions. Mathematical Structures in Computer Science 19(02), 245–296 (2009)
Immerman, N., Rabinovich, A., Reps, T., Sagiv, M., Yorsh, G.: The Boundary Between Decidability and Undecidability for Transitive-Closure Logics. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 160–174. Springer, Heidelberg (2004)
Kastenberg, H.: Graph-Based Software Specification and Verification. Ph.D. thesis, University of Twente (2008), http://eprints.eemcs.utwente.nl/13615/
König, B., Kozioura, V.: Augur 2 – A new version of a tool for the analysis of graph transformation systems. In: Proc. of the 5th Int. Workshop on Graph Transformation and Visual Modeling Techniques. ENTCS, vol. 211, pp. 201–210. Elsevier (2008)
McPeak, S., Necula, G.C.: Data Structure Specifications via Local Equality Axioms. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 476–490. Springer, Heidelberg (2005)
Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Pennemann, K.H.: Resolution-Like Theorem Proving for High-Level Conditions. In: Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds.) ICGT 2008. LNCS, vol. 5214, pp. 289–304. Springer, Heidelberg (2008)
Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: Proc. of the 17th Annual IEEE Symposium on Logic in Computer Science, pp. 55–74. IEEE Computer Society (2002)
Ribeiro, L., Dotti, F.L., da Costa, S.A., Dillenburg, F.C.: Towards theorem proving graph grammars using Event-B. In: Ermel, C., Ehrig, H., Orejas, F., Taentzer, G. (eds.) Proc. of the International Colloquium on Graph and Model Transformation 2010. ECEASST, vol. 30 (2010)
Strecker, M.: Modeling and verifying graph transformations in proof assistants. In: Mackie, I., Plump, D. (eds.) International Workshop on Computing with Terms and Graphs. ENTCS, vol. 203, pp. 135–148. Elsevier (2008)
Varró, D., Balogh, A.: The model transformation language of the VIATRA2 framework. Science of Computer Programming 68(3), 214–234 (2007)
Yorsh, G., Rabinovich, A.M., Sagiv, M., Meyer, A., Bouajjani, A.: A logic of reachable patterns in linked data-structures. The Journal of Logic and Algebraic Programming 73(1-2), 111–142 (2007)
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Strecker, M. (2012). Locality in Reasoning about Graph Transformations. In: Schürr, A., Varró, D., Varró, G. (eds) Applications of Graph Transformations with Industrial Relevance. AGTIVE 2011. Lecture Notes in Computer Science, vol 7233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34176-2_15
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DOI: https://doi.org/10.1007/978-3-642-34176-2_15
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