ICGT 2010: Graph Transformations pp 27-42 | Cite as
Graph Transformation Units Guided by a SAT Solver
Abstract
Graph transformation units are rule-based devices to model graph algorithms, graph processes, and the dynamics of systems the states of which are represented by graphs. Given a graph, various rules are applicable at various matches in general, but not any choice leads to a proper result so that one faces the problem of nondeterminism. As countermeasure, graph transformation units provide the generic concept of control conditions which allow one to cut down the nondeterminism and to choose the proper rule applications out of all possible ones. In this paper, we propose an alternative approach. For a special type of graph transformation units including the solution of many NP-complete and NP-hard problems, the successful derivations from initial to terminal graphs are described by propositional formulas. In this way, it becomes possible to use a SAT solver to find out whether there is a successful derivation for some initial graph or not and how it is built up in the positive case.
Keywords
Transformation Unit Regular Expression Graph Transformation Propositional Formula Rule ApplicationPreview
Unable to display preview. Download preview PDF.
References
- 1.Biere, A., Cimatti, A., Clarke, E., Fujita, M., Zhu, Y.: Symbolic model checking using SAT procedures instead of BDDs. In: Design Automation Conf., pp. 317–320 (1999)Google Scholar
- 2.Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2009)Google Scholar
- 3.Carnegie Mellon University, Graph Coloring Instances, http://mat.gsia.cmu.edu/COLOR/instances.html:
- 4.Cook, S.A.: The complexity of theorem-proving procedures. In: Proc. Third ACM Symposium on Theory of Computing, pp. 151–158 (1971)Google Scholar
- 5.Corradini, A., Ehrig, H., Heckel, R., Löwe, M., Montanari, U., Rossi, F.: Algebraic approaches to graph transformation part I: Basic concepts and double pushout approach. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation. Foundations, vol. 1, pp. 163–245. World Scientific, Singapore (1997)CrossRefGoogle Scholar
- 6.Eén, N., Sörensson, N.: An extensible SAT solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)CrossRefGoogle Scholar
- 7.Ehrig, H., Ehrig, K., Prange, U., Taentzer, G. (eds.): Fundamentals of Algebraic Graph Transformation. Springer, Heidelberg (2006)MATHGoogle Scholar
- 8.Ganai, M., Gupta, A.: SAT-Based Scalable Formal Verification Solutions. Series on Integrated Circuits and Systems. Springer, Heidelberg (2007)MATHCrossRefGoogle Scholar
- 9.Hölscher, K., Klempien-Hinrichs, R., Knirsch, P.: Undecidable control conditions in graph transformation units. Electronic Notes in Theoretical Computer Science 195, 95–111 (2008)CrossRefGoogle Scholar
- 10.Kreowski, H.-J., Kuske, S.: Graph transformation units with interleaving semantics. Formal Aspects of Computing 11(6), 690–723 (1999)MATHCrossRefGoogle Scholar
- 11.Kreowski, H.-J., Kuske, S., Rozenberg, G.: Graph transformation units – an overview. In: Degano, P., De Nicola, R., Meseguer, J. (eds.) Concurrency, Graphs and Models. LNCS, vol. 5065, pp. 57–75. Springer, Heidelberg (2008)CrossRefGoogle Scholar
- 12.Kuske, S.: More about control conditions for transformation units. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) TAGT 1998. LNCS, vol. 1764, pp. 323–337. Springer, Heidelberg (2000)Google Scholar
- 13.Litovski, I., Métivier, Y., Sopena, É.: Graph relabelling systems and distributed algorithms. In: Ehrig, H., Kreowski, H.-J., Montanari, U., Rozenberg, G. (eds.) Handbook of Graph Grammars and Computing by Graph Transformation. Concurrency, Parallelism, and Distribution, vol. 3, pp. 1–56. World Scientific, Singapore (1999)Google Scholar
- 14.Marques-Silva, J., Lynce, I.: Towards robust CNF encodings of cardinality constraints. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 483–497. Springer, Heidelberg (2007)CrossRefGoogle Scholar
- 15.Soeken, M., Wille, R., Kuhlmann, M., Gogolla, M., Drechsler, R.: Verifying UML/OCL models using Boolean satisfiability. In: Design, Automation and Test in Europe, pp. 1341–1344 (2010)Google Scholar
- 16.Tseitin, G.: On the complexity of derivation in propositional calculus. In: Studies in Constructive Mathematics and Mathematical Logic, Part 2, pp. 115–125 (1968); Reprinted in: Siekmann, J., Wrightson, G. (eds.): Automation of Reasoning, vol. 2, pp. 466–483. Springer, Berlin (1983)Google Scholar