Abstract
Directed model checking is a well-established technique to tackle the state explosion problem when the aim is to find error states in large systems. In this approach, the state space traversal is guided through a function that estimates the distance to nearest error states. States with lower estimates are preferably expanded during the search. Obviously, the challenge is to develop distance functions that are efficiently computable on the one hand and as informative as possible on the other hand. In this paper, we introduce the causal graph structure to the context of directed model checking. Based on causal graph analysis, we first adapt a distance estimation function from AI planning to directed model checking. Furthermore, we investigate an abstraction that is guaranteed to preserve error states. The experimental evaluation shows the practical potential of these techniques.
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References
Brafman, R.I., Domshlak, C.: Structure and complexity in planning with unary operators. Journal of Artificial Intelligence Research 18, 315–349 (2003)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press, Cambridge (2000)
Dierks, H.: Comparing model-checking and logical reasoning for real-time systems. Formal Aspects of Computing 16(2), 104–120 (2004)
Dräger, K., Finkbeiner, B., Podelski, A.: Directed model checking with distance-preserving abstractions. In: Valmari, A. (ed.) SPIN 2006. LNCS, vol. 3925, pp. 19–34. Springer, Heidelberg (2006)
Edelkamp, S., Leue, S., Lluch-Lafuente, A.: Directed explicit-state model checking in the validation of communication protocols. International Journal on Software Tools for Technology Transfer 5(2), 247–267 (2004)
Edelkamp, S., Lluch-Lafuente, A., Leue, S.: Directed explicit model checking with HSF-SPIN. In: Dwyer, M.B. (ed.) SPIN 2001. LNCS, vol. 2057, pp. 57–79. Springer, Heidelberg (2001)
Helmert, M.: A planning heuristic based on causal graph analysis. In: Zilberstein, S., Koehler, J., Koenig, S. (eds.) Proceedings of the 14th International Conference on Automated Planning and Scheduling (ICAPS 2004), pp. 161–170. AAAI Press, Menlo Park (2004)
Helmert, M.: The Fast Downward planning system. Journal of Artificial Intelligence Research 26, 191–246 (2006)
Helmert, M., Geffner, H.: Unifying the causal graph and additive heuristics. In: Rintanen, J., Nebel, B., Beck, J.C., Hansen, E. (eds.) Proceedings of the 18th International Conference on Automated Planning and Scheduling (ICAPS 2008). AAAI Press, Menlo Park (2008)
Hoffmann, J., Smaus, J.-G., Rybalchenko, A., Kupferschmid, S., Podelski, A.: Using predicate abstraction to generate heuristic functions in Uppaal. In: Edelkamp, S., Lomuscio, A. (eds.) MoChArt IV. LNCS, vol. 4428, pp. 51–66. Springer, Heidelberg (2007)
Kozen, D.: Lower bounds for natural proof systems. In: Proceedings of the 18th Annual Symposium on Foundations of Computer Science (FOCS 1977), pp. 254–266. IEEE Computer Society, Los Alamitos (1977)
Krieg-Brückner, B., Peleska, J., Olderog, E.-R., Baer, A.: The UniForM workbench, a universal development environment for formal methods. In: Woodcock, J.C.P., Davies, J., Wing, J.M. (eds.) FM 1999. LNCS, vol. 1709, pp. 1186–1205. Springer, Heidelberg (1999)
Kupferschmid, S., Hoffmann, J., Dierks, H., Behrmann, G.: Adapting an AI planning heuristic for directed model checking. In: Valmari, A. (ed.) SPIN 2006. LNCS, vol. 3925, pp. 35–52. Springer, Heidelberg (2006)
Kupferschmid, S., Hoffmann, J., Larsen, K.G.: Fast directed model checking via russian doll abstraction. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 203–217. Springer, Heidelberg (2008)
Kupferschmid, S., Wehrle, M., Nebel, B., Podelski, A.: Faster than Uppaal? In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 552–555. Springer, Heidelberg (2008)
Lamport, L.: A fast mutual exclusion algorithm. ACM Transactions on Computer Systems 5(1), 1–11 (1987)
Pearl, J.: Heuristics: Intelligent search strategies for computer problem solving. Addison-Wesley, Reading (1984)
Qian, K., Nymeyer, A.: Guided invariant model checking based on abstraction and symbolic pattern databases. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 497–511. Springer, Heidelberg (2004)
Seitz, C.L.: Ideas about arbiters. Lambda 1, 10–14 (1980)
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Wehrle, M., Helmert, M. (2009). The Causal Graph Revisited for Directed Model Checking. In: Palsberg, J., Su, Z. (eds) Static Analysis. SAS 2009. Lecture Notes in Computer Science, vol 5673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03237-0_8
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DOI: https://doi.org/10.1007/978-3-642-03237-0_8
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