Abstract
We present a symbolic extension of dependency graphs by Liu and Smolka in order to model-check weighted Kripke structures against the logic CTL with upper-bound weight constraints. Our extension introduces a new type of edges into dependency graphs and lifts the computation of fixed-points from boolean domain to nonnegative integers in order to cope with the weights. We present both global and local algorithms for the fixed-point computation on symbolic dependency graphs and argue for the advantages of our approach compared to the direct encoding of the model checking problem into dependency graphs. We implement all algorithms in a publicly available tool prototype and evaluate them on several experiments. The principal conclusion is that our local algorithm is the most efficient one with an order of magnitude improvement for model checking problems with a high number of “witnesses”.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Alur, R., Dill, D.: Automata for modeling real-time systems. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990)
Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. In: Benedetto, Sangiovanni-Vincentelli (eds.) [7], pp. 49–62
Andersen, H.R.: Model checking and boolean graphs. Theoretical Computer Science 126(1), 3–30 (1994)
Kasahara Laboratory at Waseda University. Standard task graph set, http://www.kasahara.elec.waseda.ac.jp/schedule/
Bartlett, K.A., Scantlebury, R.A., Wilkinson, P.T.: A note on reliable full-duplex transmission over half-duplex links. Communications of the ACM 12(5), 260–261 (1969)
Behrmann, G., Fehnker, A., Hune, T., Larsen, K.G., Pettersson, P., Romijn, J., Vaandrager, F.W.: Minimum-cost reachability for priced timed automata. In: Benedetto, Sangiovanni-Vincentelli (eds.) [7], pp. 147–161
Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.): HSCC 2001. LNCS, vol. 2034. Springer, Heidelberg (2001)
Bouyer, P., Larsen, K.G., Markey, N.: Model checking one-clock priced timed automata. Logical Methods in Computer Science 4(2) (2008)
Brihaye, T., Bruyère, V., Raskin, J.-F.: Model-checking for weighted timed automata. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT 2004. LNCS, vol. 3253, pp. 277–292. Springer, Heidelberg (2004)
Buchholz, P., Kemper, P.: Model checking for a class of weighted automata. Discrete Event Dynamic Systems 20, 103–137 (2010)
Cassez, F., David, A., Fleury, E., Larsen, K.G., Lime, D.: Efficient on-the-fly algorithms for the analysis of timed games. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 66–80. Springer, Heidelberg (2005)
Chang, E., Roberts, R.: An improved algorithm for decentralized extrema-finding in circular configurations of processes. Commun. of ACM 22(5), 281–283 (1979)
Kwok, Y.-K., Ahmad, I.: Benchmarking and comparison of the task graph scheduling algorithms. Journal of Parallel and Distributed Computing 59(3), 381–422 (1999)
Laroussinie, F., Markey, N., Oreiby, G.: Model-checking timed ATL for durational concurrent game structures. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 245–259. Springer, Heidelberg (2006)
Liu, X., Ramakrishnan, C.R., Smolka, S.A.: Fully local and efficient evaluation of alternating fixed points (Extended abstract). In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 5–19. Springer, Heidelberg (1998)
Liu, X., Smolka, S.A.: Simple linear-time algorithms for minimal fixed points (extended abstract). In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 53–66. Springer, Heidelberg (1998)
Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jensen, J.F., Larsen, K.G., Srba, J., Oestergaard, L.K. (2013). Local Model Checking of Weighted CTL with Upper-Bound Constraints. In: Bartocci, E., Ramakrishnan, C.R. (eds) Model Checking Software. SPIN 2013. Lecture Notes in Computer Science, vol 7976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39176-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-39176-7_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39175-0
Online ISBN: 978-3-642-39176-7
eBook Packages: Computer ScienceComputer Science (R0)