Abstract
The paper provides a solution to the fundamental problems of computing the shortest and the longest time taken by a run of a timed automaton from an initial state to a final state. It does so using the difference-bound matrix data structure to represent zones, which is a state-of-the-art heuristic to improve performance over the classical (and somewhat brute-force) region graph abstraction. The solution provided here is conceptually a marked improvement over some earlier work on the problems [16,9], in which repeated guesses (guided by binary search) and multiple model checking queries were effectively but inelegantly and less efficiently used; here only one run of the zone construction is sufficient to yield the answers. The paper then reports on a prototype implementation of the algorithms using Difference Bound Matrices (DBMs), and presents the results of its application on a realistic automatic manufacturing plant.
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References
Alur, R., Dill, D.: A theory of timed automata. TCS, 183–235 (1994)
Behrmann, G., Bouyer, P., Larsen, K.G., Radek, P.: Lower and upper bounds in zone-based abstractions of timed automata. Int. J. Softw. Tools Technol. Transf., 204–215 (2006)
Behrmann, G., Fehnker, A., Hune, T., Larsen, K.G., Pettersson, P., Romijn, J.: Efficient Guiding Towards Cost-Optimality in UPPAAL. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 174–188. Springer, Heidelberg (2001)
Behrmann, G., Larsen, K.G., Rasmussen, J.I.: Beyond liveness: Efficient parameter synthesis for time bounded liveness. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 81–94. Springer, Heidelberg (2005)
Bengtsson, J.E., Yi, W.: Timed automata: Semantics, algorithms and tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) ACPN 2003. LNCS, vol. 3098, pp. 87–124. Springer, Heidelberg (2004)
Bouyer, P.: Forward analysis of updatable timed automata. Form. Methods Syst. Des. 24, 281–320 (2004)
Bryans, J., Bowman, H., Derrick, J.: Model checking stochastic automata. ACM Transactions on Computational Logic (TOCL) 4(4), 452–492 (2003)
Clarke, E.M., Grumberg, O., Peled, D.: Model checking. MIT Press (2001)
Dalsgaard, A.E., Olesen, M.C., Toft, M., Hansen, R.R., Larsen, K.G.: METAMOC: Modular Execution Time Analysis using Model Checking. In: WCET 2010, pp. 113–123 (2010)
Dalsgaard, A.E., Hansen, R.R., Jørgensen, K.Y., Larsen, K.G., Olesen, M.C., Olsen, P., Srba, J.: opaal: A lattice model checker. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 487–493. Springer, Heidelberg (2011)
Daws, C., Yovine, S.: Two examples of verification of multirate timed automata with kronos. In: Proceedings of the 16th IEEE Real-Time Systems Symposium, RTSS 1995. IEEE Computer Society (1995)
Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Proceedings of the International Workshop on Automatic Verification Methods for Finite State Systems, pp. 197–212. Springer-Verlag New York, Inc. (1990)
Floyd, R.W.: Algorithm 97: Shortest path. Communications of the ACM (1962)
Herbreteau, F., Kini, D., Srivathsan, B., Walukiewicz, I.: Using non-convex approximations for efficient analysis of timed automata. In: FSTTCS (2011)
Horváth, A., Paolieri, M., Ridi, L., Vicario, E.: Transient analysis of non-markovian models using stochastic state classes. Performance Evaluation 69(7), 315–335 (2012)
Metzner, A.: Why model checking can improve WCET analysis. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 334–347. Springer, Heidelberg (2004)
Rokicki, T.G.: Representing and Modeling Digital Circuits. PhD thesis, Stanford University (1993)
Traonouez, L.-M., Lime, D., Roux, O.H.: Parametric model-checking of time petri nets with stopwatches using the state-class graph. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 280–294. Springer, Heidelberg (2008)
Wilhelm, R.: Why AI + ILP is good for WCET, but MC is not, nor ILP alone. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 309–322. Springer, Heidelberg (2004)
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Al-Bataineh, O., Reynolds, M., French, T. (2014). Finding Best and Worst Case Execution Times of Systems Using Difference-Bound Matrices. In: Legay, A., Bozga, M. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2014. Lecture Notes in Computer Science, vol 8711. Springer, Cham. https://doi.org/10.1007/978-3-319-10512-3_4
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DOI: https://doi.org/10.1007/978-3-319-10512-3_4
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