Abstract
Timed automata have an infinite semantics. For verification purposes, one usually uses zone based abstractions w.r.t. the maximal constants to which clocks of the timed automaton are compared. We show that by distinguishing maximal lower and upper bounds, significantly coarser abstractions can be obtained. We show soundness and completeness of the new abstractions w.r.t. reachability. We demonstrate how information about lower and upper bounds can be used to optimise the algorithm for bringing a difference bound matrix into normal form. Finally, we experimentally demonstrate that the new techniques dramatically increases the scalability of the real-time model checker Uppaal.
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., Dill, D.: A theory of timed automata. Theoretical Computer Science (TCS) 126(2), 183–235 (1994)
Abdeddaim, Y., Maler, O.: Job-shop scheduling using timed automata. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 478–492. Springer, Heidelberg (2001)
Behrmann, G., Bouyer, P., Fleury, E., Larsen, K.G.: Static guard analysis in timed automata verification. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 254–277. Springer, Heidelberg (2003)
Bozga, M., Daws, C., Maler, O., Olivero, A., Tripakis, S., Yovine, S.: Kronos: a model-checking tool for real-time systems. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 546–550. Springer, Heidelberg (1998)
Bengtsson, J.: Clocks, DBMs ans States in Timed Systems. PhD thesis, Department of Information Technology, Uppsala University, Uppsala, Sweden (2002)
Bouyer, P.: Timed automata may cause some troubles. Research Report LSV–02–9, Laboratoire Spécification et Vérification, ENS de Cachan, France (2002); Also Available as BRICS Research Report RS-02-35, Aalborg University, Denmark (2002)
Bouyer, P.: Untameable timed automata! In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 620–631. Springer, Heidelberg (2003)
Clarke, E., Grumberg, O., Peled, D.: Model-Checking. The MIT Press, Cambridge (1999)
Dill, D.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990)
Daws, C., Tripakis, S.: Model-checking of real-time reachability properties using abstractions. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 313–329. Springer, Heidelberg (1998)
Larsen, K.G., Larsson, F., Pettersson, P., Yi, W.: Efficient verification of real-time systems: Compact data structure and state-space reduction. In: Proc. 18th IEEE Real-Time Systems Symposium (RTSS 1997), pp. 14–24. IEEE Computer Society Press, Los Alamitos (1997)
Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a nutshell. Journal of Software Tools for Technology Transfer (STTT) 1(1-2), 134–152 (1997)
Rokicki, T.G.: Representing and Modeling Digital Circuits. PhD thesis, Stanford University, Stanford, USA (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Behrmann, G., Bouyer, P., Larsen, K.G., Pelánek, R. (2004). Lower and Upper Bounds in Zone Based Abstractions of Timed Automata. In: Jensen, K., Podelski, A. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2004. Lecture Notes in Computer Science, vol 2988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24730-2_25
Download citation
DOI: https://doi.org/10.1007/978-3-540-24730-2_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21299-7
Online ISBN: 978-3-540-24730-2
eBook Packages: Springer Book Archive