Abstract
In this paper we propose a timed abstraction, called acceleration, for the analysis of NCTAs, a class of networks of timed automata tailored to model systems composed out of non-deterministic cyclic agents updating shared variables. The abstraction is based on “maximal action zones”, easy to compute on the fly, which generally aggregate regions in a different way than classical zones do. The original and accelerated semantics are shown coherent in the sense that they both lead to the same untimed semantics, and satisfy the same class of positive reachability queries.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Note that, since \(L_i\cap L_j=\emptyset \) when \(i\ne j\), \(T_i\cap T_j=\emptyset \) too, so that each location or transition belongs to a single agent, avoiding confusions in the model.
- 2.
Operator X is irrelevant here since there is no true “next” state when time may evolve continuously.
- 3.
Typically, it will be \((\mathbb {R},\sup )\) or \((\mathbb {R},\inf )\).
- 4.
In particular, that means that \(g(s)\wedge g(s)=g(s)\) and \(\wedge g(S_1\cup S_2)=(\wedge g(S_1))\wedge (\wedge g(S_2))\) for any reachable state s and state sets \(S_1,S_2\).
References
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)
Arcile, J.: Sources of the MAPTs models and exploration algorithms. https://forge.ibisc.univ-evry.fr/jarcile/MAPTs/. Accessed 11 Oct 2019
Arcile, J.: Conception, modélisation et vérification formelle d’un système temps-réel d’agents coopératifs: application aux véhicules autonomes communicants. PhD thesis, Université Paris-Saclay, France; préparée à l’Université d’Evry-Val-d’Essonne: https://www.biblio.univ-evry.fr/theses/2019/2019SACLE029.pdf (2019)
Arcile, J., Devillers, R., Klaudel, H.: VerifCar: a framework for modeling and model checking communicating autonomous vehicles. Auton. Agent. Multi-Agent Syst. 33(3), 353–381 (2019). https://doi.org/10.1007/s10458-019-09409-x
Arcile, J., Devillers, R.R., Klaudel, H.: Dynamic exploration of multi-agent systems with periodic timed tasks. Fundam. Informaticae 175(1–4), 59–95 (2020)
Arcile, J., Devillers, R., Klaudel, H.: Models for dynamic exploration of the state spaces of autonomous vehicles. In: Proceedings of the International Workshop on Petri Nets and Software Engineering co-located with 41st International Conference on Application and Theory of Petri Nets and Concurrency (PETRI NETS 2020), Paris, France, June 24, 2020 (due to COVID-19: virtual conference), pp. 29–48 (2020)
Behrmann, G., Bengtsson, J., David, A., Larsen, K.G., Pettersson, P., Yi, W.: UPPAAL implementation secrets. In: Damm, W., Olderog, E.-R. (eds.) FTRTFT 2002. LNCS, vol. 2469, pp. 3–22. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45739-9_1
Behrmann, G., Bouyer, P., Larsen, K.G., Pelánek, R.: Lower and upper bounds in zone-based abstractions of timed automata. Int. J. Softw. Tools Technol. Transfer 8(3), 204–215 (2006). https://doi.org/10.1007/s10009-005-0190-0
Bengtsson, J., 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). https://doi.org/10.1007/978-3-540-27755-2_3
Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press (2001)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)
Daws, C., Olivero, A., Tripakis, S., Yovine, S.: The tool Kronos. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) HS 1995. LNCS, vol. 1066, pp. 208–219. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0020947
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). https://doi.org/10.1007/BFb0054180
Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-52148-8_17
Elliott, D., Keen, W., Miao, L.: Recent advances in connected and automated vehicles. J. Traffic Transp. Eng. (English Edition) 6(2), 109–131 (2019)
Jamroga, W., Konikowska, B., Kurpiewski, D., Penczek, W.: Multi-valued verification of strategic ability. Fundam. Informaticae 175(1–4), 207–251 (2020)
Moler, C.: Pentium division bug documents. MATLAB Central File Exchange (2021)
Pommereau, F.: ZINC: a compiler for “any language”-coloured Petri nets. IBISC, university of Evry/Paris-Saclay, Technical report (2018)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature
About this chapter
Cite this chapter
Arcile, J., Devillers, R., Klaudel, H. (2024). An Efficient State Space Construction for a Class of Timed Automata. In: Koutny, M., Bergenthum, R., Ciardo, G. (eds) Transactions on Petri Nets and Other Models of Concurrency XVII. Lecture Notes in Computer Science(), vol 14150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-68191-6_10
Download citation
DOI: https://doi.org/10.1007/978-3-662-68191-6_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-68190-9
Online ISBN: 978-3-662-68191-6
eBook Packages: Computer ScienceComputer Science (R0)