Abstract
An infinite run of a timed automaton is Zeno if it spans only a finite amount of time. Such runs are considered unfeasible and hence it is important to detect them, or dually, find runs that are non-Zeno. Over the years important improvements have been obtained in checking reachability properties for timed automata. We show that some of these very efficient optimizations make testing for Zeno runs costly. In particular we show NP-completeness for the LU-extrapolation of Behrmann et al. We analyze the source of this complexity in detail and give general conditions on extrapolation operators that guarantee a (low) polynomial complexity of Zenoness checking. We propose a slight weakening of the LU-extrapolation that satisfies these conditions.
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
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
Behrmann, G., Bouyer, P., Larsen, K.G., Pelanek, R.: Lower and upper bounds in zone-based abstractions of timed automata. Int. Journal on Software Tools for Technology Transfer 8(3), 204–215 (2006)
Behrmann, G., David, A., Larsen, K.G., Haakansson, J., Pettersson, P., Yi, W., Hendriks, M.: Uppaal 4.0. In: QEST, pp. 125–126. IEEE Computer Society, Los Alamitos (2006)
Bouyer, P.: Forward analysis of updatable timed automata. Formal Methods in System Design 24(3), 281–320 (2004)
Bowman, H., Gómez, R.: How to stop time stopping. Formal Aspects of Computing 18(4), 459–493 (2006)
Bozga, M., Daws, C., Maler, O., Olivero, A., Tripakis, S., Yovine, S.: Kronos: A model-checking tool for real-time systems. In: Vardi, M.Y. (ed.) CAV 1998. LNCS, vol. 1427, pp. 546–550. Springer, Heidelberg (1998)
Dill, D.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) AVMFSS 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990)
Gómez, R., Bowman, H.: Efficient detection of zeno runs in timed automata. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 195–210. Springer, Heidelberg (2007)
Herbreteau, F., Srivathsan, B.: Coarse abstractions make zeno behaviours difficult to detect. CoRR abs/1106.1850 (2011); Extended version with proofs
Herbreteau, F., Srivathsan, B., Walukiewicz, I.: Efficient Emptiness Check for Timed Büchi Automata. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 148–161. Springer, Heidelberg (2010)
Li, G.: Checking timed Büchi automata emptiness using LU-abstractions. In: Ouaknine, J., Vaandrager, F.W. (eds.) FORMATS 2009. LNCS, vol. 5813, pp. 228–242. Springer, Heidelberg (2009)
Tripakis, S.: Verifying progress in timed systems. In: Katoen, J.-P. (ed.) AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, pp. 299–314. Springer, Heidelberg (1999)
Tripakis, S.: Checking timed Büchi emptiness on simulation graphs. ACM Trans. on Computational Logic 10(3) (2009)
Tripakis, S., Yovine, S., Bouajjani, A.: Checking timed Büchi automata emptiness efficiently. Formal Methods in System Design 26(3), 267–292 (2005)
Wang, F.: Redlib for the formal verification of embedded systems. In: ISoLA, pp. 341–346. IEEE, Los Alamitos (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Herbreteau, F., Srivathsan, B. (2011). Coarse Abstractions Make Zeno Behaviours Difficult to Detect. In: Katoen, JP., König, B. (eds) CONCUR 2011 – Concurrency Theory. CONCUR 2011. Lecture Notes in Computer Science, vol 6901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23217-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-23217-6_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23216-9
Online ISBN: 978-3-642-23217-6
eBook Packages: Computer ScienceComputer Science (R0)