Abstract
Probabilistic timed automata are an extension of timed automata with discrete probability distributions. In previous work, a probabilistic notion of time divergence for probabilistic timed automata has been considered, which requires the divergence of time with probability 1. We show that this notion can lead to cases in which the probabilistic timed automaton satisfies a correctness requirement by making an infinite number of probabilistic transitions in a finite amount of time. To avoid such cases, we consider strict time divergence which concerns the divergence of time over all paths, rather than time divergence of paths with probability 1. We present new model-checking algorithms for probabilistic timed automata both for probabilistic and strict divergence. The algorithms have the same complexity as the previous model-checking algorithms for probabilistic timed automata.
Supported in part by the MIUR-PRIN project PaCo - Performability-Aware Computing: Logics, Models and Languages.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Clarke, E.M., Grumberg, O., Peled, D.: Model checking. MIT Press, Cambridge (1999)
Alur, R., Dill, D.L.: A theory of timed automata. TCS 126(2), 183–235 (1994)
Alur, R., Courcoubetis, C., Dill, D.L.: Model-checking for probabilistic real-time systems. In: Leach Albert, J., Monien, B., Rodríguez-Artalejo, M. (eds.) ICALP 1991. LNCS, vol. 510, pp. 115–136. Springer, Heidelberg (1991)
Hansson, H.A., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6(5), 512–535 (1994)
de Alfaro, L.: Formal verification of probabilistic systems. PhD thesis, Stanford University, Department of Computer Science (1997)
Kwiatkowska, M., Norman, G., Segala, R., Sproston, J.: Automatic verification of real-time systems with discrete probability distributions. TCS 286, 101–150 (2002)
Baier, C., Haverkort, B., Hermanns, H., Katoen, J.P.: Model-checking algorithms for continuous-time Markov chains. TSE 29(6), 524–541 (2003)
Donatelli, S., Haddad, S., Sproston, J.: Model checking stochastic and timed properties with CSLTA. TSE 35(2), 224–240 (2009)
Chen, T., Han, T., Katoen, J.-P., Mereacre, A.: Quantitative model checking of continuous-time Markov chains against timed automata specifications. In: Proc. LICS 2009. IEEE, Los Alamitos (2009)
Jensen, H.E.: Model checking probabilistic real time systems. In: Proc. of the 7th Nordic Work. on Progr. Theory, Chalmers Institute of Technology, pp. 247–261 (1996)
Kwiatkowska, M., Norman, G., Parker, D., Sproston, J.: Performance analysis of probabilistic timed automata using digital clocks. FMSD 29, 33–78 (2006)
Alur, R., Courcoubetis, C., Dill, D.L.: Model-checking in dense real-time. I & C 104(1), 2–34 (1993)
Henzinger, T., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model checking for real-time systems. I & C 111(2), 193–244 (1994)
Tripakis, S., Yovine, S., Bouajjani, A.: Checking timed Büchi automata emptiness efficiently. FMSD 26(3), 267–292 (2005)
Laroussinie, F., Sproston, J.: State explosion in almost-sure probabilistic reachability. IPL 102(6), 236–241 (2007)
Kwiatkowska, M., Norman, G., Sproston, J., Wang, F.: Symbolic model checking for probabilistic timed automata. I & C 205(7), 1027–1077 (2007)
Baier, C., Kwiatkowska, M.: Model checking for a probabilistic branching time logic with fairness. Dist. Comp. 11(3), 125–155 (1998)
Baier, C.: On the algorithmic verification of probabilistic systems, Habilitation thesis, Universität Mannheim (1998)
Chatterjee, K., Henzinger, T.A., Prabhu, V.S.: Trading infinite memory for uniform randomness in timed games. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 87–100. Springer, Heidelberg (2008)
Beauquier, D.: On probabilistic timed automata. TCS 292(1), 65–84 (2003)
Alur, R., Henzinger, T.: Real-Time System = Discrete System + Clock Variables. STTT 1, 86–109 (1997)
de Alfaro, L., Faella, M., Henzinger, T.A., Majumdar, R., Stoelinga, M.: The element of surprise in timed games. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 144–158. Springer, Heidelberg (2003)
Kemeny, J.G., Snell, J.L., Knapp, A.W.: Denumerable Markov Chains, 2nd edn. Graduate Texts in Mathematics. Springer, Heidelberg (1976)
Jurdziński, M., Laroussinie, F., Sproston, J.: Model checking probabilistic timed automata with one or two clocks. LMCS 4(3), 1–28 (2008)
Bianco, A., Alfaro, L.d.: Model checking of probabilistic and nondeterministic systems. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 499–513. Springer, Heidelberg (1995)
Chatterjee, K., Jurdziński, M., Henzinger, T.: Simple stochastic parity games. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol. 2803, pp. 100–113. Springer, Heidelberg (2003)
Alur, R., Henzinger, T., Kupferman, O.: Alternating-time temporal logic. JACM 49, 672–713 (2002)
Fecher, H., Huth, M., Piterman, N., Wagner, D.: Hintikka games for PCTL on labeled Markov chains. In: Proc. QEST 2008, pp. 169–178. IEEE, Los Alamitos (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sproston, J. (2009). Strict Divergence for Probabilistic Timed Automata. In: Bravetti, M., Zavattaro, G. (eds) CONCUR 2009 - Concurrency Theory. CONCUR 2009. Lecture Notes in Computer Science, vol 5710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04081-8_41
Download citation
DOI: https://doi.org/10.1007/978-3-642-04081-8_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04080-1
Online ISBN: 978-3-642-04081-8
eBook Packages: Computer ScienceComputer Science (R0)