Top

Published in:

2016 | OriginalPaper | Chapter

Parameter Synthesis for Parametric Interval Markov Chains

Authors : Benoît Delahaye, Didier Lime, Laure Petrucci

Published in: Verification, Model Checking, and Abstract Interpretation

Publisher: Springer Berlin Heidelberg

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Interval Markov Chains (IMCs) are the base of a classic probabilistic specification theory introduced by Larsen and Jonsson in 1991. They are also a popular abstraction for probabilistic systems. In this paper we study parameter synthesis for a parametric extension of Interval Markov Chains in which the endpoints of intervals may be replaced with parameters. In particular, we propose constructions for the synthesis of all parameter values ensuring several properties such as consistency and consistent reachability in both the existential and universal settings with respect to implementations. We also discuss how our constructions can be modified in order to synthesise all parameter values ensuring other typical properties.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Reward-Bounded Reachability Probability for Uncertain Weighted MDPs

next chapter Pointer Race Freedom

André, É., Fribourg, L., Sproston, J.: An extension of the inverse method to probabilistic timed automata. Formal Meth. Syst. Des. 42(2), 119–145 (2013)MATHCrossRef

Barbuti, R., Levi, F., Milazzo, P., Scatena, G.: Probabilistic model checking of biological systems with uncertain kinetic rates. Theor. Comput. Sci. 419, 2–16 (2012)MATHMathSciNetCrossRef

Benedikt, M., Lenhardt, R., Worrell, J.: LTL model checking of interval markov chains. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013 (ETAPS 2013). LNCS, vol. 7795, pp. 32–46. Springer, Heidelberg (2013)CrossRef

Bertrand, N., Fournier, P.: Parameterized verification of many identical probabilistic timed processes. FSTTCS. LIPIcs 24, 501–513 (2013)MathSciNet

Bertrand, N., Fournier, P., Sangnier, A.: Playing with probabilities in reconfigurable broadcast networks. In: Muscholl, A. (ed.) FOSSACS 2014 (ETAPS). LNCS, vol. 8412, pp. 134–148. Springer, Heidelberg (2014)CrossRef

Biondi, F., Legay, A., Nielsen, B.F., Wąsowski, A.: Maximizing entropy over markov processes. In: Dediu, A.-H., Martín-Vide, C., Truthe, B. (eds.) LATA 2013. LNCS, vol. 7810, pp. 128–140. Springer, Heidelberg (2013)CrossRef

Caillaud, B., Delahaye, B., Larsen, K., Legay, A., Pedersen, M., Wasowski, A.: Constraint markov chains. Theor. Comput. Sci. 412(34), 4373–4404 (2011)MATHMathSciNetCrossRef

Chakraborty, S., Katoen, J.-P.: Model checking of open interval markov chains. In: Remke, A., Manini, D., Gribaudo, M. (eds.) ASMTA 2015. LNCS, vol. 9081, pp. 30–42. Springer, Heidelberg (2015)CrossRef

Chamseddine, N., Duflot, M., Fribourg, L., Picaronny, C., Sproston, J.: Computing expected absorption times for parametric determinate probabilistic timed automata. In: QEST, pp. 254–263. IEEE Computer Society (2008)

10.

Chatterjee, K., Sen, K., Henzinger, T.A.: Model-checking \(\omega \)-regular properties of interval markov chains. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 302–317. Springer, Heidelberg (2008)CrossRef

11.

Daws, C.: Symbolic and parametric model checking of discrete-time markov chains. In: Liu, Z., Araki, K. (eds.) ICTAC 2004. LNCS, vol. 3407, pp. 280–294. Springer, Heidelberg (2005)CrossRef

12.

Dehnert, C., Junges, S., Jansen, N., Corzilius, F., Volk, M., Bruintjes, H., Katoen, J.-P., Ábrahám, E.: PROPhESY: a probabilistic parameter synthesis tool. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 214–231. Springer, Heidelberg (2015)CrossRef

13.

Delahaye, B., Katoen, J., Larsen, K., Legay, A., Pedersen, M., Sher, F., Wasowski, A.: Abstract probabilistic automata. Inf. Comput. 232, 66–116 (2013)MATHMathSciNetCrossRef

14.

Delahaye, B., Larsen, K., Legay, A., Pedersen, M., Wasowski, A.: Consistency and refinement for interval Markov chains. J. Log. Algebr. Program. 81(3), 209–226 (2012)MATHMathSciNetCrossRef

15.

Delahaye, B.: Consistency for parametric interval Markov chains. In: SynCoP, OASIcs, Schloss Dagstuhl (2015)

16.

Delahaye, B., Lime, D., Petrucci, L.: Parameter Synthesis for Parametric Interval Markov Chains. HAL research report hal-01219823 (2015)

17.

Ferrer Fioriti, L.M., Hahn, E.M., Hermanns, H., Wachter, B.: Variable probabilistic abstraction refinement. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 300–316. Springer, Heidelberg (2012)CrossRef

18.

Gori, R., Levi, F.: An analysis for proving probabilistic termination of biological systems. Theor. Comput. Sci. 471, 27–73 (2013)MATHMathSciNetCrossRef

19.

Hahn, E.M., Han, T., Zhang, L.: Synthesis for PCTL in parametric markov decision processes. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 146–161. Springer, Heidelberg (2011)CrossRef

20.

Hahn, E.M., Hermanns, H., Wachter, B., Zhang, L.: \({\sf PARAM}\): a model checker for parametric markov models. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 660–664. Springer, Heidelberg (2010)CrossRef

21.

Hahn, E., Hermanns, H., Zhang, L.: Probabilistic reachability for parametric Markov models. Software Tools for Technology Transfer 13(1), 3–19 (2011)CrossRef

22.

Jonsson, B., Larsen, K.: Specification and refinement of probabilistic processes. In: LICS, pp. 266–277. IEEE Computer (1991)

23.

Lanotte, R., Maggiolo-Schettini, A., Troina, A.: Decidability results for parametric probabilistic transition systems with an application to security. In: SEFM, pp. 114–121. IEEE Computer Society (2004)

24.

Lanotte, R., Maggiolo-Schettini, A., Troina, A.: Parametric probabilistic transition systems for system design and analysis. Formal Aspects Comput. 19(1), 93–109 (2007)MATHCrossRef

25.

Sen, K., Viswanathan, M., Agha, G.: Model-checking markov chains in the presence of uncertainties. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 394–410. Springer, Heidelberg (2006)CrossRef

Title: Parameter Synthesis for Parametric Interval Markov Chains
Authors: Benoît Delahaye
Didier Lime
Laure Petrucci
Publisher: Springer Berlin Heidelberg
Book: Verification, Model Checking, and Abstract Interpretation
Print ISBN: 978-3-662-49121-8

Electronic ISBN: 978-3-662-49122-5

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-662-49122-5_18

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner