R. Alur and D. L. Dill, Automata for modeling real-time systems, ICALP, p.322335, 1990.
DOI : 10.1007/BFb0032042

R. Alur and D. L. Dill, The theory of timed automata, REX Workshop, p.4573, 1991.

G. Andersson, P. Donalek, R. Farmer, N. Hatziargyriou, I. Kamwa et al., Causes of the 2003 Major Grid Blackouts in North America and Europe, and Recommended Means to Improve System Dynamic Performance, IEEE Transactions on Power Systems, vol.20, issue.4, 2004.
DOI : 10.1109/TPWRS.2005.857942

C. Baier and J. Katoen, Principles of model checking, 2008.

B. Barbot, S. Haddad, and C. Picaronny, Coupling and Importance Sampling for Statistical Model Checking, TACAS'12, 2012.
DOI : 10.1007/978-3-642-28756-5_23

URL : https://hal.archives-ouvertes.fr/hal-00776795

A. Basu, S. Bensalem, M. Bozga, B. Caillaud, B. Delahaye et al., Statistical abstraction and model-checking of large heterogeneous systems, LNCS, vol.6117, p.3246, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01055148

A. Basu, S. Bensalem, M. Bozga, B. Delahaye, A. Legay et al., Verication of an AFDX infrastructure using simulations and probabilities, Proceedings of the First international conference on Runtime verication, RV'10, p.330344, 2010.

A. Basu, S. Bensalem, M. Gallien, F. Ingrand, C. Lesire et al., Incremental componentbased construction and verication of a robotic system, ECAI, 2008.

A. Basu, M. Bozga, and J. Sifakis, Modeling Heterogeneous Real-time Systems in BIP, SEFM06, p.312, 2006.
URL : https://hal.archives-ouvertes.fr/tel-00527491

A. Bauer, M. Leucker, and C. Schallhart, Monitoring of realtime properties, FSTTCS, p.260272, 2006.

E. Leonard and . Baum, An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes, Inequalities, vol.3, p.18, 1972.

E. Leonard, J. A. Baum, and . Eagon, An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology, Bulletin of the American Mathematical Society, vol.73, issue.3, p.360, 1967.

E. Leonard, T. Baum, and . Petrie, Statistical inference for probabilistic functions of nite state Markov chains, The Annals of Mathematical Statistics, vol.37, issue.6, p.15541563, 1966.

L. E. Baum, T. Petrie, G. Soules, and N. Weiss, A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains, The Annals of Mathematical Statistics, vol.41, issue.1, p.164171, 1970.
DOI : 10.1214/aoms/1177697196

E. Leonard, G. R. Baum, and . Sell, Growth transformations for functions on manifolds, Pacic Journal of Mathematics, vol.27, issue.2, p.211227, 1968.

G. Behrmann, A. Fehnker, T. Hune, K. G. Larsen, P. Pettersson et al., Minimum-Cost Reachability for Priced Timed Automata, HSCC, p.147161, 2001.
DOI : 10.7146/brics.v8i3.20457

S. Bensalem, M. Bozga, B. Delahaye, and C. Jegourel, Axel Legay, and journal = Software Tools for Technology Transfer year =, 2014.

S. Bensalem, A. Lavindra-de-silva, F. Griesmayer, A. Ingrand, R. Legay et al., A Formal Approach for Incremental Construction with an Application to Autonomous Robotic Systems, SC'11, 2011.
DOI : 10.1002/rob.20206

S. Bensalem, B. Delahaye, and A. Legay, Statistical model checking: Present and future, RV, 2010.

S. Bensalem, A. L. , and E. A. Thompson, Ayoub Nouri, and Doron Peled. Synthesizing distributed scheduling implementation for probabilistic component-based systems Maximum likelihood alignment of dna sequences, MEMOCODE, 1986.

S. Bliudze and J. Sifakis, The Algebra of Connectors—Structuring Interaction in BIP, IEEE Transactions on Computers, vol.57, issue.10, p.13151330, 2008.
DOI : 10.1109/TC.2008.26

J. Bogdoll, F. Luis-maria, and . Fiorti, Arnd Hartmanns, and Holger Hermanns . Partial order methods for statistical model checking and simulation, 2011.

A. Exible, distributable statistical model checking library, Quantitative Evaluation of Systems, p.160164, 2013.

M. Broy and B. Jonsson, Model-Based Testing of Reactive Systems, Advanced Lectures [The volume is the outcome of a research seminar that was held in Schloss Dagstuhl, Lecture Notes in Computer Science, vol.3472, 2004.

F. Cérou, P. D. Moral, T. Furon, and A. Guyader, Sequential Monte Carlo for rare event estimation, Statistics and Computing, vol.22, p.795808, 2012.

F. Cérou, T. Furon, A. Guyader, and C. Jegourel, Estimating the probability of false alarm for a zero-bit watermarking technique

F. Cérou and A. Guyader, Adaptive multilevel splitting for rare event analysis. Stochastic Analysis and Applications, p.417443, 2007.

H. Chockler, K. Even, and E. Yahav, Finding rare numerical stability errors in concurrent computations, Proceedings of the 2013 International Symposium on Software Testing and Analysis, ISSTA 2013, p.1222, 2013.
DOI : 10.1145/2483760.2483791

H. Chockler, E. Farchi, B. Godlin, and S. Novikov, Crossentropy based testing, FMCAD, p.101108, 2007.

H. Chockler, A. Ivrii, A. Matsliah, S. F. Rollini, and N. Sharygina, Using cross-entropy for satisability, SAC, pp.1196-1203, 2013.

N. Chomsky and M. Schützenberger, The algebraic theory of context-free languages, Studies in Logic and the Foundations of Mathematics, p.118161, 1963.

E. M. Clarke and E. Emerson, Design and synthesis of synchronization skeletons using branching-time temporal logic, Logic of Programs, p.5271, 1981.

E. M. Clarke and P. Zuliani, Statistical model checking for cyberphysical systems, ATVA, p.112, 2011.

P. Cousot and R. Cousot, Abstract interpretation: A unied lattice model for static analysis of programs by construction or approximation of xpoints, POPL, p.238252, 1977.

P. Boer, V. F. Nicola, and R. Y. Rubinstein, Adaptive importance sampling simulation of queueing networks, Winter Simulation Conference, p.646655, 2000.

P. Del and M. , Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications. Probability and Its Applications, 2004.

P. Del, M. , and E. Rio, Concentration inequalities for mean eld particle models, The Annals of Applied Probability, vol.21, p.10171052, 2011.

W. Edsger and . Dijkstra, Guarded commands, nondeterminacy and formal derivation of programs, Commun. ACM, vol.18, issue.8, p.453457, 1975.

L. Joseph and . Doob, What is a stochastic process?, American Mathematical Monthly, vol.49, p.648653, 1942.

L. Joseph and . Doob, Stochastic process, 1953.

E. , A. Emerson, and J. Y. Halpern, Sometimes and Not Never revisited: On branching versus linear time, POPL, p.127140, 1983.

Y. Falcone, M. Jaber, T. Nguyen, M. Bozga, and S. Bensalem, Runtime verication of component-based systems, In SEFM, p.204220, 2011.

Y. Falcone, M. Jaber, T. Nguyen, M. Bozga, and S. Bensalem, Runtime verication of component-based systems in the BIP framework with formally-proved sound and complete instrumentation, p.127, 2013.

B. Finkbeiner and H. Sipma, Checking nite traces using alternating automata, Form. Methods Syst. Des, vol.24, issue.2, p.101127, 2004.

D. Gelperin and B. Hetzel, The growth of software testing, Communications of the ACM, vol.31, issue.6, p.31687695, 1988.
DOI : 10.1145/62959.62965

D. Giannakopoulou and K. Havelund, Automata-based verication of temporal properties on running programs, Proceedings of the 16th IEEE international conference on Automated software engineering, ASE '01, p.412, 2001.

T. Daniel and . Gillespie, Exact stochastic simulation of coupled chemical reactions, Journal of Physical Chemistry, vol.81, p.23402361, 1977.

P. Godefroid, Partial-Order Methods for the Verication of Concurrent Systems -An Approach to the State-Explosion Problem, Lecture Notes in Computer Science, vol.1032, 1996.

P. Godefroid, Model checking for programming languages using VeriSoft, Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages , POPL '97, p.174186, 1997.
DOI : 10.1145/263699.263717

R. Grosu and S. A. Smolka, Monte Carlo Model Checking, TACAS, p.271286, 2005.
DOI : 10.1007/978-3-540-31980-1_18

M. John, D. C. Hammersley, and . Handscomb, Monte Carlo methods, 1964.

S. Hart, M. Sharir, and A. Pnueli, Termination of probabilistic concurrent program, ACM Trans. Program. Lang. Syst, vol.5, issue.3, p.356380, 1983.

K. Havelund and T. Pressburger, Model checking JAVA programs using JAVA PathFinder, International Journal on Software Tools for Technology Transfer (STTT), vol.2, issue.4, p.366381, 2000.
DOI : 10.1007/s100090050043

K. Havelund and G. Rosu, Synthesizing Monitors for Safety Properties, TACAS, LNCS, p.342356, 2002.
DOI : 10.1007/3-540-46002-0_24

P. Heidelberger, Fast simulation of rare events in queueing and reliability models, ACM Transactions on Modeling and Computer Simulation, vol.5, issue.1, p.4385, 1995.
DOI : 10.1145/203091.203094

A. Thomas and . Henzinger, The theory of hybrid automata, LICS

T. A. Henzinger, R. Jhala, R. Majumdar, and G. Sutre, Software verication with BLAST, SPIN, p.235239, 2003.
DOI : 10.1007/3-540-44829-2_17

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

T. Hérault and R. Lassaigne, Frédéric Magniette, and Sylvain Peyronnet Approximate Probabilistic Model Checking, VMCAI, p.7384, 2004.

W. Hoeding, Probability inequalities, Journal of the American Statistical Association, vol.58, p.1330, 1963.

W. Hoeding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, vol.58, issue.301, p.1330, 1963.

G. J. Holzmann, E. Najm, and A. Serhrouchni, SPIN model checking: an introduction, International Journal on Software Tools for Technology Transfer (STTT), vol.2, issue.4, p.321327, 2000.
DOI : 10.1007/s100090050039

T. Homem-de and . Mello, A Study on the Cross-Entropy Method for Rare-Event Probability Estimation, INFORMS Journal on Computing, vol.19, issue.3, p.381394, 2007.
DOI : 10.1287/ijoc.1060.0176

X. Huang, J. Seyster, S. Callanan, K. Dixit, R. Grosu et al., Software monitoring with controllable overhead, International Journal on Software Tools for Technology Transfer, vol.38, issue.2, p.327347, 2012.
DOI : 10.1007/s10009-010-0184-4

. Research-triangle-institute, The economic impacts of inadequate infrastructure for software testing, 2002.

D. N. Jansen, J. Katoen, M. Oldenkamp, M. Stoelinga, and I. S. Zapreev, How Fast and Fat Is Your Probabilistic Model Checker? An Experimental Performance Comparison, HVC
DOI : 10.1007/978-3-540-77966-7_9

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

C. Jegourel, A. Legay, and S. Sedwards, Cross-Entropy Optimisation of Importance Sampling Parameters for Statistical Model Checking, CAV, 2012.
DOI : 10.1007/978-3-642-31424-7_26

URL : https://hal.archives-ouvertes.fr/hal-01087341

C. Jegourel, A. Legay, and S. Sedwards, A Platform for High Performance Statistical Model Checking ??? PLASMA, TACAS, p.498503, 2012.
DOI : 10.1007/978-3-642-28756-5_37

URL : https://hal.archives-ouvertes.fr/hal-01087824

C. Jégourel, A. Legay, and S. Sedwards, Importance Splitting for Statistical Model Checking Rare Properties, CAV, p.576591, 2013.
DOI : 10.1007/978-3-642-39799-8_38

C. Jegourel, A. Legay, and S. Sedwards, An eective heuristic for adaptive importance splitting in statistical model checking, ISoLA, 2014.

A. Jensen, Marko chains as an aid in the study of Marko processes, Scandinavian Actuarial Journal, p.8791, 1953.

S. Juneja and P. Shahabuddin, Fast Simulation of Markov Chains with Small Transition Probabilities, Management Science, vol.47, issue.4, p.547562, 2001.
DOI : 10.1287/mnsc.47.4.547.9827

H. Kahn and . Stochastic, Monte Carlo) Attenuation Analysis, 1949.

H. Kahn and T. E. Harris, Estimation of Particle Transmission by Random Sampling, In Applied Mathematics, vol.5, 1951.

H. Kahn and A. W. Marshall, Methods of Reducing Sample Size in Monte Carlo Computations, Journal of the Operations Research Society of America, vol.1, issue.5, 1953.
DOI : 10.1287/opre.1.5.263

K. Kalajdzic, E. Bartocci, S. A. Smolka, S. D. Stoller, and R. Grosu, Runtime verication with particle ltering, RV, p.149166, 2013.
DOI : 10.1007/978-3-642-40787-1_9

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

K. Kalajdzic, C. Jegourel, E. Bartocci, A. Legay, S. Smolka et al., Model checking as control: Feedback control for statistical model checking of cyber-physical systems, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01087977

J. Katoen and I. S. Zapreev, Simulation-Based CTMC Model Checking: An Empirical Evaluation, 2009 Sixth International Conference on the Quantitative Evaluation of Systems, p.3140, 2009.
DOI : 10.1109/QEST.2009.25

I. S. Joost-pieter-katoen, E. Zapreev, H. Moritz-hahn, D. N. Hermanns, and . Jansen, The ins and outs of the probabilistic model checker MRMC

A. N. Kolmogorov, Grundbegrie der Wahrscheinlichkeitsrechnung, 1933.

M. Krunz, R. Sass, and H. D. Hughes, Statistical characteristics and multiplexing of MPEG streams, Proceedings of INFOCOM'95, p.455462, 1995.
DOI : 10.1109/INFCOM.1995.515909

M. Krunz and S. K. Tripathi, On the characterization of VBR MPEG streams, SIGMETRICS, p.192202, 1997.

S. Kullback, Information Theory and Statistics, 1968.

M. Z. Kwiatkowska, G. Norman, and D. Parker, PRISM: Probabilistic Symbolic Model Checker, Computer Performance Evaluation / TOOLS, p.200204, 2002.
DOI : 10.1007/3-540-46029-2_13

M. Z. Kwiatkowska, G. Norman, and D. Parker, PRISM 2.0: a tool for probabilistic model checking, First International Conference on the Quantitative Evaluation of Systems, 2004. QEST 2004. Proceedings., p.322323, 2004.
DOI : 10.1109/QEST.2004.1348048

A. Lagnoux, RARE EVENT SIMULATION, Probability in the Engineering and Informational Sciences, p.4566, 2006.
DOI : 10.1214/aoap/1034968137

URL : https://hal.archives-ouvertes.fr/hal-00644139

S. Laplante and R. Lassaigne, Frédéric Magniez, Sylvain Peyronnet, and Michel de Rougemont Probabilistic abstraction for model checking: An approach based on property testing, ACM TCS, vol.8, issue.4, 2007.

G. Kim and . Larsen, Verication of timed and hybrid systems, In ICATPN, p.3942, 2000.

K. G. Larsen, P. Pettersson, and W. Yi, Uppaal in a nutshell, International Journal on Software Tools for Technology Transfer, vol.1, issue.1-2, p.134152, 1997.
DOI : 10.1007/s100090050010

A. Legay and B. Delahaye, Statistical model checking : An overview. CoRR, abs, 1005.
DOI : 10.1007/978-3-642-16612-9_11

URL : https://hal.archives-ouvertes.fr/inria-00591593

A. Legay, S. Sedwards, and L. Traonouez, Scalable verication of Markov decision processes, 4th Workshop on Formal Methods in the Development of Software (FMDS 2014), 2014.

D. Lehmann and M. O. Rabin, On the Advantage of Free Choice: A Symmetric and Fully Distributed Solution to the Dining Philosophers Problem (Extended Abstract), Proc. 8th Ann. Symposium on Principles of Programming Languages, p.133138, 1981.

G. Nancy, C. Leveson, and . Turner, Investigation of the therac-25 accidents, IEEE Computer, vol.26, issue.7, p.1841, 1993.

J. Lions, Ariane 501 inquiry board report, 1996.

L. Kenneth and . Mcmillan, Symbolic model checking, Kluwer, 1993.

N. Metropolis and S. Ulam, The Monte Carlo Method, Journal of the American Statistical Association, vol.44, issue.247, p.335341, 1949.
DOI : 10.1080/01621459.1949.10483310

M. Otto and . Nikodym, Sur une généralisation des intégrales de m.j. radon, Fundamenta Mathematicae, vol.15, p.131179, 1930.

A. Nouri, A. Legay, S. Bensalem, and M. Bozga, SBIP: A statistical model checking extension for the BIP framework, First Workshop on Statistical Model Checking, 2013.

M. Okamoto, Some inequalities relating to the partial sum of binomial probabilities, Annals of the Institute of Statistical Mathematics, vol.7, issue.1, p.2935, 1959.
DOI : 10.1007/BF02883985

E. Parzen, Stochastic Processes, 1962.
DOI : 10.1137/1.9781611971125

A. Pnueli, The temporal logic of programs, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977), p.4657, 1977.
DOI : 10.1109/SFCS.1977.32

N. Arthur and . Prior, Time and Modality, 1957.

D. El, R. , and N. Pekergin, Statistical model checking using perfect simulation, ATVA, p.120134, 2009.

R. Lawrence and . Rabiner, A tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE, vol.77, issue.2, p.257286, 1989.

A. Balaji-raman, D. Nouri, M. Gangadharan, A. Bozga, M. Basu et al., Stochastic modeling and performance analysis of multimedia socs, ICSAMOS, p.145154, 2013.

. Daniël-reijsbergen, W. Pieter-tjerk-de-boer, B. Scheinhardt, and . Haverkort, Rare Event Simulation for Highly Dependable Systems with Fast Repairs, 2010 Seventh International Conference on the Quantitative Evaluation of Systems, pp.69336-355, 2012.
DOI : 10.1109/QEST.2010.39

. Daniël-reijsbergen, W. R. Pieter-tjerk-de-boer, B. R. Scheinhardt, and . Haverkort, Rare Event Simulation for Highly Dependable Systems with Fast Repairs, 2010 Seventh International Conference on the Quantitative Evaluation of Systems, p.336355, 2012.
DOI : 10.1109/QEST.2010.39

N. Rescher and A. Urquhart, Temporal Logic, 1971.
DOI : 10.1007/978-3-7091-7664-1

A. Ridder, Importance Sampling Simulations of Markovian Reliability Systems Using Cross-Entropy, Annals of Operations Research, vol.40, issue.7, p.119136, 2005.
DOI : 10.1007/s10479-005-5727-9

A. Ridder, Asymptotic optimality of the cross-entropy method for Markov chain problems, Procedia Computer Science, vol.1, issue.1, pp.1571-1578, 2010.
DOI : 10.1016/j.procs.2010.04.176

P. Christian, G. Robert, and . Casella, Monte Carlo statistical methods, 2004.

G. Rosu and S. Bensalem, Allen linear (interval) temporal logic translation to LTL and monitor synthesis, CAV, p.263277, 2006.

G. Rubino and B. Tun, Rare Event Simulation using Monte Carlo Methods, 2009.
DOI : 10.1002/9780470745403

URL : https://hal.archives-ouvertes.fr/hal-00787654

R. Y. Rubinstein, The Cross-Entropy Method for Combinatorial and Continuous Optimization, p.127190, 1999.

K. Sen, M. Viswanathan, and G. Agha, Statistical Model Checking of Black-Box Probabilistic Systems, CAV, p.202215
DOI : 10.1007/978-3-540-27813-9_16

K. Sen, M. Viswanathan, and G. Agha, On Statistical Model Checking of Stochastic Systems, CAV, p.266280, 2005.
DOI : 10.1007/11513988_26

K. Sen, M. Viswanathan, and G. A. Agha, VESTA: A statistical model-checker and analyzer for probabilistic systems, Second International Conference on the Quantitative Evaluation of Systems (QEST'05), pp.251-252, 2005.
DOI : 10.1109/QEST.2005.42

P. Shahabuddin, Importance Sampling for the Simulation of Highly Reliable Markovian Systems, Management Science, vol.40, issue.3, p.333352, 1994.
DOI : 10.1287/mnsc.40.3.333

E. John, R. W. Shore, and . Johnson, Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy, IEEE Transactions on Information Theory, vol.26, issue.1, p.2637, 1980.

J. Sifakis, A unied approach for studying the properties of transition systems, Theor. Comput. Sci, vol.18, p.227258, 1982.

L. Ruslan and . Stratonovich, Conditional Markov processes. Theory of Probability and its Applications, p.156178, 1960.

M. Y. Vardi, Automatic verication of probabilistic concurrent nite-state programs, FOCS, p.327338, 1985.

M. Y. Vardi, Alternating automata and program verication, Computer Science Today, p.471485, 1995.
DOI : 10.1007/bfb0015261

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

M. Villén-altamirano and J. Villén-altamirano, RESTART: A Method for Accelerating Rare Event Simulations, Queueing, Performance and Control in ATM, p.7176, 1991.

M. Villén-altamirano and J. Villén-altamirano, RESTART: a straightforward method for fast simulation of rare events, Proceedings of Winter Simulation Conference, p.282289, 1994.
DOI : 10.1109/WSC.1994.717150

A. Wald, Sequential tests of statistical hypotheses, Annals of Mathematical Statistics, vol.16, issue.2, p.117186, 1945.

D. Wijesekera and J. Srivastava, Quality of service (QoS) metrics for continuous media, Multimedia Tools and Applications, vol.3, issue.No. 1, p.127166, 1996.
DOI : 10.1007/BF00429748

P. Wolper, Lectures on formal methods and performance analysis. chapter Constructing automata from temporal logic formulas: a tutorial, pp.261-277, 2002.

L. S. Håkan and . Younes, Probabilistic verication for "black-box" systems, CAV, p.253265, 2005.

L. S. Håkan and . Younes, Verication and Planning for Stochastic Processes with Asynchronous Events, 2005.

L. S. Håkan, E. M. Younes, P. Clarke, and . Zuliani, Statistical verication of probabilistic properties with unbounded until, SBMF, p.144160, 2010.

L. S. Håkan, R. G. Younes, and . Simmons, Statistical probabilistic model checking with a focus on time-bounded properties, Inf. Comput, vol.204, issue.9, pp.1368-1409, 2006.

L. S. Håkan and . Younes, YMER: A Statistical Model Checker, LNCS, vol.3576, p.171179

L. S. Håkan, R. G. Younes, and . Simmons, Probabilistic verication of discrete event systems using acceptance sampling, CAV, p.2339

L. Zhang, H. Hermanns, and D. N. Jansen, Logic and Model Checking for Hidden Markov Models, p.98112, 2005.
DOI : 10.1109/83.199925

P. Zuliani, C. Baier, and E. M. Clarke, Rare-event verication for stochastic hybrid systems, In HSCC, p.217226, 2012.

P. Zuliani, A. Platzer, and E. M. Clarke, Bayesian statistical model checking with application to Stateow/Simulink verication. Formal Methods in System Design, p.338367, 2013.