Numerical vs. statistical probabilistic model checking

International Journal on Software Tools for Technology Transfer

Volumn 8, Issue 3, 2006, Pages 216-228

  Younes, Håkan L S ^a   Kwiatkowska, Marta ^b   Norman, Gethin ^b   Parker, David ^b  

^a Carnegie Mellon University   (United States)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Hypothesis testing; Markov chains; Temporal logic; Transient analysis; Uniformisation

Indexed keywords

EID: 33747766605     PISSN: 14332779     EISSN: 14332787     Source Type: Journal    
DOI: 10.1007/s10009-005-0187-8     Document Type: Conference Paper

References (37)

1. Alur, R., Henzinger, T.A.: Reactive modules. Formal Methods Syst. Des. 15 (1), 7-48 (1999)
2. Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Verifying continuous time Markov chains. In: Alur, R., Henzinger, T.A. (eds.) Proceedings of the 8th International Conference on Computer-Aided Verification. Lecture Notes in Computer Science, vol. 1102, pp. 269-276. Springer, Berlin Heidelberg New York (1996)
3. Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Modelchecking continuous-time Markov chains. ACM Trans. Comput. Logic 1 (1), 162-170 (2000)
4. Bahar, R.I., Frohm, E.A., Gaona, C.M., Hachtel, G.D., Macii, E., Pardo, A., Somenzi, F.: Algebraic decision diagrams and their applications. In: Proceedings of the IEEE/ACM International Conference on Computer-Aided Design, pp. 188-191. IEEE Press, New York (1993)
5. Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: Model checking continuous-time Markov chains by transient analysis. In: Emerson, E.A., Sistla, A.P. (eds.) Proceedings of the 12th International Conference on Computer-Aided Verification, Lecture Notes in Computer Science, vol. 1855, pp. 358-372. Springer, Berlin Heidelberg New York (2000)
6. Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: Model-checking algorithms for continuous-time Markov chains. IEEE Trans Softw. Eng. 29 (6), 524-541 (2003)
7. Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. C-35 (8), 677-691 (1986)
8. Buchholz, P.: A new approach combining simulation and randomization for the analysis of large continuous time Markov chains. ACM Trans. Model. Comput. Simulat. 8 (2), 194-222 (1998)
9. Clarke, E.M., McMillan, K.L., Zhao, X., Fujita, M.: Spectral transforms for large Boolean functions with applications to technology mapping. In: Proceedings of the 30th International Conference on Design Automation, pp. 54-60. ACM Press, New York (1993)
10. Fox, B.L.: Numerical methods for transient Markov chains. Technical Report No. 810. School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY (1988)
11. Fox, B.L., Glynn, P.W.: Computing Poisson probabilities. Commun. ACM 31 (4), 440-445 (1988)
12. Fujita, M., McGeer, P.C., Yang, J.C.-Y.: Multiterminal binary decision diagrams: An efficient data structure for matrix representation. Formal Methods Syst. Des. 10 (2/3), 149-169 (1997)
13. Hermanns, H., Meyer-Kayser, J., Siegle, M.: Multi terminal binary decision diagrams to represent and analyse continuous time Markov chains. In: Plateau, B., Stewart, W.J., Silva, M. (eds.) Proceedings of the 3rd International Workshop on the Numerical Solution of Markov Chains, pp. 188-207. Prensas Universitarias de Zaragoza (1999)
14. Hogg, R.V., Craig, A.T.: Introduction to Mathematical Statistics, 4th edn. Macmillan, New York (1978)
15. Ibe, O.C., Trivedi, K.S.: Stochastic Petri net models of polling systems. IEEE J. Select. Areas Commun. 8 (9), 1649-1657 (1990)
16. Infante López, G.G., Hermanns, H., Katoen, J.-P.: Beyond memoryless distributions: Model cDecking semi-Markov chains. In: de Alfaro, L., Gilmore, S. (eds.) Proceedings of the 1st Joint International PAPM-PROBMIV Workshop. Lecture Notes in Computer Science, vol. 2165, pp. 57-70. Springer, Berlin Heidelberg New York (2001)
17. Jensen, A.: Markoff chains as an aid in the study of Markoff processes. Skandinavisk Aktuarietidskrift 36, 87-91 (1953)
18. Katoen, J.-P., Kwiatkowska, M., Norman, G., Parker, D.: Faster and symbolic CTMC model checking. In: De Alfaro, L., Gilmore, S. (eds.) Proceedings of the 1st Joint International PAPM-PROBMIV Workshop. Lecture Notes in Computer Science, vol. 2165, pp. 23-38. Springer, Berlin Heidelberg New York (2001)
19. Kwiatkowska, M., Norman, G., Parker, D.: PRISM: Probabilistic symbolic model checker. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) Proceedings of the 12th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation. Lecture Notes in Computer Science, vol. 2324, pp. 200-204. Springer, Berlin Heidelberg New York (2002)
20. Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic symbolic model checking with PRISM: A hybrid approach. Int. J. Softw. Tools Technol. Transfer 6 (2), 128-142 (2004)
21. Kwiatkowska, M., Norman, G., Segala, R., Sproston, J.: Verifying quantitative properties of continuous probabilistic timed automata. In: Palamidessi, C. (ed.) Proceedings of the 11th International Conference on Concurrency Theory. Lecture Notes in Computer Science, vol. 1877, pp. 123-137. Springer, Berlin Heidelberg New York (2000)
22. Lai, T.L.: Nearly optimal squential tests of composite hypotheses. Ann. Stat. 16 (2), 856-886 (1988)
23. Lai, T.L.: SequSntial analysis: some classical problems and new challenges. Statistica Sinica 11 (2), 303-408 (2001)
24. Malhotra, M., Muppala, J.K., Trivedi, K.S.: Stiffnesstolerant methods for transient analysis of stiff Markov chains. Microelectron. Reliabil. 34 (11), 1825-1841 (1994)
25. Parker, D.: Implementation of symbolic model checking for probabilistic systems. PhD Thesis, University of Birmingham (2002)
26. Reibman, A., Trivedi, K.S.: Numerical transient analysis of Markov models. Comput. Operat. Res. 15 (1), 19-36 (1988)
27. Schwarz, G.: Asymptotic shapes of Bayes sequential testing regions. Ann. Math. Stat. 33 (1), 224-236 (1962)
28. Sen, K., Viswanathan, M., Agha, G.: Statistical model checking of black-box probabilistic systems. In: Alur, R., Peled, D.A. (eds.) Proceedings of the 16th International Conference on Computer-Aided Verification. Lecture Notes in Computer Science, vol. 3114, pp. 202-215. Springer, Berlin Heidelberg New York (2004)
29. Shanthikumar, J.G., Sargent, R.G.: A unifying view of hybrid simulation/ analytic models and modeling. Operat. Res. 31 (6), 1030-1052 (1983)
30. Stewart,W.J.: A comparison of numerical techniques in Markov modeling. Commun. ACM 21 (2), 144-152 (1978)
31. Teichroew, D., Lubin, J.F.: Computer simulation - Discussion of the techniques and comparison of languages. Commun. ACM 9 (10), 723-741 (1966)
32. Wald, A.: Sequential tests of statistical hypotheses. Ann. Math. Stat. 16 (2), 117-186 (1945)
33. Wald, A.: Sequential Analysis. Wiley, New York (1947)
34. Wald, A., Wolfowitz, J.: Optimum character of the sequential probability ratio test. Ann. Math. Stat. 19 (3), 326-339 (1948)
35. Younes, H.L.S.: Probabilistic verification for "black-box" systems. In: Etessami, K., Rajamani, S. (eds.) Proceedings of the 17th International Conference on Computer-Aided Verification. Springer, Berlin Heidelberg New York (2005)
36. Younes, H.L.S., Musliner, D.J., Simmons, R.G.: A framework for planning in continuous-time stochastic domains. In: Giunchiglia, E., Muscettola, N., Nau, D.S. (eds.) Proceedings of the 13th International Conference on Automated Planning and Scheduling, pp. 195-204. AAAI Press, Meno Park, CA (2003)
37. Younes, H.L.S., Simmons, R.G.: Probabilistic verification of discrete event systems using acceptance sampling. In: Brinksma, E., Larsen, K.G. (eds.) Proceedings of the 14th International Conference on Computer-Aided Verification. Lecture Notes in Computer Science, vol. 2404, pp. 223-235. Springer, Berlin Heidelberg New York (2002)