Statistical probabilistic model checking with a focus on time-bounded properties

Information and Computation

Volumn 204, Issue 9, 2006, Pages 1368-1409

  Younes, Håkan L S ^a   Simmons, Reid G ^a  

^a Carnegie Mellon University   (United States)

Author keywords

Acceptance sampling; Hypothesis testing; Probabilistic verification; Stochastic processes; Temporal logic; Transient analysis

Indexed keywords

ACCEPTANCE TESTS; CONTINUOUS TIME SYSTEMS; DISCRETE EVENT SIMULATION; MARKOV PROCESSES; NUMERICAL METHODS; RANDOM PROCESSES; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; TEMPORAL LOGIC; TESTING; TRANSIENT ANALYSIS;

ACCEPTANCE SAMPLING; CONTINUOUS TIME MARKOV CHAIN; HYPOTHESIS TESTING; NUMERICAL SOLUTION METHOD; PROBABILISTIC MODEL CHECKING; PROBABILISTIC VERIFICATION; STATISTICAL HYPOTHESIS TESTING; STOCHASTIC DISCRETE EVENT SYSTEMS;

MODEL CHECKING;

EID: 84855207965     PISSN: 08905401     EISSN: 10902651     Source Type: Journal    
DOI: 10.1016/j.ic.2006.05.002     Document Type: Article

References (71)

1. R. Alur, C. Courcoubetis, D. L. Dill, Model-checking for probabilistic real-time systems, in: J. L. Albert, B. Monien, M. R. Artalejo (Eds.), Proceedings of the 18th International Colloquium on Automata, Languages and Programming, Springer, Berlin, 1991, pp. 115-126.
2. R. Alur, C. Courcoubetis, D. L. Dill, Model-checking in dense real-time, Inform. Comput. 104(1993) 2-34.
3. R. Alur, D. L. Dill, A theory of timed automata, Theoret. Comput. Sci. 126(1994) 183-235.
4. T. W. Anderson, M. Friedman, A limitation of the optimum property of the sequential probability ratio test, in: I. Olkin, S. G. Ghurye, W. Hoeffding, W. G. Madow, H. B. Mann (Eds.), Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling, Stanford University Press, Stanford, California, 1960, pp. 57-69.
5. A. Aziz, K. Sanwal, V. Singhal, R. K. Brayton, Verifying continuous time Markov chains, in: R. Alur, T. A. Henzinger (Eds.), Proceedings of the 8th International Conference on Computer Aided Verification, Springer, Berlin, 1996, pp. 269-276. (Pubitemid 126101287)
6. A. Aziz, K. Sanwal, V. Singhal, R. K. Brayton, Model-checking continuous-time Markov chains, ACM Trans. Comput. Log. 1(2000) 162-170.
7. R. I. Bahar, E. A. Frohm, C. M. Gaona, G. D. Hachtel, E. Macii, A. Pardo, F. Somenzi, Algebraic decision diagrams and their applications, in: Proceedings of the 1993 IEEE ACM International Conference on Computer-Aided Design, IEEE Computer Society Press, Sliver Spring, MD, 1993, pp. 188-191.
8. C. Baier, B. R. Haverkort, H. Hermanns, J.-P. Katoen, Model checking continuous-time Markov chains by transient analysis, in: E. A. Emerson, A. P. Sistla (Eds.), Proceedings of the 12th International Conference on Computer Aided Verification, Springer, Berlin, 2000, pp. 358-372.
9. C. Baier, B. R. Haverkort, H. Hermanns, J.-P. Katoen, Model-checking algorithms for continuous-time Markov chains, IEEE Trans. Softw. Eng. 29(2003) 524-541.
10. C. Baier, J.-P. Katoen, H. Hermanns, Approximate symbolic model checking of continuous-time Markov chains, in: J. C. M. Baeten, S. Mauw (Eds.), Proceedings of the 10th International Conference on Concurrency Theory, Springer, Berlin, 1999, pp. 146-161.
11. M. S. Bartlett, An Introduction to Stochastic Processes with Special Reference to Methods and Applications, second ed., Cambridge University Press, London, 1966.
12. P. Bratley, B. L. Fox, L. E. Schrage, A Guide to Simulation, second ed., Springer, Berlin, 1987.
13. P. Buchholz, J.-P. Katoen, P. Kemper, C. Tepper, Model-checking large structured Markov chains, J. Log. Algebr. Program. 56(2003) 69-97.
14. E. Çinlar, Introduction to Stochastic Processes, Prentice-Hall, Englewood Cliffs, New Jersey, 1975.
15. E. M. Clarke, E. A. Emerson, Design and synthesis of synchronization skeletons using branching time temporal logic, in: D. Kozen (Ed.), Proceedings of the 1981 Workshop on Logics of Programs, Springer, Berlin, 1982, pp. 52-71.
16. E. M. Clarke, E. A. Emerson, A. P. Sistla, Automatic verification of finite-state concurrent systems using temporal logic specifications, ACM Trans. Program. Lang. Syst. 8(1986) 244-263. (Pubitemid 16633197)
17. E. M. Clarke, K. L. McMillan, X. Zhao, M. Fujita, Spectral transforms for large Boolean functions with applications to technology mapping, in: Proceedings of the 30th International Conference on Design Automation, ACM Press, New York, 1993, pp. 54-60.
18. J. L. Doob, Stochastic Processes, Wiley, New York, 1953.
19. A. J. Duncan, Quality Control and Industrial Statistics, fourth ed., Richard D. Irwin, Homewood, Illinois, 1974.
20. E. A. Emerson, A. K. Mok, A. P. Sistla, J. Srinivasan, Quantitative temporalreasoning, Real-Time Syst. 4(1992) 331-352.
21. B. L. Fox, P. W. Glynn, Computing Poisson probabilities, Commun. ACM 31(1988) 440-445.
22. M. Fujita, P. C. McGeer, J. C.-Y. Yang, Multi-terminal binary decision diagrams: an efficient data structure for matrix representation, Formal Methods Syst. Des. 10(1997) 149-169. (Pubitemid 127506985)
23. P. W. Glynn, A GSMP formalism for discrete event systems, Proc. IEEE 77(1989) 14-23.
24. R. Grosu, S. A. Smolka, Monte Carlo model checking, in: N. Halbwachs, L. D. Zuck (Eds.), Proceedings of the 11th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, Springer, Berlin, 2005, pp. 271-286. (Pubitemid 41273747)
25. F. E. Grubbs, On designing single sampling inspection plans, Ann. Math. Stat. 20(1949) 242-256.
26. P. R. Halmos, Measure Theory, Van Nostrand Reinhold Company, New York, 1950.
27. H. Hansson, B. Jonsson, A framework for reasoning about time and reliability, in: Proceedings of the Real-Time Systems Symposium, IEEE Computer Society Press, Sliver Spring, MD, 1989, pp. 102-111.
28. H. Hansson, B. Jonsson, A logic for reasoning about time and reliability, Formal Aspects Comput. 6(1994) 512-535.
29. S. Hart, M. Sharir, Probabilistic temporal logics for finite and bounded models, in: Proceedings of the Sixteenth ACM Symposium on Theory of Computing, ACM SIGACT, 1984, pp. 1-13.
30. C. Hastings Jr., Approximations for Digital Computers, Princeton University Press, Princeton, New Jersey, 1955.
31. B. R. Haverkort, H. Hermanns, J.-P. Katoen, On the use of model checking techniques for dependability evaluation, in: Proceedings of the 19th IEEE Symposium on Reliable Distributed Systems, IEEE Computer Society, Sliver Spring, MD, 2000, pp. 228-237. (Pubitemid 32026844)
32. P. Heidelberger, Fast simulation of rare events in queueing and reliability models, ACM Trans. Model. Comput. Simul. 5(1995) 43-85.
33. H. Hermanns, J. Meyer-Kayser, M. Siegle, Multi terminal binary decision diagrams to represent and analyse continuous time Markov chains, in: B. Plateau, W. J. Stewart, M. Silva (Eds.), Proceedings of the 3rd International Workshop on the Numerical Solution of Markov Chains, Prensas Universitarias de Zaragoza, 1999, pp. 188-207.
34. P. G. Hoel, S. C. Port, C. J. Stone, Introduction to Stochastic Processes, Houghton Mifflin Company, Boston, 1972.
35. R. V. Hogg, A. T. Craig, Introduction to Mathematical Statistics, fourth ed., Macmillan Publishing, New York, 1978.
36. A. Hordijk, D. L. Iglehart, R. Schassberger, Discrete time methods for simulating continuous time Markov chains, Adv. Appl. Probab. 8(1976) 772-788.
37. R. A. Howard, Dynamic probabilistic systems, Markov Models, Wiley, New York, 1971.
38. R. A. Howard, Dynamic probabilistic systems, Semi-Markov and Decision Processes, Wiley, New York, 1971.
39. O. C. Ibe, K. S. Trivedi, Stochastic Petri net models of polling systems, IEEE J. Sel. Areas Commun. 8(1990) 1649-1657.
40. G. G. Infante López, H. Hermanns, J.-P. Katoen, Beyond memoryless distributions: model checking semi-Markov chains, in: L. de Alfaro, S. Gilmore (Eds.), Proceedings of the 1st Joint International PAPM-PROBMIV Workshop, Springer, Berlin, 2001, pp. 57-70. (Pubitemid 33332542)
41. A. Jensen, Markoff chains as an aid in the study of Markoff processes, Scand. Actuar. J. 36(1953) 87-91.
42. J.-P. Katoen, M. Kwiatkowska, G. Norman, D. Parker, Faster and symbolic CTMC model checking, in: L. de Alfaro, S. Gilmore (Eds.), Proceedings of the 1st Joint International PAPM-PROBMIV Workshop, Springer, Berlin, 2001, pp. 23-38. (Pubitemid 33332540)
43. J.-P. Katoen, I. S. Zapreev, Safe on-the-fly steady-state detection for time-bounded reachability, in: Proceedings of the Third International Conference on the Quantitative Evaluation of Systems, IEEE Computer Society, 2006 (in press).
44. A. Kolmogoroff, Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung, Math. Ann. 104(1931) 415-458.
45. M. Kwiatkowska, G. Norman, D. Parker, Probabilistic symbolic model checking with PRISM: a hybrid approach, Int. J. Softw. Tools Techn. Transfer 6(2004) 128-142.
46. M. Kwiatkowska, G. Norman, R. Segala, J. Sproston, Verifying quantitative properties of continuous probabilistic timed automata, in: C. Palamidessi (Ed.), Proceedings of the 11th International Conference on Concurrency Theory, Springer, Berlin, 2000, pp. 123-137.
47. T. L. Lai, Nearly optimal sequential tests of composite hypotheses, Ann. Stat. 16(1988) 856-886.
48. T. L. Lai, Sequential analysis: some classical problems and new challenges, Stat. Sin. 11(2001) 303-408. (Pubitemid 33669754)
49. R. Lassaigne, S. Peyronnet, Approximate verification of probabilistic systems, in: H. Hermanns, R. Segala (Eds.), Proceedings of the 2nd Joint International PAPM-PROBMIV Workshop, Springer, Berlin, 2002, pp. 213-214.
50. M. Malhotra, J. K. Muppala, K. S. Trivedi, Stiffness-tolerant methods for transient analysis of stiff Markov chains, Microelectron. Reliab. 34(1994) 1825-1841. (Pubitemid 124014830)
51. K. Matthes, Zur Theorie der Bedienungsprozesse, in: J. Kožešník (Ed.), Transactions of the Third Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Publishing House of the Czechoslovak Academy of Sciences, 1962, pp. 513-528.
52. W. M. McCormack, R. G. Sargent, Analysis of future event set algorithms for discrete event simulation, Commun. ACM 24(1981) 801-812.
53. D. Michie, "Memo" functions and machine learning, Nature 218(1968) 19-22.
54. D. Parker, Implementation of symbolic model checking for probabilistic systems, Ph. D. thesis, School of Computer Science, University of Birmingham, Birmingham, United Kingdom, 2002.
55. A. Pnueli, The temporal logic of programs, in: Proceedings of the 18th Annual Symposium on Foundations of Computer Science, IEEE Computer Society, Sliver Spring, MD, 1977, pp. 46-57.
56. A. Reibman, K. S. Trivedi, Numerical transient analysis of Markov models, Comput. Oper. Res. 15(1988) 19-36. (Pubitemid 18547006)
57. N. Rescher, A. Urquhart, Temporal Logic, Springer, New York, 1971.
58. G. Schwarz, Asymptotic shapes of Bayes sequential testing regions, Ann. Math. Stat. 33(1962) 224-236.
59. R. Segala, Modeling and verification of randomized distributed real-time systems, Ph. D. thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, MIT-LCS-TR-676, 1995.
60. K. Sen, M. Viswanathan, G. Agha, Statistical model checking of black-box probabilistic systems, in: R. Alur, D. A. Peled (Eds.), Proceedings of the 16th International Conference on Computer Aided Verification, Springer, Berlin, 2004, pp. 202-215.
61. K. Sen, M. Viswanathan, G. Agha, Onstatistical model checkingofstochastic systems, in:K. Etessami, S. K. Rajamani (Eds.), Proceedings of the 17th International Conference on Computer Aided Verification, Springer, Berlin, 2005, pp. 266-280.
62. A. Wald, Sequential tests of statistical hypotheses, Ann. Math. Stat. 16(1945) 117-186.
63. A. Wald, Sequential Analysis, Wiley, New York, 1947.
64. A. Wald, J. Wolfowitz, Optimum character of the sequential probability ratio test, Ann. Math. Stat. 19(1948) 326-339.
65. H. L. S. Younes, Probabilistic verification for "black-box" systems, in: K. Etessami, S. K. Rajamani (Eds.), Proceedings of the 17th International Conference on Computer Aided Verification, Springer, Berlin, 2005, pp. 253-265.
66. H. L. S. Younes, Verification and planning for stochastic processes with asynchronous events, Ph. D. thesis, Computer Science Department, Carnegie Mellon University, Pittsburgh, Pennsylvania, CMU-CS-05-105, 2005.
67. H. L. S. Younes, Ymer: a statistical model checker, in: K. Etessami, S. K. Rajamani (Eds.), Proceedings of the 17th International Conference on Computer Aided Verification, Springer, Berlin, 2005, pp. 429-433. (Pubitemid 41431754)
68. H. L. S. Younes, Error control for probabilistic model checking, in: E. A. Emerson, K. S. Namjoshi (Eds.), Proceedings of the 7th International Conference on Verification, Model Checking, and abstrcr Interpretation, Springer, Berlin, 2006, pp. 142-156. (Pubitemid 43973664)
69. H. L. S. Younes, M. Kwiatkowska, G. Norman, D. Parker, Numerical vs. statistical probabilistic model checking, Int. J. Softw. Tools Techn. Transfer 8(2006) 216-228. (Pubitemid 44445181)
70. H. L. S. Younes, D. J. Musliner, Probabilistic plan verification through acceptance sampling, in: F. Kabanza, S. Thiébaux (Eds.), Proceedings of the AIPS-02 Workshop on Planning via Model Checking, 2002, pp. 81-88.
71. H. L. S. Younes, R. G. Simmons, Probabilistic verification of discrete event systems using acceptance sampling, in: E. Brinksma, K. G. Larsen (Eds.), Proceedings of the 14th International Conference on Computer Aided Verification, Springer, Berlin, 2002, pp. 223-235.