Approximate symbolic model checking of continuous-time Markov chains

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1664 LNCS, Issue , 1999, Pages 146-161

  Baier, Christel ^a   Katoen, Joost Pieter ^b,c   Hermanns, Holger ^c  

^a UNIVERSITY OF MANNHEIM   (Germany)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^c UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER CIRCUITS; CONTINUOUS TIME SYSTEMS; INTEGRAL EQUATIONS; MARKOV PROCESSES; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

CONTINUOUS STOCHASTIC LOGIC; CONTINUOUS TIME MARKOV CHAIN; MODEL CHECKING PROBLEM; NUMERICAL INTEGRATIONS; STEADY STATE PROBABILITIES; SYMBOLIC MODEL CHECKING; SYSTEM OF LINEAR EQUATIONS; VOLTERRA INTEGRAL EQUATIONS;

MODEL CHECKING;

EID: 41149144239     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-48320-9_12     Document Type: Conference Paper

References (27)

1. A. Aziz, K. Sanwal, V. Singhal and R. Brayton. Verifying continuous time Markov chains. In CAV, LNCS 1102, pp. 269-276, 1996.
2. A. Aziz, V. Singhal, F. Balarin, R. Brayton and A. Sangiovanni- Vincentelli. It usually works: the temporal logic of stochastic systems. In CAV, LNCS 939, pp. 155-165, 1995.
3. I. Bahar, E. Frohm, C. Gaona, G. Hachtel, E. Macii, A. Padro and F. Somenzi. Algebraic decision diagrams and their applications. Formal Methods in System Design, 10(2/3): 171-206, 1997.
4. C. Baier. On algorithmic verification methods for probabilistic systems. Habilitation thesis (submitted), Univ. Mannheim, 1998.
5. C. Baier, E. Clarke, V. Hartonas-Garmhausen, M. Kwiatkowska, and M. Ryan. Symbolic model checking for probabilistic processes. In ICALP, LNCS 1256, pp. 430-440, 1997.
6. C. Baier and M. Kwiatkowska. Model checking for a probabilistic branching-time logic with fairness. Distr. Comp., 11(3): 125-155, 1998.
7. D. Beauquier and A. Slissenko. Polytime model checking for timed probabilistic computation tree logic. Acta Inf., 35: 645-664, 1998.
8. A. Bianco and L. de Alfaro. Model checking of probabilistic and nondeterministic systems. In FSTTCS, LNCS 1026, pp. 499-513, 1995.
9. R. Bryant. Graph-based algorithms for boolean function manipulation. IEEE Trans. on Comp., C-35(8): 677-691, 1986.
10. W. Chan, R. Anderson, P. Beame, S. Burns, F. Modugno, D. Notkin and J.D. Reese. Model checking large software specifications. IEEE Trans. on Softw. Eng., 24(7): 498-519, 1998.
11. I. Christoff and L. Christoff. Reasoning about safety and liveness properties for probabilistic systems. In FSTTCS, LNCS 652, pp 342-355, 1992.
12. E. Clarke, M. Fujita, P. McGeer, J. Yang and X. Zhao. Multi-terminal binary decision diagrams: an efficient data structure for matrix representation. In Proc. IEEE Int. Workshop on Logic Synthesis, pp. 1-15, 1993.
13. E. Clarke, O. Grumberg and D. Long. Verification tools for finite-state concurrent programs. In A Decade of Concurrency, LNCS 803, pp. 124-175, 1993.
14. C. Courcoubetis and M. Yannakakis. Verifying temporal properties of finite-state probabilistic programs. In FOCS, pp. 338-345, 1988.
15. C. Courcoubetis and M. Yannakakis. The complexity of probabilistic verification. J. ACM, 42(4): 857-907, 1995.
16. L. de Alfaro. How to specify and verify the long-run average behavior of probabilistic systems. In LICS, 1998.
17. L. de Alfaro. Stochastic transition systems. In CONCUR, LNCS 1466, pp. 423-438, 1998.
18. G. Hachtel, E. Macii, A. Padro and F. Somenzi. Markovian analysis of large finitestate machines. IEEE Trans. on Comp. Aided Design of Integr. Circ. and Sys., 15(12): 1479-1493, 1996.
19. H. Hansson and B. Jonsson. A logic for reasoning about time and probability. Form. Asp. of Comp., 6: 512-535, 1994.
20. V. Hartonas-Garmhausen, S. Campos and E.M. Clarke. ProbVerus: probabilistic symbolic model checking. In Formal Methods for Real-Time and Probabilistic Systems (ARTS), LNCS 1601, pp. 96-110, 1999.
21. H. Hermanns. Interactive Markov Chains. Ph.D thesis, U. Erlangen-Nürnberg, 1998.
22. H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Sci. of Comp. Programming, 1999.
23. A. Pnueli, L. Zuck. Probabilistic verification. Inf. and Comp., 103,: 1-29, 1993.
24. W. Press, B. Flannery, S. Teukolsky and W. Vetterling. Numerical Recipes in C: The Art of Scientific Computing. Cambridge Univ. Press, 1989.
25. W. Stewart. Introduction to the Numerical Solution of Markov Chains. Princeton Univ. Press, 1994.
26. K.S. Trivedi, J.K. Muppala, S.P. Woolet, and B.R. Haverkort. Composite performance and dependability analysis. Performance Evaluation, 14: 197-215, 1992.
27. M.Y. Vardi. Automatic verification of probabilistic concurrent finite state programs. In FOCS, pp 327-338, 1985.