Abstract
Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17,6] and the continuous time setting [4,8]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker (E ⊢ MC 2), where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore we report on first successful applications of the tool to non-trivial examples, highlighting lessons learned during development and application of E ⊢ MC 2.
supported by the German Research Council DFG under HE 1408/6-1.
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M. Ajmone Marsan, G. Conte, and G. Balbo. A class of generalised stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Tr. on Comp. Sys., 2(2): 93–122, 1984. 348, 358
L. de Alfaro, M.Z. Kwiatkowska, G. Norman, D. Parker and R. Segala. Symbolic model checking for probabilistic processes using MTBDDs and the Kronecker representation. In TACAS, LNCS (this volume), 2000. 349
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: 155–165, 1995. 347
A. Aziz, K. Sanwal, V. Singhal and R. Brayton. Verifying continuous time Markov chains. In CAV, LNCS 1102: 269–276, 1996. 347, 348
C. Baier. On algorithmic verification methods for probabilistic systems. Habilitation thesis, Univ. of Mannheim, 1999. 347, 352
C. Baier, E. Clarke, V. Hartonas-Garmhausen, M. Kwiatkowska, and M. Ryan. Symbolic model checking for probabilistic processes. In ICALP, LNCS 1256: 430–440, 1997. 347
C. Baier, B.R. Haverkort, H. Hermanns and J.-P. Katoen. Model checking continuous-time Markov chains by transient analysis. 2000 (submitted). 360
C. Baier, J.-P. Katoen and H. Hermanns. Approximate symbolic model checking of continuous-time Markov chains. In CONCUR, LNCS 1664: 146–162, 1999. 347, 348, 349, 350, 351, 352, 360
C. Baier and M. Kwiatkowska. On the verification of qualitative properties of probabilistic processes under fairness constraints. Inf. Proc. Letters, 66(2): 71–79, 1998. 350, 353
I. Christoff and L. Christoff. Reasoning about safety and liveness properties for probabilistic systems. In FSTTCS, LNCS 652: 342–355, 1992. 347
E.M. Clarke, E.A. Emerson and A.P. Sistla. Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Tr. on Progr. Lang. and Sys., 8(2): 244–263, 1986. 350, 351
A.E. Conway and N.D. Georganas. Queueing Networks — Exact Computational Algorithms. MIT Press, 1989. 348, 355
C. Courcoubetis and M. Yannakakis. Verifying temporal properties of finite-state probabilistic programs. In Proc. IEEE Symp. on Found. of Comp. Sci., pp. 338–345, 1988. 347, 352
D.D. Deavours and W.H. Sanders. An efficient disk-based tool for solving very large Markov models. In Comp. Perf. Ev., LNCS 1245: 58–71, 1997. 352
L. Fredlund. The timing and probability workbench: a tool for analysing timed processes. Tech. Rep. No. 49, Uppsala Univ., 1994. 348
G. Hachtel, E. Macii, A. Padro and F. Somenzi. Markovian analysis of large finite-state machines. IEEE Tr. on CAD of Integr. Circ. and Sys., 15(12): 1479–1493, 1996. 360
H. Hansson and B. Jonsson. A logic for reasoning about time and reliability. Form. Asp. of Comp., 6(5): 512–535, 1994. 347, 348, 352, 353, 360
V. Hartonas-Garmhausen, S. Campos and E.M. Clarke. ProbVerus: probabilistic symbolic model checking. In ARTS, LNCS 1601: 96–111, 1999. 348
B.R. Haverkort. Performance of Computer Communication Systems: A Model-Based Approach. John Wiley & Sons, 1998. 351
B.R. Haverkort and I.G. Niemegeers. Performability modelling tools and techniques. Perf. Ev., 25: 17–40, 1996. 350
H. Hermanns, U. Herzog and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sci., 2000 (to appear). 348
H. Hermanns, U. Herzog, U. Klehmet, V. Mertsiotakis and M. Siegle. Compositional performance modelling with the TIPPtool. Perf. Ev., 39(1–4): 5–35, 2000. 351, 359
H. Hermanns, J. Meyer-Kayser and M. Siegle. Multi-terminal binary decision diagrams to represent and analyse continuous-time Markov chains. In Proc. 3rd Int. Workshop on the Num. Sol. of Markov Chains, pp. 188–207, 1999. 355, 356, 360
J. Hillston. A Compositional Approach to Performance Modelling. Cambridge University Press, 1996. 348
O.C. Ibe and K.S. Trivedi. Stochastic Petri net models of polling systems. IEEE J. on Sel. Areas in Comms., 8(9): 1649–1657, 1990. 358
B. Plateau and K. Atif, Stochastic automata networks for modeling parallel systems. IEEE Tr. on Softw. Eng., 17(10): 1093–1108, 1991. 348
W. Stewart. Introduction to the Numerical Solution of Markov Chains. Princeton Univ. Press, 1994. 348, 349, 350, 351, 355
R.E. Tarjan. Depth-first search and linear graph algorithms. SIAM J. of Comp., 1: 146–160, 1972. 351
M.Y. Vardi. Automatic verification of probabilistic concurrent finite state programs. In Proc. IEEE Symp. on Found. of Comp. Sci., pp. 327–338, 1985. 347
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Hermanns, H., Katoen, JP., Meyer-Kayser, J., Siegle, M. (2000). A Markov Chain Model Checker. In: Graf, S., Schwartzbach, M. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2000. Lecture Notes in Computer Science, vol 1785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46419-0_24
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DOI: https://doi.org/10.1007/3-540-46419-0_24
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