Abstract
The branching-time temporal logic PCTL* has been intro- duced to specify quantitative properties over probability systems, such as discrete-time Markov chains. Until now, however, no logics have been defined to specify properties over hidden Markov models (HMMs). In HMMs the states are hidden, and the hidden processes produce a se- quence of observations. In this paper we extend the logic PCTL* to POCTL*. With our logic one can state properties such as “there is at least a 90 percent probability that the model produces a given sequence of observations” over HMMs. Subsequently, we give model checking algorithms for POCTL* over HMMs.
Parts of this work was carried out while the third author was with the Max-Planck- Institut für Informatik, Saarbrüucken. This work is partially supported by the NWO – DFG bilateral project VOSS, the NWO Vernieuwingsimpuls award 016.023.010, and by the DFG as part of the Transregional Collaborative Research Center SFB/TR 14 AVACS.
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Andova, S., Hermanns, H., Katoen, J.-P.: In: Larsen, K.G., Niebert, P. (eds.) FORMATS 2003. LNCS, vol. 2791, pp. 88–104. Springer, Heidelberg (2004)
Baier, C.: On Algorithmic Verifiation Methods for Probabilistic Systems, Habilitations- schrift zur Erlangung der venia legendi der Fakultät für Mathematik and Informatik, Universität Mannheim (1998)
Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: Efficient computation of time-bounded reachability probabilities in uniform continuous-time markov decision processes. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 61–76. Springer, Heidelberg (2004)
Bianco, A., de Alfaro, L.: Model Checking of Probabilistic and Nondeterministic Systems. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 499–513. Springer, Heidelberg (1995)
Birney, E.: Hidden Markov models in biological sequence analysis. IBM Journal of Research and Development 45(3), 449–454 (2001)
Courcoubetis, C., Yannakakis, M.: Verifying Temporal Properties of Finite- State Probabilistic Programs. In: FOCS, pp. 338–345. IEEE Computer Society Press, Los Alamitos (October 1988)
Courcoubetis, C., Yannakakis, M.: The Complexity of Probabilistic Verification. Journal of the ACM 42(4), 857–907 (1995)
de Alfaro, L.: Formal Verification of Probabilistic Systems. PhD thesis, Stanford University, Technical report STAN-CS-TR-98-1601 (1997)
François, J.-M., Leduc, G.: Mobility prediction’s in°uence on QoS in wireless networks: A study on a call admission algorithm. In: 3rd International Symposium on Modeling and Optimization in Mobile, Ad-Hoc and Wireless Networks, pp. 238–247. IEEE Computer Society, Los Alamitos (2005)
Gerth, R., Peled, D., Vardi, M.Y., Wolper, P.: Simple On-the-fly Automatic Verification of Linear Temporal Logic. In: PSTV, vol. 38, pp. 3–18. Chapman & Hall, Boca Raton (1995)
Hansson, H., Jonsson, B.: A Logic for Reasoning about Time and Reliability. Formal Aspects of Computing 6(5), 512–535 (1994)
Hauskrecht, M.: Value-Function Approximations for Partially Observable Markov Decision Processes. Journal of Artificial Intelligence Research 13, 33–94 (2000)
Jurafsky, D., Martin, J.H.: Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistics, and Speech Recognition. Prentice Hall, Englewood Cliffs (2000)
Nicola, R.D., Vaandrager, F.W.: Action versus state based logics for transition systems. In: Guessarian, I. (ed.) LITP 1990. LNCS, vol. 469, pp. 407–419. Springer, Heidelberg (1990)
Pevzner, P.A.: Computational Molecular Biology: An Algorithmic Approach. The MIT Press, Cambridge (2000)
Poupart, P.: Approximate Value-Directed Belief State Monitoring for Partially Observable Markov Decision Processes. Master’s thesis, University of British Columbia (November 2000)
Rabiner, L.R.: A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition. Proceedings of the IEEE 77(2), 257–286 (1989)
Safra, S.: On the complexity ω-automata. In: FOCS, pp. 319–327 (1988)
Safra, S.: Exponential determinization ω-automata with strong-fairness accep- tance condition. In: STOC, pp. 275–282 (1992)
Salamatian, K., Vaton, S.: Hidden markov modeling for network communication channels. In: SIGMETRICS, pp. 92–101. ACM Press, New York (2001)
Vardi, M.Y., Wolper, P.: An Automata-Theoretic Approach to Automatic Program Verification. In: LICS, pp. 332–345. IEEE Computer Society Press, Los Alamitos (1986)
Vlontzos, J.A., Kung, S.Y.: Hidden Markov models for character recognition. IEEE Transactions on Image Processing 1, 539–543 (1992)
Wolper, P., Vardi, M.Y., Sistla, A.P.: Reasoning about Infinite Computation Paths. In: FOCS 1983, pp. 185–194. IEEE Computer Society Press, Los Alamitos (1982)
Zhang, L., Hermanns, H., Jansen, D.N.: Logic and Model Checking for Hidden Markov Chais. AVACS Technical Report No. 6, SFB/TR 14 AVACS (May 2005) ISSN: 1860-9821, http://www.avacs.org
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Zhang, L., Hermanns, H., Jansen, D.N. (2005). Logic and Model Checking for Hidden Markov Models. In: Wang, F. (eds) Formal Techniques for Networked and Distributed Systems - FORTE 2005. FORTE 2005. Lecture Notes in Computer Science, vol 3731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11562436_9
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