Abstract
We study the problem of effective controller synthesis for finite-state Markov decision processes (MDPs) and the class of properties definable in the logic PCTL extended with long-run average propositions. We show that the existence of such a controller is decidable, and we give an algorithm which computes the controller if it exists. We also address the issue of “controller robustness”, i.e., the problem whether there is a controller which still guarantees the satisfaction of a given property when the probabilities in the considered MDP slightly deviate from their original values. From a practical point of view, this is an important aspect since the probabilities are often determined empirically and hence they are inherently imprecise. We show that the existence of robust controllers is also decidable, and that such controllers are effectively computable if they exist.
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References
Baier, C., Größer, M., Leucker, M., Bollig, B., Ciesinski, F.: Controller synthesis for probabilistic systems. In: Proceedings of IFIP TCS 2004, Kluwer Academic Publishers, Dordrecht (2004)
Bouyer, P., D’Souza, D., Madhusudan, P., Petit, A.: Timed control with partial observability. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 180–192. Springer, Heidelberg (2003)
Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. JACM 42(4), 857–907 (1995)
de Alfaro, L.: How to specify and verify the long-run average behavior of probabilistic systems. In: Proceedings of LICS 1998, pp. 454–465. IEEE Computer Society Press, Los Alamitos (1998)
de Alfaro, L., Faella, M., Henzinger, T., Majumdar, R., Stoelinga, M.: The element of surprise in timed games. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 144–158. Springer, Heidelberg (2003)
Grigoriev, D.: Complexity of deciding Tarski algebra. Journal of Symbolic Computation 5(1]-2), 65–108 (1988)
Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6, 512–535 (1994)
Nilim, A., El Ghaoui, L.: Robustness in markov decision problems with uncertain transition matrices. In: Proceedings of NIPS 2003, MIT Press, Cambridge (2003)
Segala, R., Lynch, N.A.: Probabilistic simulations for probabilistic processes. NJC 2(2), 250–273 (1995)
Tarski, A.: A Decision Method for Elementary Algebra and Geometry. Univ. of California Press, Berkeley (1951)
Hunt Jr., W.A., Somenzi, F. (eds.): CAV 2003. LNCS, vol. 2725, pp. 58–64. Springer, Heidelberg (2003)
Zwick, U., Paterson, M.: The complexity of mean payoff games on graphs. TCS 158 1&2, 343–359 (1996)
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Kučera, A., Stražovský, O. (2005). On the Controller Synthesis for Finite-State Markov Decision Processes. In: Sarukkai, S., Sen, S. (eds) FSTTCS 2005: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2005. Lecture Notes in Computer Science, vol 3821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11590156_44
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DOI: https://doi.org/10.1007/11590156_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30495-1
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