Abstract
We consider the problem of computing the value and an optimal strategy for minimizing the expected termination time in one-counter Markov decision processes. Since the value may be irrational and an optimal strategy may be rather complicated, we concentrate on the problems of approximating the value up to a given error ε > 0 and computing a finite representation of an ε-optimal strategy. We show that these problems are solvable in exponential time for a given configuration, and we also show that they are computationally hard in the sense that a polynomial-time approximation algorithm cannot exist unless P=NP.
The full version of this paper can be found at http://arxiv.org/abs/1205.1473 .
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Brázdil, T., Kučera, A., Novotný, P., Wojtczak, D. (2012). Minimizing Expected Termination Time in One-Counter Markov Decision Processes. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31585-5_16
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DOI: https://doi.org/10.1007/978-3-642-31585-5_16
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