[BFK08]
T. Brázdil, V. Forejt and A. Kučera.
Controller Synthesis and Verification for Markov Decision Processes with Qualitative Branching Time Objectives.
In L. Aceto, I. Damgaard, L. Goldberg, M. Halldórsson, A. Ingólfsdóttir and I. Walukiewicz (editors), Proc. 35th Int. Colloq. Automata, Languages and Programming, Part II (ICALP'08), volume 5126 of LNCS, pages 148-159, Springer.
2008.
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Notes:
The original publication is available at link.springer.com.
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Abstract.
We show that the controller synthesis and verification problems for
Markov decision processes with qualitative PECTL∗ objectives are 2-EXPTIME
complete. More precisely, the algorithms are polynomial in the size of a given
Markov decision process and doubly exponential in the size of a given qualitative
PECTL∗ formula. Moreover, we show that if a given qualitative PECTL∗ objective is achievable by some strategy, then it is also achievable by an effectively
constructible one-counter strategy, where the associated complexity bounds are
essentially the same as above. For the fragment of qualitative PCTL objectives,
we obtain EXPTIME completeness and the algorithms are only singly exponential in the size of the formula.
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