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@inproceedings{875871, author = {Brázdil, Tomáš and Brožek, Václav and Etessami, Kousha and Kučera, Antonín and Wojtczak, Dominik}, address = {Neuveden}, booktitle = {Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms}, keywords = {Markov decision proces; probability; one counter MDP; reachability; termination}, language = {eng}, location = {Neuveden}, isbn = {978-0-89871-698-6}, pages = {863-874}, publisher = {SIAM}, title = {One-Counter Markov Decision Processes}, url = {http://www.siam.org/proceedings/soda/2010/SODA10_070_brazdilt.pdf}, year = {2010} }
TY - JOUR ID - 875871 AU - Brázdil, Tomáš - Brožek, Václav - Etessami, Kousha - Kučera, Antonín - Wojtczak, Dominik PY - 2010 TI - One-Counter Markov Decision Processes PB - SIAM CY - Neuveden SN - 9780898716986 KW - Markov decision proces KW - probability KW - one counter MDP KW - reachability KW - termination UR - http://www.siam.org/proceedings/soda/2010/SODA10_070_brazdilt.pdf N2 - We study One-Counter Markov Decision Processes (OC-MDPs), which extend finite-state MDPs with an unbounded counter. The counter can be incremented, decremented, or not changed during each state transition. Basic objectives for OC-MDPs include ``termination'' (Does the OC-MDP reach counter 0?) and ``limit'' questions (Is the limsup value infinity?). We may ask what is the optimal probability of such objectives, or ask for the existence and synthesis of optimal strategies. We show that several quantitative and almost-sure limit problems can be answered in polynomial time, and that almost-sure termination problems (without selection of desired terminal states) can also be answered in polynomial time. On the other hand, we show that the almost-sure termination problem with selected terminal states is PSPACE-hard and we provide an exponential time algorithm for this problem. We also characterize classes of strategies that suffice for optimality in several of these settings. ER -
BRÁZDIL, Tomáš, Václav BROŽEK, Kousha ETESSAMI, Antonín KUČERA a Dominik WOJTCZAK. One-Counter Markov Decision Processes. In \textit{Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms}. Neuveden: SIAM, 2010, s.~863-874. ISBN~978-0-89871-698-6.
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