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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 and Dominik WOJTCZAK. One-Counter Markov Decision Processes. In \textit{Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms}. Neuveden: SIAM, 2010, p.~863-874. ISBN~978-0-89871-698-6.
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