Combinations of Qualitative Winning for Stochastic Parity Games

K. Chatterjee, N. Piterman, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 6.

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Conference Paper | Published | English
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LIPIcs
Abstract
We study Markov decision processes and turn-based stochastic games with parity conditions. There are three qualitative winning criteria, namely, sure winning, which requires all paths to satisfy the condition, almost-sure winning, which requires the condition to be satisfied with probability 1, and limit-sure winning, which requires the condition to be satisfied with probability arbitrarily close to 1. We study the combination of two of these criteria for parity conditions, e.g., there are two parity conditions one of which must be won surely, and the other almost-surely. The problem has been studied recently by Berthon et al. for MDPs with combination of sure and almost-sure winning, under infinite-memory strategies, and the problem has been established to be in NP cap co-NP. Even in MDPs there is a difference between finite-memory and infinite-memory strategies. Our main results for combination of sure and almost-sure winning are as follows: (a) we show that for MDPs with finite-memory strategies the problem is in NP cap co-NP; (b) we show that for turn-based stochastic games the problem is co-NP-complete, both for finite-memory and infinite-memory strategies; and (c) we present algorithmic results for the finite-memory case, both for MDPs and turn-based stochastic games, by reduction to non-stochastic parity games. In addition we show that all the above complexity results also carry over to combination of sure and limit-sure winning, and results for all other combinations can be derived from existing results in the literature. Thus we present a complete picture for the study of combinations of two qualitative winning criteria for parity conditions in MDPs and turn-based stochastic games.
Publishing Year
Date Published
2019-08-01
Volume
140
Article Number
6
Conference
CONCUR: International Conference on Concurrency Theory
Conference Location
Amsterdam, Netherlands
Conference Date
2019-08-27 – 2019-08-30
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Cite this

Chatterjee K, Piterman N. Combinations of Qualitative Winning for Stochastic Parity Games. In: Vol 140. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:6. doi:10.4230/LIPICS.CONCUR.2019.6
Chatterjee, K., & Piterman, N. (2019). Combinations of Qualitative Winning for Stochastic Parity Games (Vol. 140, p. 6). Presented at the CONCUR: International Conference on Concurrency Theory, Amsterdam, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.CONCUR.2019.6
Chatterjee, Krishnendu, and Nir Piterman. “Combinations of Qualitative Winning for Stochastic Parity Games,” 140:6. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.CONCUR.2019.6.
K. Chatterjee and N. Piterman, “Combinations of Qualitative Winning for Stochastic Parity Games,” presented at the CONCUR: International Conference on Concurrency Theory, Amsterdam, Netherlands, 2019, vol. 140, p. 6.
Chatterjee K, Piterman N. 2019. Combinations of Qualitative Winning for Stochastic Parity Games. CONCUR: International Conference on Concurrency Theory, LIPIcs, vol. 140. 6.
Chatterjee, Krishnendu, and Nir Piterman. Combinations of Qualitative Winning for Stochastic Parity Games. Vol. 140, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 6, doi:10.4230/LIPICS.CONCUR.2019.6.
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