Abstract
We consider two-player zero-sum partial-observation stochastic games on graphs. Based on the information available to the players these games can be classified as follows: (a) general partial-observation (both players have partial view of the game); (b) one-sided partial-observation (one player has partial-observation and the other player has complete-observation); and (c) perfect-observation (both players have complete view of the game). The one-sided partial-observation games subsumes the important special case of one-player partial-observation stochastic games (or partial-observation Markov decision processes (POMDPs)). Based on the randomization available for the strategies, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization. We consider all these classes of games with reachability, and parity objectives that can express all ω-regular objectives. The analysis problems are classified into the qualitative analysis that asks for the existence of a strategy that ensures the objective with probability 1; and the quantitative analysis that asks for the existence of a strategy that ensures the objective with probability at least λ ∈ (0,1).
In this talk we will cover a wide range of results: for perfect-observation games; for POMDPs; for one-sided partial-observation games; and for general partial-observation games.
The research was partly supported by Austrian Science Fund (FWF) Grant No P 23499- N23, FWF NFN Grant No S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award.
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References
Baier, C., Bertrand, N., Größer, M.: On decision problems for probabilistic Büchi automata. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 287–301. Springer, Heidelberg (2008)
Bertrand, N., Genest, B., Gimbert, H.: Qualitative determinacy and decidability of stochastic games with signals. In: LICS, pp. 319–328. IEEE Computer Society (2009)
Chatterjee, K.: Stochastic ω-Regular Games. PhD thesis, UC Berkeley (2007)
Chatterjee, K., Chmelik, M., Tracol, M.: What is decidable about partially observable Markov decision processes with omega-regular objectives. In: Proceedings of CSL 2013: Computer Science Logic (2013)
Chatterjee, K., Doyen, L.: The complexity of partial-observation parity games. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 1–14. Springer, Heidelberg (2010)
Chatterjee, K., Doyen, L.: Partial-observation stochastic games: How to win when belief fails. In: Proceedings of LICS 2012: Logic in Computer Science, pp. 175–184. IEEE Computer Society Press (2012)
Chatterjee, K., Doyen, L.: Games with a weak adversary. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014, Part II. LNCS, vol. 8573, pp. 110–121. Springer, Heidelberg (2014)
Chatterjee, K., Doyen, L., Gimbert, H., Henzinger, T.A.: Randomness for free. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 246–257. Springer, Heidelberg (2010)
Chatterjee, K., Doyen, L., Henzinger, T.A.: Qualitative analysis of partially-observable Markov decision processes. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 258–269. Springer, Heidelberg (2010)
Chatterjee, K., Doyen, L., Henzinger, T.A.: A survey of partial-observation stochastic parity games. Formal Methods in System Design 43(2), 268–284 (2013)
Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Algorithms for omega-regular games of incomplete information. Logical Methods in Computer Science, 3(3:4) (2007)
Chatterjee, K., Doyen, L., Nain, S., Vardi, M.Y.: The complexity of partial-observation stochastic parity games with finite-memory strategies. In: Muscholl, A. (ed.) FOSSACS 2014 (ETAPS). LNCS, vol. 8412, pp. 242–257. Springer, Heidelberg (2014)
Chatterjee, K., Jurdziński, M., Henzinger, T.A.: Simple stochastic parity games. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol. 2803, pp. 100–113. Springer, Heidelberg (2003)
Chatterjee, K., Jurdziński, M., Henzinger, T.: Quantitative stochastic parity games. In: SODA 2004, pp. 121–130. SIAM (2004)
Chatterjee, K., Tracol, M.: Decidable problems for probabilistic automata on infinite words. In: LICS, pp. 185–194 (2012)
Condon, A.: The complexity of stochastic games. I&C 96(2), 203–224 (1992)
Nain, S., Vardi, M.Y.: Solving partial-information stochastic parity games. In: LICS, pp. 341–348 (2013)
Paz, A.: Introduction to probabilistic automata (Computer science and applied mathematics). Academic Press (1971)
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Chatterjee, K. (2014). Partial-Observation Stochastic Reachability and Parity Games. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_1
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DOI: https://doi.org/10.1007/978-3-662-44522-8_1
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