The complexity of stochastic games
Information and Computation
The complexity of probabilistic verification
Journal of the ACM (JACM)
Competitive Markov decision processes
Competitive Markov decision processes
Languages, automata, and logic
Handbook of formal languages, vol. 3
Quantitative solution of omega-regular games380872
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Concurrent Omega-Regular Games
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
The complexity of quantitative concurrent parity games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Reduction of stochastic parity to stochastic mean-payoff games
Information Processing Letters
Pure stationary optimal strategies in Markov decision processes
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Hi-index | 0.00 |
We study infinite stochastic games played by two-players over a finite state space, with objectives specified by sets of infinite traces. The games are concurrent (players make moves simultaneously and independently), stochastic (the next state is determined by a probability distribution that depends on the current state and chosen moves of the players) and infinite (proceeds for infinite number of rounds). The analysis of concurrent stochastic games can be classified into: quantitative analysis, analyzing the optimum value of the game; and qualitative analysis, analyzing the set of states with optimum value 1. We consider concurrent games with tail objectives, i.e., objectives that are independent of the finite-prefix of traces, and show that the class of tail objectives are strictly richer than the ω-regular objectives. We develop new proof techniques to extend several properties of concurrent games with ω-regular objectives to concurrent games with tail objectives. We prove the positive limit-one property for tail objectives, that states for all concurrent games if the optimum value for a player is positive for a tail objective Φ at some state, then there is a state where the optimum value is 1 for Φ, for the player. We also show that the optimum values of zero-sum (strictly conflicting objectives) games with tail objectives can be related to equilibrium values of nonzero-sum (not strictly conflicting objectives) games with simpler reachability objectives. A consequence of our analysis presents a polynomial time reduction of the quantitative analysis of tail objectives to the qualitative analysis for the sub-class of one-player stochastic games (Markov decision processes).