The complexity of stochastic games
Information and Computation
The complexity of probabilistic verification
Journal of the ACM (JACM)
The complexity of mean payoff games on graphs
Theoretical Computer Science
Competitive Markov decision processes
Competitive Markov decision processes
Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
Concurrent Omega-Regular Games
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Quantitative solution of omega-regular games
Journal of Computer and System Sciences - STOC 2001
Strategy Improvement for Concurrent Reachability Games
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Theoretical Computer Science
Simple stochastic games with few random vertices are easy to solve
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Recursive concurrent stochastic games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Solving simple stochastic games with few coin toss positions
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety objective to stay forever in a given set of states, and its dual, the reachability objective to reach a given set of states. First, we present a simple proof of the fact that in concurrent reachability games, for all @e0, memoryless @e-optimal strategies exist. A memoryless strategy is independent of the history of plays, and an @e-optimal strategy achieves the objective with probability within @e of the value of the game. In contrast to previous proofs of this fact, our proof is more elementary and more combinatorial. Second, we present a strategy-improvement (a.k.a. policy-iteration) algorithm for concurrent games with reachability objectives. Finally, we present a strategy-improvement algorithm for turn-based stochastic games (where each player selects moves in turns) with safety objectives. Our algorithms yield sequences of player-1 strategies which ensure probabilities of winning that converge monotonically (from below) to the value of the game.