Theoretical Computer Science
Games, Time, and Probability: Graph Models for System Design and Analysis
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
25 Years of Model Checking
Termination criteria for solving concurrent safety and reachability games
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Exact algorithms for solving stochastic games: extended abstract
Proceedings of the forty-third annual ACM symposium on Theory of computing
The complexity of solving reachability games using value and strategy iteration
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
A survey of stochastic ω-regular games
Journal of Computer and System Sciences
Heuristics for probabilistic timed automata with abstraction refinement
MMB'12/DFT'12 Proceedings of the 16th international GI/ITG conference on Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance
Solving simple stochastic games with few coin toss positions
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Strategy improvement for concurrent reachability and turn-based stochastic safety games
Journal of Computer and System Sciences
Stochastic parity games on lossy channel systems
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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A concurrent reachability game is a two-player game played on a graph: at each state, the players simultaneously and independently select moves; the two moves determine jointly a probability distribution over the successor states. The objective for player 1 consists in reaching a set of target states; the objective for player 2 is to prevent this, so that the game is zero-sum. Our contributions are two-fold. First, we present a simple proof of the fact that in concurrent reachability games, for allå 0, memoryless å-optimal strategies exist. A memoryless strategy is independent of the history of plays, and an å-optimal strategy achieves the objective with probability within a of the value of the game. In contrast to previous proofs of this fact, which rely on the limit behavior of discounted games using advanced Puisieux series analysis, our proof is elementary and combinatorial. Second, we present a strategy-improvement (a.k.a. policy-iteration) algorithm for concurrent games with reachability objectives.