The complexity of stochastic games
Information and Computation
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
Finite State Markovian Decision Processes
Finite State Markovian Decision Processes
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
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
Solving simple stochastic games with few coin toss positions
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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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. We present in this paper a strategy improvement algorithm for computing the value of a concurrent safety game, that is, the maximal probability with which player 1 can enforce the safety objective. The algorithm yields a sequence of player-1 strategies which ensure probabilities of winning that converge monotonically to the value of the safety game. Our result is significant because the strategy improvement algorithm provides, for the first time, a way to approximate the value of a concurrent safety game from below. Since a value iteration algorithm, or a strategy improvement algorithm for reachability games, can be used to approximate the same value from above, the combination of both algorithms yields a method for computing a converging sequence of upper and lower bounds for the values of concurrent reachability and safety games. Previous methods could approximate the values of these games only from one direction, and as no rates of convergence are known, they did not provide a practical way to solve these games.