On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
The complexity of stochastic games
Information and Computation
Theoretical Computer Science
The complexity of mean payoff games on graphs
Theoretical Computer Science
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
Modularity for Timed and Hybrid Systems
CONCUR '97 Proceedings of the 8th International Conference on Concurrency Theory
EMSOFT '02 Proceedings of the Second International Conference on Embedded Software
Optimal strategies in priced timed game automata
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Trading Infinite Memory for Uniform Randomness in Timed Games
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Average-Price and Reachability-Price Games on Hybrid Automata with Strong Resets
FORMATS '08 Proceedings of the 6th international conference on Formal Modeling and Analysis of Timed Systems
An accelerated algorithm for 3-color parity games with an application to timed games
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Timed alternating-time temporal logic
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
Minimum-time reachability in timed games
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
A game-theoretic approach to fault diagnosis and identification of hybrid systems
Theoretical Computer Science
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We consider real-time games where the goal consists, for each player, in maximizing the average reward he or she receives per time unit. We consider zero-sum rewards, so that a reward of +r to one player corresponds to a reward of –r to the other player. The games are played on discrete-time game structures which can be specified using a two-player version of timed automata whose locations are labeled by reward rates. Even though the rewards themselves are zero-sum, the games are not, due to the requirement that time must progress along a play of the game. Since we focus on control applications, we define the value of the game to a player to be the maximal average reward per time unit that the player can ensure. We show that, in general, the values to players 1 and 2 do not sum to zero. We provide algorithms for computing the value of the game for either player; the algorithms are based on the relationship between the original, infinite-round game, and a derived game that is played for only finitely many rounds. As memoryless optimal strategies exist for both players in both games, we show that the problem of computing the value of the game is in NP∩coNP.