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Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such games is $PSPACE$-complete, although it is fixed-parameter tractable with the number of reachability objectives as parameter. Moreover, we consider the memory requirements for both players and give matching upper and lower bounds on the size of winning strategies. In order to allow more efficient algorithms, we consider subclasses of generalized reachability games. We show that bounding the size of the reachability sets gives two natural subclasses where deciding the winner can be done efficiently.
The use of monotonicity and Tarskis theorem in existence proofs of equilibria is very widespread in economics, while Tarskis theorem is also often used for similar purposes in the context of verification. However, there has been relatively little in
We consider the complexity properties of modern puzzle games, Hexiom, Cut the Rope and Back to Bed. The complexity of games plays an important role in the type of experience they provide to players. Back to Bed is shown to be PSPACE-Hard and the firs
In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally efficient, runnin
Computers are known to solve a wide spectrum of problems, however not all problems are computationally solvable. Further, the solvable problems themselves vary on the amount of computational resources they require for being solved. The rigorous analy
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