Games with Imperfect Information: Theory and Algorithms

We study observation-based strategies for two-player turnbased games played on graphs with parity objectives. An observationbased strategy relies on imperfect information about the history of a play, namely, on the past sequence of observations. Such games occur in the synthesis of a controller that does not see the private state of the plant. Our main results are twofold. First, we give a fixed-point algorithm for computing the set of states from which a player can win with a deterministic observation-based strategy. Second, we give an algorithm for computing the set of states from which a player can win with probability 1 with a randomized observation-based strategy for a reachability objective. This set is of interest because in the absence of perfect information, randomized strategies are more powerful than deterministic ones.