Optimal Strategy Synthesis for Stochastic Boolean Games

In this study, we regard a classification of winning strategy and payoff function over infinite plays. The central goal is to examine the values of the game and then to determine the existence of optimal (∈-optimal) strategy. Furthermore, we are interested in the subject of what sort of optimal (∈-optimal) strategy exists. We first review on generalised reachability games and then we introduce a new game, called Boolean games and concentrate on games with a Boolean combination of the reachability games. The primary contribution is on the existence of ∈-optimal finite memory strategy of each player for any ∈ > 0. We also prove every player has no ∈-optimal memoryless strategy for some Boolean game.