Games with bound guess actions

We introduce games with (bound) guess actions. These are games in which the players may be asked along the play to provide numbers that need to satisfy some bounding constraints. These are natural extensions of domination games occurring in the regular cost function theory. In this paper we consider more specifically the case where the constraints to be bounded are regular cost functions, and the long term goal is an ω-regular winning condition. We show that such games are decidable on finite arenas.