  Infinite-state games are a commonly used model for the synthesis of reactive
systems with unbounded data domains. Symbolic methods for solving such games
need to be able to construct intricate arguments to establish the existence of
winning strategies. Often, large problem instances require prohibitively
complex arguments. Therefore, techniques that identify smaller and simpler
sub-problems and exploit the respective results for the given game-solving task
are highly desirable. In this paper, we propose the first such technique for
infinite-state games. The main idea is to enhance symbolic game-solving with
the results of localized attractor computations performed in sub-games. The
crux of our approach lies in identifying useful sub-games by computing
permissive winning strategy templates in finite abstractions of the
infinite-state game. The experimental evaluation of our method demonstrates
that it outperforms existing techniques and is applicable to infinite-state
games beyond the state of the art.
