Symbolic Fixpoint Algorithms for Logical LTL Games

Two-player games are a fruitful way to represent and reason about several important synthesis tasks. These tasks include controller synthesis (where one asks for a controller for a given plant such that the controlled plant satisfies a given temporal specification), program repair (setting values of variables to avoid exceptions), and synchronization synthesis (adding lock/unlock statements in multi-threaded programs to satisfy safety assertions). In all these applications, a solution directly corresponds to a winning strategy for one of the players in the induced game. In turn, logically-specified games offer a powerful way to model these tasks for large or infinite-state systems. Much of the techniques proposed for solving such games typically rely on abstraction-refinement or template-based solutions. In this paper, we show how to apply classical fixpoint algorithms, that have hitherto been used in explicit, finite-state, settings, to a symbolic logical setting. We implement our techniques in a tool called GENSys-LTL and show that they are not only effective in synthesizing valid controllers for a variety of challenging benchmarks from the literature, but often compute maximal winning regions and maximally-permissive controllers. We achieve 46.38X speed-up over the state of the art and also scale well for non-trivial LTL specifications.