Asynchronous Omega-Regular Games with Partial Information

We address the strategy problem for ω-regular two-player games with partial information, played on finite game graphs. We consider two different kinds of observability on a general model, a standard synchronous and an asynchronous one. In the asynchronous setting, moves which have no visible effect for a player are hidden completely from that player. We generalize the usual powerset construction for eliminating partial information to arbitrary, not necessarily observation based, winning conditions, both in the synchronous and in the asynchronous case, and we show that this generalized construction effectively preserves ω-regular winning conditions. From this we infer decidability of the strategy problem for arbitrary ω-regular winning conditions, in both cases. We also show that our ω-regular framework is sufficient for reasoning about synchronous and asynchronous knowledge by proving that any formula of the epistemic temporal specification formalism ETL can be effectively translated into an S1S-formula defining the same specification.