From Quasi-Dominions to Progress Measures

In this paper we revisit the approaches to the solution of parity games based on progress measures and show how the notion of quasi dominions can be integrated with those approaches. The idea is that, while progress measure based techniques typically focus on one of the two players, little information is gathered on the other player during the solution process. Adding quasi dominions provides additional information on this player that can be leveraged to accelerate convergence to a progress measure. To accommodate quasi dominions, however, a non trivial refinement of the approach is necessary. In particular, we need to introduce a novel notion of measure and a new approach to prove correctness of the resulting solution technique.