Synthesising game solving techniques
When trying to find errors in programs, or to show that none remain, when trying to automatically produce protocol adapters that guarantee that systems seamlessly work together, and when checking if a specifications can be implemented, algorithm that solve infinite-duration games on graphs do the lion's share of the work. These are games with winning condition that range from parity through mean- or discounted payoff to simple stochastic reachability.

These games are connected by a chain of reductions, so that the latter can be considered as a generalisation of the further, in the sense that there exists a polynomial time reduction to simple stochastic games. When a new result that improves the complexity status of one of these games appears in the literature, it is very interesting, not only from a theoretical point of view, to study whether the improvement can be transferred to another type of game. This specific goal can be achieved in two ways: by building a new optimal reduction or by transferring the algorithmic advancements into a new solver for a game with a different winning condition. This is particularly interesting for practical advancements, like exploiting dominions, and theoretical advancements, such as the introduction of quasi-polynomial time algorithms.

As these recent advances are currently only available for parity games, we will answer the question of whether these advances translate to the more general classes and investigate the more fundamental question of whether these games are inter reducible: are there backwards translations that justify to consider these games as representatives of an individual complexity class, or is there evidence that back-translations are not possible? This will allow us to uncover connections and differences between the types of infinite-duration games that can lead to the proof of equivalence or inequality of the complexity of the classes of games and to the discovery of tighter reductions and faster algorithms.