The Descriptive Complexity of Parity Games

Abstract.

The question of whether the winning regions in parity games can be computed efficiently is one of the most important open problems in the field of infinite games. In this talk, I will talk about another aspect of the complexity of parity games - their logical definability. I will show how various parameters such as the number of priorities and whether we consider finite or infinite arenas affect the logical resources needed to define winning regions. I will also relate this to the study of Parity games on restricted classes of arenas.