Last week, Thomas Colcombet presented a proof of Positional Determinacy for Parity Games, following a forward approach. In this second part, I will present a completely different proof of the same result based on ideas by Muller and Schupp, following a backward approach.

I will highlight the differences between the two approaches, and the applications of both techniques. In particular, I will explain why backward approaches naturally induce determinization procedures for automata over infinite words.

The talk will be self-contained, and in particular I will quickly recall all required definitions at the beginning.