Week 1: Omega-automata: Buechi, Muller, Rabin and Street acceptance condition, closure under union, intersection and complementation, proof that deterministic Buechi automata are weaker than non-deterministic ones, definition of regular expressions.
Week 2: Proof that regular expressions, the logic S1S and Buechi automata are equivalent. Complexity of the emptiness and universality problems for Buechi automata.
Week 3: Games: winning conditions, strategies, memoryless determinancy. Proof that reachability games are determined.