Attractor Decompositions in Games and Automata

Explore the concept of attractor decompositions in games and automata through this 37-minute lecture by Marcin Jurdzinski from the University of Warwick. Delve into the decomposition of graphs satisfying the parity condition and learn how their structure can be represented by ordered trees. Discover how attractor decompositions and their corresponding trees serve as a measure of structural complexity for winning strategies in parity games. Examine two key examples: the relationship between Lehtinen's register number and the Strahler number of attractor decomposition trees, and a quasi-polynomial translation from alternating parity automata to alternating weak automata on words. Gain insights into this collaborative research involving Laure Daviaud, Karoliina Lehtinen, and Thejaswini K.S., presented as part of the "Games and Equilibria in System Design and Analysis" series at the Simons Institute.