# 20.9 Memory requirements for generalized reachability games

Given a regular language $$L$$ (on finite words), we consider the condition over omega-words "having a prefix in $$L$$". We want to characterize the optimal memory requirements for this condition over finite arenas. The memory requirements for the opponent were characterized by Colcombet, Fijalkow and Horn in the 2012 paper "Playing Safe" (that also holds for infinite arenas).