  The window mechanism was introduced by Chatterjee et al. to reinforce
mean-payoff and total-payoff objectives with time bounds in two-player
turn-based games on graphs. It has since proved useful in a variety of
settings, including parity objectives in games and both mean-payoff and parity
objectives in Markov decision processes.
  We study window parity objectives in timed automata and timed games: given a
bound on the window size, a path satisfies such an objective if, in all states
along the path, we see a sufficiently small window in which the smallest
priority is even. We show that checking that all time-divergent paths of a
timed automaton satisfy such a window parity objective can be done in
polynomial space, and that the corresponding timed games can be solved in
exponential time. This matches the complexity class of timed parity games,
while adding the ability to reason about time bounds. We also consider
multi-dimensional objectives and show that the complexity class does not
increase. To the best of our knowledge, this is the first study of the window
mechanism in a real-time setting.
