  We consider two-player games played in real time on game structures with
clocks and parity objectives. The games are concurrent in that at each turn,
both players independently propose a time delay and an action, and the action
with the shorter delay is chosen. To prevent a player from winning by blocking
time, we restrict each player to strategies that ensure that the player cannot
be responsible for causing a zeno run. First, we present an efficient reduction
of these games to turn-based (i.e., nonconcurrent) finite-state (i.e., untimed)
parity games. The states of the resulting game are pairs of clock regions of
the original game. Our reduction improves the best known complexity for solving
timed parity games. Moreover, the rich class of algorithms for classical parity
games can now be applied to timed parity games.
  Second, we consider two restricted classes of strategies for the player that
represents the controller in a real-time synthesis problem, namely,
limit-robust and bounded-robust strategies. Using a limit-robust strategy, the
controller cannot choose an exact real-valued time delay but must allow for
some nonzero jitter in each of its actions. If there is a given lower bound on
the jitter, then the strategy is bounded-robust. We show that exact strategies
are more powerful than limit-robust strategies, which are more powerful than
bounded-robust strategies for any bound. For both kinds of robust strategies,
we present efficient reductions to standard timed automaton games. These
reductions provide algorithms for the synthesis of robust real-time
controllers.
