  In a reachability-time game, players Min and Max choose moves so that the
time to reach a final state in a timed automaton is minimised or maximised,
respectively. Asarin and Maler showed decidability of reachability-time games
on strongly non-Zeno timed automata using a value iteration algorithm. This
paper complements their work by providing a strategy improvement algorithm for
the problem. It also generalizes their decidability result because the proposed
strategy improvement algorithm solves reachability-time games on all timed
automata. The exact computational complexity of solving reachability-time games
is also established: the problem is EXPTIME-complete for timed automata with at
least two clocks.
