  The deterministic membership problem for timed automata asks whether the
timed language recognised by a nondeterministic timed automaton can be
recognised by a deterministic timed automaton. We show that the problem is
decidable when the input automaton is a one-clock nondeterministic timed
automaton without epsilon transitions and the number of clocks of the
deterministic timed automaton is fixed. We show that the problem in all the
other cases is undecidable, i.e., when either 1) the input nondeterministic
timed automaton has two clocks or more, or 2) it uses epsilon transitions, or
3) the number of clocks of the output deterministic automaton is not fixed.
