Determinisability of register and timed automata

The deterministic membership problem for timed automata asks whether the language given by a nondeterministic automaton can be recognised automaton. An analogous stated in setting of register automata. We draw complete decidability/complexity landscape problem, both and For automata, we prove that is decidable when input one-register (possibly with epsilon transitions) number registers output fixed. This optimal: show all other cases undecidable, i.e., either (1) has two or more (even without transitions), (2) it uses guessing, (3) not follows similar pattern. one-clock transitions clocks Again, this more, transitions,