An undecidable problem for timed automata

The reachability problem for timed automata is decidable when the coefficie nts in the guards are rational numbers. We show that the reachability probl em is undecidable when the coefficients are chosen from the set {1, root 2} . A consequence of this is that the parameter synthesis problem for timed a utomata with even a single parameter is undecidable. We discuss why such un decidability results arise in timed and hybrid systems, what they mean, and if it is possible to "get around" them.