  A timed network consists of an arbitrary number of initially identical
1-clock timed automata, interacting via hand-shake communication. In this
setting there is no unique central controller, since all automata are initially
identical. We consider the universal safety problem for such controller-less
timed networks, i.e., verifying that a bad event (enabling some given
transition) is impossible regardless of the size of the network.
  This universal safety problem is dual to the existential coverability problem
for timed-arc Petri nets, i.e., does there exist a number $m$ of tokens, such
that starting with $m$ tokens in a given place, and none in the other places,
some given transition is eventually enabled.
  We show that these problems are PSPACE-complete.
