Timed automata can be studied in not only a dense-time setting but also a
  discrete-time setting. The most common example of discrete-time semantics
  is the so called \emph{sampled} semantics (i.e., discrete semantics with a
  fixed time granularity $\epsilon$).  In the real-time setting, the
  universality problem is known to be undecidable for timed automata.  In
  this work, we study the universality question for the languages accepted
  by timed automata with sampled semantics.  On the negative side, we show
  that deciding whether for all sampling periods $\epsilon$ a timed
  automaton accepts all timed words in $\epsilon$-sampled semantics is as
  hard as in the real-time case, i.e., undecidable. On the positive side, we
  show that checking whether there is a sampling period such that a timed
  automaton accepts all untimed words in $\epsilon$-sampled semantics is
  decidable.  Our proof uses clock difference relations, developed to
  characterize the reachability relation for timed automata in connection
  with sampled semantics.