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The reachability problem for timed automata asks if a given automaton has a run leading to an accepting state, and the liveness problem asks if the automaton has an infinite run which visits accepting states infinitely often. Both these problems are known to be Pspace-complete. We show that if P Pspace, the liveness problem is more difficult than the reachability problem; in other words we exhibit a family of automata for which solving the reachability problem with the standard algorithm is indoi:10.1145/3372310 fatcat:tqyrs77ozrfulhhoigmi7pus4q