  Given the versatility of timed automata a huge body of work has evolved that
considers extensions of timed automata. One extension that has received a lot
of interest is timed automata with a, possibly unbounded, stack, also called
the pushdown timed automata (PDTA) model. While different algorithms have been
given for reachability in different variants of this model, most of these
results are purely theoretical and do not give rise to efficient
implementations. One main reason for this is that none of these algorithms (and
the implementations that exist) use the so-called zone-based abstraction, but
rely either on the region-abstraction or other approaches, which are
significantly harder to implement.
  In this paper, we show that a naive extension of the zone based reachability
algorithm for the control state reachability problem of timed automata is not
sound in the presence of a stack. To understand this better we give an
inductive rule based view of the zone reachability algorithm for timed
automata. This alternate view allows us to analyze and adapt the rules to also
work for pushdown timed automata. We obtain the first zone-based algorithm for
PDTA which is terminating, sound and complete. We implement our algorithm in
the tool TChecker and perform experiments to show its efficacy, thus leading
the way for more practical approaches to the verification of pushdown timed
systems.
