  Updatable timed automata (UTA) are extensions of classic timed automata that
allow special updates to clock variables, like x:= x - 1, x := y + 2, etc., on
transitions. Reachability for UTA is undecidable in general. Various subclasses
with decidable reachability have been studied. A generic approach to UTA
reachability consists of two phases: first, a static analysis of the automaton
is performed to compute a set of clock constraints at each state; in the second
phase, reachable sets of configurations, called zones, are enumerated. In this
work, we improve the algorithm for the static analysis. Compared to the
existing algorithm, our method computes smaller sets of constraints and
guarantees termination for more UTA, making reachability faster and more
effective. As the main application, we get an alternate proof of decidability
and a more efficient algorithm for timed automata with bounded subtraction, a
class of UTA widely used for modelling scheduling problems. We have implemented
our procedure in the tool TChecker and conducted experiments that validate the
benefits of our approach.
