The paper considers the controller synthesis problem for timed automata with Büchi objectives, where the controller's delay choices are subject to small perturbations. The authors generalize the existing work by allowing for punctual guards, i.e., transitions that can be taken after a unique delay, to be taken by the controller without perturbation.
The key contributions are:
The authors introduce a new notion of "robustly iterable" cycles, which characterizes cycles that the controller can repeat infinitely often despite the perturbations. This notion generalizes the existing characterization of winning cycles in the absence of punctual guards.
They show that the problem remains in PSPACE despite the presence of punctual guards, by adapting the reasoning about the region abstraction and the reachability relation along cycles.
The authors introduce the concept of "slices" - a partition of regions into convex polyhedra that represent equivalence classes of the reachability relation along a robustly iterable cycle. This allows them to precisely characterize the sets of valuations that the controller can enforce staying within.
The paper provides a comprehensive analysis of the robust controller synthesis problem in the presence of punctual guards, extending the existing techniques to handle this more general setting.
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