  We present novel algorithms solving the satisfiability problem and the model
checking problem for Visibly Linear Dynamic Logic (VLDL) in asymptotically
optimal time via a reduction to the emptiness problem for tree automata with
B\"uchi acceptance. Since VLDL allows for the specification of important
properties of recursive systems, this reduction enables the efficient analysis
of such systems.
  Furthermore, as the problem of tree automata emptiness is well-studied, this
reduction enables leveraging the mature algorithms and tools for that problem
in order to solve the satisfiability problem and the model checking problem for
VLDL.
