  Although Dynamic Epistemic Logic (DEL) is an influential logical framework
for representing and reasoning about information change, little is known about
the computational complexity of its associated decision problems. In fact, we
only know that for public announcement logic, a fragment of DEL, the
satisfiability problem and the model-checking problem are respectively
PSPACE-complete and in P. We contribute to fill this gap by proving that for
the DEL language with event models, the model-checking problem is,
surprisingly, PSPACE-complete. Also, we prove that the satisfiability problem
is NEXPTIME-complete. In doing so, we provide a sound and complete tableau
method deciding the satisfiability problem.
