Abstract
We establish the precise complexity of the model
checking problem for the main logics of knowledge
and time. While this problem was known to be
non-elementary for agents with perfect recall, with
a number of exponentials that increases with the alternation of knowledge operators, the precise complexity of the problem when the maximum alternation is fixed has been an open problem for twenty
years. We close it by establishing improved upper bounds for CTL* with knowledge, and providing matching lower bounds that also apply for epistemic extensions of LTL and CTL