  In temporal planning, many different temporal network formalisms are used to
model real world situations. Each of these formalisms has different features
which affect how easy it is to determine whether the underlying network of
temporal constraints is consistent. While many of the simpler models have been
well-studied from a computational complexity perspective, the algorithms
developed for advanced models which combine features have very loose complexity
bounds. In this paper, we provide tight completeness bounds for strong, weak,
and dynamic controllability checking of temporal networks that have conditions,
disjunctions, and temporal uncertainty. Our work exposes some of the subtle
differences between these different structures and, remarkably, establishes a
guarantee that all of these problems are computable in PSPACE.
