  Given a two-sided noetherian ring $A$ with a dualizing complex, we show that
the big finitistic dimension of $A$ is finite if and only if every bounded
below Gorenstein-projective-acyclic cochain complex of Gorenstein-projective
$A$-modules is contractible. If $A$ is further assumed to be an Artin algebra,
we also prove a Gorenstein variant of a theorem of Rickard, showing its
finitistic dimension is finite in case its Gorenstein-injective derived
category is generated by the Gorenstein-injective modules.
