I adapt the complexity as action prescription (CA) to a semi-classical model of two-dimensional dilaton gravity and determine the rate of increase of holographic complexity for an evaporating black hole. The results are consistent with previous numerical results for semi-classical black hole complexity using a volume prescription (CV) in the same model, but the CA calculation is fully analytic and provides a non-trivial positive test for the holographic representation of the black hole interior. Time permitting, I would like to share some developments in fluid dynamics without boost symmetries.