  Recently a Complexity-Action (CA) duality conjecture has been proposed, which
relates the quantum complexity of a holographic boundary state to the action of
a Wheeler-DeWitt (WDW) patch in the anti-de Sitter (AdS) bulk. In this paper we
further investigate the duality conjecture for stationary AdS black holes and
derive some exact results for the growth rate of action within the
Wheeler-DeWitt (WDW) patch at late time approximation, which is supposed to be
dual to the growth rate of quantum complexity of holographic state. Based on
the results from the general $D$-dimensional Reissner-Nordstr\"{o}m (RN)-AdS
black hole, rotating/charged Ba\~{n}ados-Teitelboim-Zanelli (BTZ) black hole,
Kerr-AdS black hole and charged Gauss-Bonnet-AdS black hole, we present a
universal formula for the action growth expressed in terms of some
thermodynamical quantities associated with the outer and inner horizons of the
AdS black holes. And we leave the conjecture unchanged that the stationary AdS
black hole in Einstein gravity is the fastest computer in nature.
