correspondence. To do so, we need to define a portion of spacetime in which the gravitational action is evaluated. Since the final formulas for the growth rate are simply given by taking the flat space limit from the AdS/CFT calculation, we can check the results of various potential regions. Our main achievement in this paper is that the evaluation of the gravitational action must be done on a region that is given by the intersection of four WDW patches. The boundary of two of these patches connects past singularity to the future one by crossing from past null infinity. The boundary of other patches starts from past null infinity and using future null infinity eventually reaches to the future singularity. Using this portion of spacetime we show that the rate of complexity growth is zero for the initial times and for the late times is exactly the same as what one finds by taking the flat-space limit from the AdS/CFT calculation.

Despite CFT$_2$, the rate of complexity growth is a constant for the BMSFT$_2$ and differs from Lloyd’s bound [@Lloyd:limit] by a logarithmic term. In higher dimensions, this rate is not a constant and approaches Lloyd’s bound from above. This 