M+ M \log \frac{\mathfrak{a}^2}{8 G_{N} M}\right), \qquad d=2.$$

The parameters appearing in these formulas are explained in section 3. According to flat/BMSFT correspondence, Eq. is the rate of complexity growth for BMSFT$_{d}$, $d \geq 3$, and Eq. is the same rate for BMSFT$_2$. Our goal in this paper is to directly calculate both of these formulas by using the CA proposal in asymptotically flat spacetimes. The background geometries that we use in this paper are asymptotically flat two-sided black holes in spacetime dimensions greater than three and two-sided FSC in three dimensions. All of these geometries are given by taking the flat-space limit from their corresponding asymptotically AdS counterparts. The on-shell action in the flat case is evaluated on a particular region of spacetime, which is given by the intersection of two WDW patches. The null surfaces bounding these patches are anchored on the future or past null infinity. However, their intersection points meet neither past nor future null infinity. We show that despite the vanishing bulk term in the on-shell action, the results and are deducible from the boundary and joint terms.

The paper is organized as follows: In section two we start from preliminaries. Section three and four 