[@Stanford:2014jda; @Alishahiha:2015rta; @Barbon:2015ria; @Barbon:2015soa] (complexity=volume (CV) proposal) . Both of these conjectures have been proposed in the context of AdS/CFT correspondence.

In this paper, we want to use the CA conjecture and calculate the rate of complexity growth in BMSFT by using flat-space holography. As mentioned above, an approach for improving flat-space holography is given by taking the flat-space limit from the AdS/CFT calculations[^1]. The corresponding computation of the rate of complexity growth in the context of AdS/CFT has been done in [@Carmi:2017jqz] (see also [@Cai:2016xho]-[@Moosa:2017yiz]). Therein, the gravitational action is evaluated in the background of eternal two-sided black holes. It was assumed that these geometries are the holographic duals of thermofield double states in the boundary theory [@Maldacena:2001kr].

The final answer of [@Carmi:2017jqz] for the rate of complexity growth is given in terms of bulk parameters. It is not difficult to take the flat-space limit from these results. One can check that taking the flat-space limit from the results of [@Carmi:2017jqz] yields the following expressions for the rate of complexity growth: [^2]

$$\label{result for d4}
\dot{\mathcal{C}} = \frac{1}{\pi}\frac{d I}{d \mu}=\frac{1}{\pi}\left[ 2 M - \frac{r_M^{d-2} \Omega_{d-1} (d-1)}{16 \pi G_{N}  }f(r_M)\log \frac{-\mathfrak{a}^2}{f(r_M)}\right], \qquad d\geq 3,$$

$$\label{result d3}
\dot{\mathcal{C}}= \frac{1}{\pi} \left( 2 