list of papers related to the flat-space holography see the references of [@Riegler:2017fqv] and [@Prohazka:2017lqb].

After the remarkable work of Ryu and Takayanagi [@Ryu:2006bv] (which proposes a holographic description for the entanglement entropy of CFT in the context of AdS/CFT), it seems that we can translate all of the information physics to the gravitational counterpart by the virtue of holography. There are other aspects of information physics that seem natural to find their holographic picture. One of the most important physical quantities in information physics is complexity (see [@complexity; @1; @Aaronson:2016vto] for reviews). The complexity measures the number of gates that are needed to achieve a desirable state from an initial state. There are two different proposals for the holographic complexity. Here, we will focus on the complexity equals action (CA) conjecture that was proposed in [@Brown:2015bva; @Brown:2015lvg]. According to this proposal, the boundary complexity is given by the bulk gravitational action that is evaluated on a region of spacetime known as the Wheeler-DeWitt (WDW) path. It is a portion of space-time bounded by null surfaces anchored at the related time on the boundary. There is a different proposal that relates the complexity to the volume of an anchored region 