  We systematically explore the construction of Nielsen's circuit complexity to
a non-Lorentzian field theory keeping in mind its connection with flat
holography. We consider a 2d boundary field theory dual to 3d asymptotically
flat spacetimes with infinite-dimensional BMS_3 as the asymptotic symmetry
algebra. We compute the circuit complexity functional in two distinct ways. For
the Virasoro group, the complexity functional resembles the geometric action on
its co-adjoint orbit. Using the limiting approach on the relativistic results,
we show that it is possible to write BMS complexity in terms of the geometric
action on BMS co-adjoint orbit. However, the limiting approach fails to capture
essential information about the conserved currents generating BMS
supertranslations. Hence, we refine our analysis using the intrinsic approach.
Here, we use only the symmetry transformations and group product laws of BMS to
write the complexity functional. The refined analysis shows a richer structure
than only the geometric action. Lastly, we extremize and solve the equations of
motion (for a simple solution) in terms of the group paths and connect our
results with available literature.
