  In this paper, according to CA duality, we study complexity growth of
Born-Infeld (BI) black holes. As a comparison, we study action growth of dyonic
black holes in Einstein-Maxwell gravity at the beginning. We study action
growth of electric BI black holes in dRGT massive gravity, and find BI black
holes in massive gravity complexify faster than the Einstein gravity
counterparts. We study action growth of the purely electric and magnetic
Einstein-Born-Infeld (EBI) black holes in general dimensions and the dyonic EBI
black holes in four-dimensions, and find the manners of action growth are
different between electric and magnetic EBI black holes. In all the gravity
systems we considered, we find action growth rates vanish for the purely
magnetic black holes, which is unexpected. In order to ameliorate the
situation, we add the boundary term of matter field to the action and discuss
the outcomes of the addition.
