  In four dimensions, we consider a generalized scalar-tensor theory where the
coupling functions only depend on the kinetic term of the scalar field. For
this model, we obtain a set of hairy Anti-de-Sitter black hole solutions,
allowing us to calculate the computational complexity, according to the
Complexity equals Action conjecture. To perform this, the system contains a
particle moving on the boundary, corresponding to the insertion of a
fundamental string in the bulk. The effect string is given by the Nambu-Goto
term, analyzing the time development of this system. Together with the above,
we calculate the shear viscosity, where the viscosity/entropy density ratio can
violate the Kovtun-Son-Starinets bound for a suitable choice of coupling
functions.
