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We determine the effect on the computational complexity of a conformalanomaly using the Complexity=Action prescription of the gauge/gravitycorrespondence. To allow the involvement of said anomaly, we extend previousstudies to include arbitrary values for the anisotropic parameter and themagnetic field respectively on the Mateos-Trancanelli and the D'Hoker-Krausholographic models. Our main result is that the rate of change of thecomputational complexity is independent of the conformal anomaly in both cases.In addition, this allows us to also show that, if so desired, the saturation ofLloyd's bound at infinite time can be used as a renormalization condition.

Insensitivity of the complexity rate of change to the conformal anomaly and Lloyd's bound as a possible renormalization condition