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To study the effect of parity-violation on the rate of complexity growth, byusing "Complexity=Action" conjecture, we find the complexity growth rates indifferent solutions of the chiral theory of Topologically Massive Gravity (TMG)and parity-preserving theory of New Massive Gravity (NMG). Using the results,one can see that decreasing the parameter $\mu$, which increases the effect ofChern-Simons term and increases chirality, would increase the rate of growth ofcomplexity. Also one can observe a stronger correlation between complexitygrowth and temperature rather than complexity growth and entropy. At the end wecomment on the possible meaning of the deforming term of chiral Liouvilleaction for the rate of complexity growth of warped CFTs in the Tensor NetworkRenormalization picture.

On complexity growth in massive gravity theories, the effects of chirality and more