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In this paper, we investigate the action growth in various backgrounds in Einstein-Maxwell-dilaton theory. We calculate the full time evolution of action growth in the anti--de Sitter dilaton black hole and find it approaches the late time bound from above. We investigate the black hole which is asymptotically Lifshitz and obtain its late time and full time behavior. We find the violation of Lloyd bound in the late time limit and show the full time behavior approaching the late time bound from above and exhibiting some new features for z sufficiently large.
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An et al. (2018) studied this question.
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