  Repetition avoidance has been studied since Thue's work. In this paper, we
considered another type of repetition, which is called pseudo-power. This
concept is inspired by Watson-Crick complementarity in DNA sequence and is
defined over an antimorphic involution $\phi$. We first classify the alphabet
$\Sigma$ and the antimorphic involution $\phi$, under which there exists
sufficiently long pseudo-$k$th-power-free words. Then we present algorithms to
test whether a finite word $w$ is pseudo-$k$th-power-free.
