Pseudo-Power Avoidance

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 $\varphi$. We first classify the alphabet $\mathrm{\Sigma }$ and the antimorphic involution $\varphi$, 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.