  This paper investigates the state complexities of subword-closed and
superword-closed languages, comparing them to regular languages. We focus on
the square root operator and the substitution operator. We establish an
exponential lower bound for superword-closed languages for the k-th root. For
subword-closed languages we analyze in detail a specific instance of the square
root problem for which a quadratic complexity is proven. For the substitution
operator, we show an exponential lower bound for the general substitution. We
then find some conditions for which we prove a quadratic upper bound.
