  In this paper we consider the weighted $k$-Hamming and $k$-Edit distances,
that are natural generalizations of the classical Hamming and Edit distances.
As main results of this paper we prove that for any $k\geq 2$ the
DECIS-$k$-Hamming problem is $\mathbb{P}$-SPACE-complete and the DECIS-$k$-Edit
problem is NEXPTIME-complete.
