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.

翻译：本文考虑了加权 $k$-汉明距离与 $k$-编辑距离，它们是经典汉明距离与编辑距离的自然推广。作为本文的主要结果，我们证明了对于任意 $k\geq 2$，DECIS-$k$-汉明问题是 $\mathbb{P}$-SPACE-完全的，而 DECIS-$k$-编辑问题是 NEXPTIME-完全的。