We study the average edit distance between two random strings. More precisely, we adapt a technique introduced by Lueker in the context of the average longest common subsequence of two random strings to improve the known upper bound on the average edit distance. We improve all the known upper bounds for small alphabets. We also provide a new implementation of Lueker technique to improve the lower bound on the average length of the longest common subsequence of two random strings for all small alphabets of size other than $2$ and $4$.

翻译：我们研究两个随机字符串之间的平均编辑距离。具体而言，我们采用Lueker在研究两个随机字符串的平均最长公共子序列时引入的技术，以改进已知的平均编辑距离上界。对于小字母表，我们改进了所有已知的上界结果。此外，我们提出了一种Lueker技术的新实现方法，针对所有大小不为$2$和$4$的小字母表，改进了两个随机字符串平均最长公共子序列长度的下界。