SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 721-729, January 2020.
Given two random finite sequences from $[k]^n$ such that a prefix of the first sequence is a suffix of the second, we examine the length of their longest common subsequence (LCS). If $\ell$ is the length of the overlap, we prove that the expected length of an LCS is approximately $\max(\ell, {E}[L_n])$, where $L_n$ is the length of an LCS between two independent random sequences. We also obtain tail bounds on this quantity.

中文翻译：

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重叠词之间最长的公共子序列的长度

SIAM离散数学杂志，第34卷，第1期，第721-729页，2020年1月。
给定两个来自$ [k] ^ n $的随机有限序列，使得第一个序列的前缀为第二个的后缀，我们研究了它们最长的公共子序列（LCS）的长度。如果$ \ ell $是重叠的长度，我们证明LCS的预期长度约为$ \ max（\ ell，{E} [L_n]）$，其中$ L_n $是介于两个独立的随机序列。我们还获得了该数量的尾边界。