A factor C of a string S is called a cover of S, if each position of S is contained in an occurrence of C. Breslauer (1992) [3] proposed a well-known $\mathcal{O}(n)$-time algorithm that computes the shortest cover of every prefix of a string of length n. We show an $\mathcal{O}(n\log n)$-time and $\mathcal{O}(n)$-space algorithm that computes the shortest cover of every cyclic shift of a string of length n and an $\mathcal{O}(n)$-time algorithm that computes the shortest among these covers. We also provide a combinatorial characterization of shortest covers of cyclic shifts of Fibonacci strings that leads to efficient algorithms for computing these covers.

We further consider the bound on the number of different lengths of shortest covers of cyclic shifts of the same string of length n. We show that this number is $\mathrm{\Theta }(\log n)$ for Fibonacci strings.

一个因素Ç串的小号被称为的盖小号，如果每个位置小号包含在的发生Ç。Breslauer（1992）[3]提出了一个著名的$\mathcal{Ø}（ñ）$计算长度为n的字符串的每个前缀的最短覆盖时间的实时算法。我们展示了$\mathcal{Ø}（ñ\mathrm{日志}ñ）$-时间和 $\mathcal{Ø}（ñ）$空间算法，计算长度为n且长度为n的字符串的每个循环移位的最短覆盖$\mathcal{Ø}（ñ）$时间算法，计算这些覆盖范围中最短的时间。我们还提供了斐波那契弦的循环移位的最短覆盖的组合特征，这导致了用于计算这些覆盖的有效算法。

我们进一步考虑长度为n的同一字符串的循环移位的最短覆盖的不同长度的数量的界限。我们证明这个数字是$\mathrm{\Theta }（\mathrm{日志}ñ）$ 用于斐波那契弦。