  Covers are a kind of quasiperiodicity in strings. A string $C$ is a cover of
another string $T$ if any position of $T$ is inside some occurrence of $C$ in
$T$. The shortest and longest cover arrays of $T$ have the lengths of the
shortest and longest covers of each prefix of $T$, respectively. The literature
has proposed linear-time algorithms computing longest and shortest cover arrays
taking border arrays as input. An equivalence relation $\approx$ over strings
is called a substring consistent equivalence relation (SCER) iff $X \approx Y$
implies (1) $|X| = |Y|$ and (2) $X[i:j] \approx Y[i:j]$ for all $1 \le i \le j
\le |X|$. In this paper, we generalize the notion of covers for SCERs and prove
that existing algorithms to compute the shortest cover array and the longest
cover array of a string $T$ under the identity relation will work for any SCERs
taking the accordingly generalized border arrays.
