A proper factor u of a string y is a cover of y if every letter of y is within some occurrence of u in y. The concept generalises the notion of periods of a string. An integer array is the minimal-cover (resp. maximal-cover) array of y if is the minimal (resp. maximal) length of covers of , or zero if no cover exists.
In this paper, we present a constructive algorithm checking the validity of an array as a minimal-cover or maximal-cover array of some string. When the array is valid, the algorithm produces a string over an unbounded alphabet whose cover array is the input array. All algorithms run in linear time due to an interesting combinatorial property of cover arrays: the sum of important values in a cover array is bounded by twice the length of the string.