Abstract
A closed string contains a proper factor occurring as both a prefix and a suffix but not elsewhere in the string. Closed strings were introduced by Fici (WORDS 2011) as objects of combinatorial interest. In this paper, we extend this definition to k-closed strings, for which a level of approximation is permitted up to a number of Hamming distance errors, set by the parameter k. We then address the problem of identifying whether or not a given string of length n over an integer alphabet is k-closed and additionally specifying the border resulting in the string being k-closed. Specifically, we present an O(kn)-time and O(n)-space algorithm to achieve this along with the pseudocode of an implementation.