A cover (or quasiperiod) of a string S is a shorter string C such that every position of S is contained in some occurrence of C as a substring. The notion of covers was introduced by Apostolico and Ehrenfeucht over 30 years ago [Theor. Comput. Sci. 1993] and it has received significant attention from the combinatorial pattern matching community. In this note, we show how to efficiently test whether S admits a cover. Our tester can also be translated into a streaming algorithm.
Cite
@article{arxiv.2508.02231,
title = {Testing Quasiperiodicity},
author = {Christine Awofeso and Ben Bals and Oded Lachish and Solon P. Pissis},
journal= {arXiv preprint arXiv:2508.02231},
year = {2025}
}