An efficient algorithm to test square-freeness of strings compressed by straight-line programs

We give a simple algorithm that, given a straight-line program of size n for a string S of length N, tests whether S is square-free in O(n4logN) time and O(n2) space. The algorithm also allows us to test square-freeness on an arbitrary composition system of size c for S, in O(c4log5N) time and O(c2log2N) space, which is faster than using the algorithm by Ga̧sieniec, Karpinski, Plandowski, and Rytter (1996) [4]. ► Simple algorithm for square-freeness testing on compressed texts. ► Asymptotically faster than previous methods. ► Describes conversion from arbitrary composition system to small SLPs.