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

Authors:
Hideo Bannai;Travis Gagie;Tomohiro I;Shunsuke Inenaga;Gad M. Landau;Moshe Lewenstein
Affiliations:
Department of Informatics, Kyushu University, Japan;Department of Computer Science and Engineering, Aalto University, Finland;Department of Informatics, Kyushu University, Japan;Department of Informatics, Kyushu University, Japan;Department of Computer Science, University of Haifa, Israel and Department of Computer Science and Engineering, NYU-Poly, USA;Department of Computer Science, Bar Ilan University, Israel
Venue:
Information Processing Letters
Year:
2012

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Abstract

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(n^4logN) time and O(n^2) space. The algorithm also allows us to test square-freeness on an arbitrary composition system of size c for S, in O(c^4log^5N) time and O(c^2log^2N) space, which is faster than using the algorithm by Ga@?sieniec, Karpinski, Plandowski, and Rytter (1996) [4].