### 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 ^{4}logN) 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 ^{4}log ^{5}N) time and O(c ^{2}log ^{2}N) space, which is faster than using the algorithm by Ga̧sieniec, Karpinski, Plandowski, and Rytter (1996) [4].

Original language | English |
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Pages (from-to) | 711-714 |

Number of pages | 4 |

Journal | Information Processing Letters |

Volume | 112 |

Issue number | 19 |

DOIs | |

Publication status | Published - Oct 15 2012 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications

### Cite this

*Information Processing Letters*,

*112*(19), 711-714. https://doi.org/10.1016/j.ipl.2012.06.017

**An efficient algorithm to test square-freeness of strings compressed by straight-line programs.** / Bannai, Hideo; Gagie, Travis; Tomohiro, I.; Inenaga, Shunsuke; Landau, Gad M.; Lewenstein, Moshe.

Research output: Contribution to journal › Article

*Information Processing Letters*, vol. 112, no. 19, pp. 711-714. https://doi.org/10.1016/j.ipl.2012.06.017

}

TY - JOUR

T1 - An efficient algorithm to test square-freeness of strings compressed by straight-line programs

AU - Bannai, Hideo

AU - Gagie, Travis

AU - Tomohiro, I.

AU - Inenaga, Shunsuke

AU - Landau, Gad M.

AU - Lewenstein, Moshe

PY - 2012/10/15

Y1 - 2012/10/15

N2 - 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 Ga̧sieniec, Karpinski, Plandowski, and Rytter (1996) [4].

AB - 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 Ga̧sieniec, Karpinski, Plandowski, and Rytter (1996) [4].

UR - http://www.scopus.com/inward/record.url?scp=84864150942&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864150942&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2012.06.017

DO - 10.1016/j.ipl.2012.06.017

M3 - Article

VL - 112

SP - 711

EP - 714

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 19

ER -