### Abstract

In this paper we study the problem of deciding whether a given compressed string contains a square. A string x is called a square if x = zz and z = u ^{k} implies k = 1 and u = z. A string w is said to be square-free if no substrings of w are squares. Many efficient algorithms to test if a given string is square-free, have been developed so far. However, very little is known for testing square-freeness of a given compressed string. In this paper, we give an O(max(n ^{2}, n log ^{2} N))-time O(n ^{2})-space solution to test square-freeness of a given compressed string, where n and N are the size of a given compressed string and the corresponding decompressed string, respectively. Our input strings are compressed by balanced straight line program (BSLP). We remark that BSLP has exponential compression, that is, N = O(2 ^{n}). Hence no decompress-then-test approaches can be better than our method in the worst case.

Original language | English |
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Title of host publication | Theory of Computing 2009 - Proceedings of the Fifteenth Computing |

Subtitle of host publication | The Australasian Theory Symposium, CATS 2009 |

Publication status | Published - 2009 Dec 1 |

Event | Theory of Computing 2009 - 15th Computing: The Australasian Theory Symposium, CATS 2009 - Wellington, New Zealand Duration: 2009 Jan 20 → 2009 Jan 23 |

### Publication series

Name | Conferences in Research and Practice in Information Technology Series |
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Volume | 94 |

ISSN (Print) | 1445-1336 |

### Other

Other | Theory of Computing 2009 - 15th Computing: The Australasian Theory Symposium, CATS 2009 |
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Country | New Zealand |

City | Wellington |

Period | 09/1/20 → 09/1/23 |

### Keywords

- Balanced straight line program
- Repetitions
- Squares
- String algorithm
- Text compression

### ASJC Scopus subject areas

- Computer Networks and Communications
- Computer Science Applications
- Hardware and Architecture
- Information Systems
- Software

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## Cite this

*Theory of Computing 2009 - Proceedings of the Fifteenth Computing: The Australasian Theory Symposium, CATS 2009*(Conferences in Research and Practice in Information Technology Series; Vol. 94).