### Abstract

We solve the problems of detecting and counting various forms of regularities in a string represented as a Straight Line Program (SLP). Given an SLP of size n that represents a string s of length N, our algorithm computes all runs and squares in s in O(n^{3} h) time and O(n^{2}) space, where h is the height of the derivation tree of the SLP. We also show an algorithm to compute all gapped-palindromes in O(n^{3} h + gnhlog N) time and O(n^{2}) space, where g is the length of the gap. The key technique of the above solution also allows us to compute the periods and covers of the string in O(n^{2} h) time and O(nh(n + log^{2} N)) time, respectively.

Original language | English |
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Title of host publication | Mathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings |

Publisher | Springer Verlag |

Pages | 571-582 |

Number of pages | 12 |

ISBN (Print) | 9783642403125 |

DOIs | |

Publication status | Published - Jan 1 2013 |

Event | 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013 - Klosterneuburg, Austria Duration: Aug 26 2013 → Aug 30 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8087 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013 |
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Country | Austria |

City | Klosterneuburg |

Period | 8/26/13 → 8/30/13 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Mathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings*(pp. 571-582). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8087). Springer Verlag. https://doi.org/10.1007/978-3-642-40313-2_51