### Abstract

We show an efficient pattern-matching algorithm for strings that are succinctly described in terms of straight-line programs, in which the constants are symbols and the only operation is the concatenation. In this paper, both text T and pattern P are given by straight-line programs T and P . The length of the text T (pattern P, resp.) may grow exponentially with respect to its description size ||T|| -- n (||P|| = m, resp.). We show a new combinatorial property concerning with the periodic occurrences of a pattern in a text. Based on this property, we develop an O(n^{2}m^{2}) time algorithm using O(nm) space, which outputs a compact representation of all occurrences of P in T. This is superior to the algorithm proposed by Karpinski et al.[11], which runs in O((n + m)^{4} log (n + m)) time using O((n + m)^{3}) space, and finds only one occurrence. Moreover, our algorithm is much simpler than theirs.

Original language | English |
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Title of host publication | Combinatorial Pattern Matching - 8th Annual Symposium, CPM 1997, Proceedings |

Editors | Alberto Apostolico, Alberto Apostolico, Jotun Hein |

Publisher | Springer Verlag |

Pages | 1-11 |

Number of pages | 11 |

ISBN (Print) | 9783540632207 |

DOIs | |

Publication status | Published - 1997 |

Event | 8th Annual Symposium on Combinatorial Pattern Matching, CPM 1997 - Aarhus, Denmark Duration: Jun 30 1997 → Jul 2 1997 |

### 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 | 1264 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 8th Annual Symposium on Combinatorial Pattern Matching, CPM 1997 |
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Country | Denmark |

City | Aarhus |

Period | 6/30/97 → 7/2/97 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Combinatorial Pattern Matching - 8th Annual Symposium, CPM 1997, Proceedings*(pp. 1-11). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1264). Springer Verlag. https://doi.org/10.1007/3-540-63220-4_45