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CPM

1995

Springer

1995

Springer

We consider strings which are succinctly described. The description is in terms of straight-line programs in which the constants are symbols and the only operation is the concatenation. Such descriptions correspond to systems of recurrences or to context-free grammars generating single words. The descriptive size of a string is the length n of a straight-line program (or size of a grammar) which deﬁnes this string. Usually the strings of descriptive size n are of exponential length. Fibonacci and Thue-Morse words are examples of such strings. We show that for a pattern P and text T of descriptive sizes n, m, an occurrence of P in T can be found (if there is any) in time polynomial with respect to n. This is nontrivial, since the actual lengths of P and T could be exponential, and none of the known string-matching algorithms is directly applicable. Our ﬁrst tool is the periodicity lemma, which allows to represent some sets of exponentially many positions in terms of feasibly many a...

Related Content

Added |
25 Aug 2010 |

Updated |
25 Aug 2010 |

Type |
Conference |

Year |
1995 |

Where |
CPM |

Authors |
Marek Karpinski, Wojciech Rytter, Ayumi Shinohara |

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