### Abstract

There is a close relationship between formal language theory and data compression. Since 1990's various types of grammar-based text compression algorithms have been introduced. Given an input string, a grammar-based text compression algorithm constructs a context-free grammar that only generates the string. An interesting and challenging problem is pattern matching on context-free grammars P of size m and T of size n, which are the descriptions of pattern string P of length M and text string T of length N, respectively. The goal is to solve the problem in time proportional only to m and n, not to M nor N. Kieffer et al. introduced a very practical grammar-based compression method called multilevel pattern matching code (MPM code). In this paper, we propose an efficient pattern matching algorithm which, given two MPM grammars P and T, performs in O(mn ^{2}) time with O(mn) space. Our algorithm outperforms the previous best one by Miyazaki et al. which requires O(m ^{2}n ^{2}) time and O(mn) space.

Original language | English |
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Pages (from-to) | 225-236 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 3340 |

Publication status | Published - 2004 Dec 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)