### Abstract

A number of different techniques have been introduced in the last few decades to create ε-free automata representing regular expressions such as the Glushkov automata, follow automata, or Antimirov automata. This paper presents a simple and unified view of all these construction methods both for unweighted and weighted regular expressions. It describes simpler algorithms with time complexities at least as favorable as that of the best previously known techniques, and provides a concise proof of their correctness. Our algorithms are all based on two standard automata operations: epsilon-removal and minimization. This contrasts with the multitude of complicated and special-purpose techniques previously described in the literature, and makes it straightforward to generalize these algorithms to the weighted case. In particular, we extend the definition and construction of follow automata to the case of weighted regular expressions over a closed semiring and present the first algorithm to compute weighted Antimirov automata.

Original language | English (US) |
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Title of host publication | Mathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings |

Pages | 110-121 |

Number of pages | 12 |

Volume | 4162 LNCS |

State | Published - 2006 |

Event | 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006 - Stara Lesna, Slovakia Duration: Aug 28 2006 → Sep 1 2006 |

### 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 | 4162 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006 |
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Country | Slovakia |

City | Stara Lesna |

Period | 8/28/06 → 9/1/06 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Mathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings*(Vol. 4162 LNCS, pp. 110-121). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4162 LNCS).

**A unified construction of the Glushkov, follow, and antimirov automata.** / Allauzen, Cyril; Mohri, Mehryar.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Mathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings.*vol. 4162 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4162 LNCS, pp. 110-121, 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006, Stara Lesna, Slovakia, 8/28/06.

}

TY - GEN

T1 - A unified construction of the Glushkov, follow, and antimirov automata

AU - Allauzen, Cyril

AU - Mohri, Mehryar

PY - 2006

Y1 - 2006

N2 - A number of different techniques have been introduced in the last few decades to create ε-free automata representing regular expressions such as the Glushkov automata, follow automata, or Antimirov automata. This paper presents a simple and unified view of all these construction methods both for unweighted and weighted regular expressions. It describes simpler algorithms with time complexities at least as favorable as that of the best previously known techniques, and provides a concise proof of their correctness. Our algorithms are all based on two standard automata operations: epsilon-removal and minimization. This contrasts with the multitude of complicated and special-purpose techniques previously described in the literature, and makes it straightforward to generalize these algorithms to the weighted case. In particular, we extend the definition and construction of follow automata to the case of weighted regular expressions over a closed semiring and present the first algorithm to compute weighted Antimirov automata.

AB - A number of different techniques have been introduced in the last few decades to create ε-free automata representing regular expressions such as the Glushkov automata, follow automata, or Antimirov automata. This paper presents a simple and unified view of all these construction methods both for unweighted and weighted regular expressions. It describes simpler algorithms with time complexities at least as favorable as that of the best previously known techniques, and provides a concise proof of their correctness. Our algorithms are all based on two standard automata operations: epsilon-removal and minimization. This contrasts with the multitude of complicated and special-purpose techniques previously described in the literature, and makes it straightforward to generalize these algorithms to the weighted case. In particular, we extend the definition and construction of follow automata to the case of weighted regular expressions over a closed semiring and present the first algorithm to compute weighted Antimirov automata.

UR - http://www.scopus.com/inward/record.url?scp=33750044039&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750044039&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33750044039

SN - 3540377913

SN - 9783540377917

VL - 4162 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 110

EP - 121

BT - Mathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings

ER -