### Abstract

The problem of computing the similarity between two sequences arises in many areas such as computational biology and natural language processing. A common measure of the similarity of two strings is their edit-distance, that is the minimal cost of a series of symbol insertions, deletions, or substitutions transforming one string into the other. In several applications such as speech recognition or computational biology, the objects to compare are distributions over strings, i.e., sets of strings representing a range of alternative hypotheses with their associated weights or probabilities. We define the edit-distance of two distributions over strings and present algorithms for computing it when these distributions are given by automata. In the particular case where two sets of strings are given by unweighted automata, their edit-distance can be computed using the general algorithm of composition of weighted transducers combined with a single-source shortest-paths algorithm. In the general case, we show that general weighted automata algorithms over the appropriate semirings can be used to compute the edit-distance of two weighted automata exactly. These include classical algorithms such as the composition and -removal of weighted transducers and a new and simple synchronization algorithm for weighted transducers which, combined with -removal, can be used to normalize weighted transducers with bounded delays. Our algorithm for computing the edit-distance of weighted automata can be used to improve the word accuracy of automatic speech recognition systems. It can also be extended to provide an edit-distance automaton useful for re-scoring and other post-processing purposes in the context of large-vocabulary speech recognition.

Original language | English (US) |
---|---|

Pages (from-to) | 957-982 |

Number of pages | 26 |

Journal | International Journal of Foundations of Computer Science |

Volume | 14 |

Issue number | 6 |

DOIs | |

State | Published - 2003 |

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### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

**Edit-distance of weighted automata : General definitions and algorithms.** / Mohri, Mehryar.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Edit-distance of weighted automata

T2 - General definitions and algorithms

AU - Mohri, Mehryar

PY - 2003

Y1 - 2003

N2 - The problem of computing the similarity between two sequences arises in many areas such as computational biology and natural language processing. A common measure of the similarity of two strings is their edit-distance, that is the minimal cost of a series of symbol insertions, deletions, or substitutions transforming one string into the other. In several applications such as speech recognition or computational biology, the objects to compare are distributions over strings, i.e., sets of strings representing a range of alternative hypotheses with their associated weights or probabilities. We define the edit-distance of two distributions over strings and present algorithms for computing it when these distributions are given by automata. In the particular case where two sets of strings are given by unweighted automata, their edit-distance can be computed using the general algorithm of composition of weighted transducers combined with a single-source shortest-paths algorithm. In the general case, we show that general weighted automata algorithms over the appropriate semirings can be used to compute the edit-distance of two weighted automata exactly. These include classical algorithms such as the composition and -removal of weighted transducers and a new and simple synchronization algorithm for weighted transducers which, combined with -removal, can be used to normalize weighted transducers with bounded delays. Our algorithm for computing the edit-distance of weighted automata can be used to improve the word accuracy of automatic speech recognition systems. It can also be extended to provide an edit-distance automaton useful for re-scoring and other post-processing purposes in the context of large-vocabulary speech recognition.

AB - The problem of computing the similarity between two sequences arises in many areas such as computational biology and natural language processing. A common measure of the similarity of two strings is their edit-distance, that is the minimal cost of a series of symbol insertions, deletions, or substitutions transforming one string into the other. In several applications such as speech recognition or computational biology, the objects to compare are distributions over strings, i.e., sets of strings representing a range of alternative hypotheses with their associated weights or probabilities. We define the edit-distance of two distributions over strings and present algorithms for computing it when these distributions are given by automata. In the particular case where two sets of strings are given by unweighted automata, their edit-distance can be computed using the general algorithm of composition of weighted transducers combined with a single-source shortest-paths algorithm. In the general case, we show that general weighted automata algorithms over the appropriate semirings can be used to compute the edit-distance of two weighted automata exactly. These include classical algorithms such as the composition and -removal of weighted transducers and a new and simple synchronization algorithm for weighted transducers which, combined with -removal, can be used to normalize weighted transducers with bounded delays. Our algorithm for computing the edit-distance of weighted automata can be used to improve the word accuracy of automatic speech recognition systems. It can also be extended to provide an edit-distance automaton useful for re-scoring and other post-processing purposes in the context of large-vocabulary speech recognition.

UR - http://www.scopus.com/inward/record.url?scp=4544382124&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4544382124&partnerID=8YFLogxK

U2 - 10.1142/S0129054103002114

DO - 10.1142/S0129054103002114

M3 - Article

AN - SCOPUS:4544382124

VL - 14

SP - 957

EP - 982

JO - International Journal of Foundations of Computer Science

JF - International Journal of Foundations of Computer Science

SN - 0129-0541

IS - 6

ER -