### Abstract

problem of the computation of a distance between two probabilistic automata arises in a variety of statistical learning problems. This paper presents an exhaustive analysis of the problem of computing the L _{p} distance between two automata. We give efficient exact and approximate algorithms for computing these distances for p even and prove the problem to be NP-hard for all odd values of p, thereby completing previously known hardness results. We also give an efficient algorithm for computing the Hellinger distance between unambiguous probabilistic automata. Our results include a general algorithm for the computation of the norm of an unambiguous probabilistic automaton based on a monoid morphism and efficient algorithms for the specific case of the computation of the L _{p} norm. Finally, we also describe an efficient algorithm for testing the equivalence of two arbitrary probabilistic automata A _{1} and A _{2} based on Schiitzenberger's standardization with a running time complexity of O(|Σ| (\A _{1}\ + |A _{2}|)3), a significant improvement over the previously best algorithm reported for this problem.

Original language | English (US) |
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Title of host publication | Implementation and Application of Automata - 11th International Conference, CIAA 2006, Proceedings |

Pages | 137-149 |

Number of pages | 13 |

Volume | 4094 LNCS |

State | Published - 2006 |

Event | 11th International Conference on Implementation and Application of Automata, CIAA 2006 - Taipei, Taiwan, Province of China Duration: Aug 21 2006 → Aug 23 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 | 4094 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 11th International Conference on Implementation and Application of Automata, CIAA 2006 |
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Country | Taiwan, Province of China |

City | Taipei |

Period | 8/21/06 → 8/23/06 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Implementation and Application of Automata - 11th International Conference, CIAA 2006, Proceedings*(Vol. 4094 LNCS, pp. 137-149). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4094 LNCS).

**On the computation of some standard distances between probabilistic automata.** / Cortes, Corinna; Mohri, Mehryar; Rastogi, Ashish.

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

*Implementation and Application of Automata - 11th International Conference, CIAA 2006, Proceedings.*vol. 4094 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4094 LNCS, pp. 137-149, 11th International Conference on Implementation and Application of Automata, CIAA 2006, Taipei, Taiwan, Province of China, 8/21/06.

}

TY - GEN

T1 - On the computation of some standard distances between probabilistic automata

AU - Cortes, Corinna

AU - Mohri, Mehryar

AU - Rastogi, Ashish

PY - 2006

Y1 - 2006

N2 - problem of the computation of a distance between two probabilistic automata arises in a variety of statistical learning problems. This paper presents an exhaustive analysis of the problem of computing the L p distance between two automata. We give efficient exact and approximate algorithms for computing these distances for p even and prove the problem to be NP-hard for all odd values of p, thereby completing previously known hardness results. We also give an efficient algorithm for computing the Hellinger distance between unambiguous probabilistic automata. Our results include a general algorithm for the computation of the norm of an unambiguous probabilistic automaton based on a monoid morphism and efficient algorithms for the specific case of the computation of the L p norm. Finally, we also describe an efficient algorithm for testing the equivalence of two arbitrary probabilistic automata A 1 and A 2 based on Schiitzenberger's standardization with a running time complexity of O(|Σ| (\A 1\ + |A 2|)3), a significant improvement over the previously best algorithm reported for this problem.

AB - problem of the computation of a distance between two probabilistic automata arises in a variety of statistical learning problems. This paper presents an exhaustive analysis of the problem of computing the L p distance between two automata. We give efficient exact and approximate algorithms for computing these distances for p even and prove the problem to be NP-hard for all odd values of p, thereby completing previously known hardness results. We also give an efficient algorithm for computing the Hellinger distance between unambiguous probabilistic automata. Our results include a general algorithm for the computation of the norm of an unambiguous probabilistic automaton based on a monoid morphism and efficient algorithms for the specific case of the computation of the L p norm. Finally, we also describe an efficient algorithm for testing the equivalence of two arbitrary probabilistic automata A 1 and A 2 based on Schiitzenberger's standardization with a running time complexity of O(|Σ| (\A 1\ + |A 2|)3), a significant improvement over the previously best algorithm reported for this problem.

UR - http://www.scopus.com/inward/record.url?scp=33749396846&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749396846&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33749396846

SN - 354037213X

SN - 9783540372134

VL - 4094 LNCS

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

SP - 137

EP - 149

BT - Implementation and Application of Automata - 11th International Conference, CIAA 2006, Proceedings

ER -