### Abstract

This paper presents an exhaustive analysis of the problem of computing the L _{p} distance of two probabilistic automata. It gives efficient exact and approximate algorithms for computing these distances for p even and proves the problem to be NP-hard for all odd values of p, thereby completing previously known hardness results. It further proves the hardness of approximating the L _{p} distance of two probabilistic automata for odd values of p. Similar techniques to those used for computing the L _{p} distance also yield efficient algorithms for computing the Hellinger distance of two unambiguous probabilistic automata both exactly and approximately. A problem closely related to the computation of a distance between probabilistic automata is that of testing their equivalence. This paper also describes an efficient algorithm for testing the equivalence of two arbitrary probabilistic automata A _{1} and A _{2} in time O(|Σ| (|A _{1}| + |A _{2}|) ^{3}), a significant improvement over the previously best reported algorithm for this problem.

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

Pages (from-to) | 761-779 |

Number of pages | 19 |

Journal | International Journal of Foundations of Computer Science |

Volume | 18 |

Issue number | 4 |

DOIs | |

State | Published - Aug 2007 |

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### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

*International Journal of Foundations of Computer Science*,

*18*(4), 761-779. https://doi.org/10.1142/S0129054107004966

**L p distance and equivalence of probabilistic automata.** / Cortes, Corinna; Mohri, Mehryar; Rastogi, Ashish.

Research output: Contribution to journal › Article

*International Journal of Foundations of Computer Science*, vol. 18, no. 4, pp. 761-779. https://doi.org/10.1142/S0129054107004966

}

TY - JOUR

T1 - L p distance and equivalence of probabilistic automata

AU - Cortes, Corinna

AU - Mohri, Mehryar

AU - Rastogi, Ashish

PY - 2007/8

Y1 - 2007/8

N2 - This paper presents an exhaustive analysis of the problem of computing the L p distance of two probabilistic automata. It gives efficient exact and approximate algorithms for computing these distances for p even and proves the problem to be NP-hard for all odd values of p, thereby completing previously known hardness results. It further proves the hardness of approximating the L p distance of two probabilistic automata for odd values of p. Similar techniques to those used for computing the L p distance also yield efficient algorithms for computing the Hellinger distance of two unambiguous probabilistic automata both exactly and approximately. A problem closely related to the computation of a distance between probabilistic automata is that of testing their equivalence. This paper also describes an efficient algorithm for testing the equivalence of two arbitrary probabilistic automata A 1 and A 2 in time O(|Σ| (|A 1| + |A 2|) 3), a significant improvement over the previously best reported algorithm for this problem.

AB - This paper presents an exhaustive analysis of the problem of computing the L p distance of two probabilistic automata. It gives efficient exact and approximate algorithms for computing these distances for p even and proves the problem to be NP-hard for all odd values of p, thereby completing previously known hardness results. It further proves the hardness of approximating the L p distance of two probabilistic automata for odd values of p. Similar techniques to those used for computing the L p distance also yield efficient algorithms for computing the Hellinger distance of two unambiguous probabilistic automata both exactly and approximately. A problem closely related to the computation of a distance between probabilistic automata is that of testing their equivalence. This paper also describes an efficient algorithm for testing the equivalence of two arbitrary probabilistic automata A 1 and A 2 in time O(|Σ| (|A 1| + |A 2|) 3), a significant improvement over the previously best reported algorithm for this problem.

UR - http://www.scopus.com/inward/record.url?scp=34547532480&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547532480&partnerID=8YFLogxK

U2 - 10.1142/S0129054107004966

DO - 10.1142/S0129054107004966

M3 - Article

VL - 18

SP - 761

EP - 779

JO - International Journal of Foundations of Computer Science

JF - International Journal of Foundations of Computer Science

SN - 0129-0541

IS - 4

ER -