### 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) |
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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 |

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

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## Cite this

_{p}distance and equivalence of probabilistic automata.

*International Journal of Foundations of Computer Science*,

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