### Abstract

This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with ε-transitions. It gives an algorithm for testing the exponential ambiguity of an automaton A in time O(|A|_{E}^{2}, and finite or polynomial ambiguity in time O(|A|_{E}^{3}, where |A| _{E} denotes the number of transitions of A. These complexities significantly improve over the previous best complexities given for the same problem. Furthermore, the algorithms presented are simple and based on a general algorithm for the composition or intersection of automata. We also give an algorithm to determine in time O(|A|_{E}^{3} the degree of polynomial ambiguity of a polynomially ambiguous automaton A. Finally, we present an application of our algorithms to an approximate computation of the entropy of a probabilistic automaton.

Original language | English (US) |
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Title of host publication | Developments in Language Theory - 12th International Conference, DLT 2008, Proceedings |

Pages | 108-120 |

Number of pages | 13 |

DOIs | |

State | Published - Oct 27 2008 |

Event | 12th International Conference on Developments in Language Theory, DLT 2008 - Kyoto, Japan Duration: Sep 16 2008 → Sep 19 2008 |

### 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 | 5257 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 12th International Conference on Developments in Language Theory, DLT 2008 |
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Country | Japan |

City | Kyoto |

Period | 9/16/08 → 9/19/08 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Developments in Language Theory - 12th International Conference, DLT 2008, Proceedings*(pp. 108-120). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5257 LNCS). https://doi.org/10.1007/978-3-540-85780-8_8