### 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 |

Volume | 5257 LNCS |

DOIs | |

State | Published - 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) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Developments in Language Theory - 12th International Conference, DLT 2008, Proceedings*(Vol. 5257 LNCS, 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

**General algorithms for testing the ambiguity of finite automata.** / Allauzen, Cyril; Mohri, Mehryar; Rastogi, Ashish.

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

*Developments in Language Theory - 12th International Conference, DLT 2008, Proceedings.*vol. 5257 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5257 LNCS, pp. 108-120, 12th International Conference on Developments in Language Theory, DLT 2008, Kyoto, Japan, 9/16/08. https://doi.org/10.1007/978-3-540-85780-8_8

}

TY - GEN

T1 - General algorithms for testing the ambiguity of finite automata

AU - Allauzen, Cyril

AU - Mohri, Mehryar

AU - Rastogi, Ashish

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=54249107645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=54249107645&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-85780-8_8

DO - 10.1007/978-3-540-85780-8_8

M3 - Conference contribution

SN - 3540857796

SN - 9783540857792

VL - 5257 LNCS

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

SP - 108

EP - 120

BT - Developments in Language Theory - 12th International Conference, DLT 2008, Proceedings

ER -