### Abstract

We present efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with ε-transitions. We give 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. Additionally, we give an algorithm to determine in time O(|A|_{E}
^{3}) the degree of polynomial ambiguity of a polynomially ambiguous automaton A and present an application of our algorithms to an approximate computation of the entropy of a probabilistic automaton. We also study the double-tape ambiguity of finite-state transducers. We show that the general problem is undecidable and that it is NP-hard for acyclic transducers. We present a specific analysis of the double-tape ambiguity of transducers with bounded delay. In particular, we give a characterization of double-tape ambiguity for synchronized transducers with zero delay that can be tested in quadratic time and give an algorithm for testing the double-tape ambiguity of transducers with bounded delay.

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

Pages (from-to) | 883-904 |

Number of pages | 22 |

Journal | International Journal of Foundations of Computer Science |

Volume | 22 |

Issue number | 4 |

DOIs | |

State | Published - Jun 2011 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

**General algorithms for testing the ambiguity of finite automata and the double-tape ambiguity of finite-state transducers.** / Allauzen, Cyril; Mohri, Mehryar; Rastogi, Ashish.

Research output: Contribution to journal › Article

*International Journal of Foundations of Computer Science*, vol. 22, no. 4, pp. 883-904. https://doi.org/10.1142/S0129054111008477

}

TY - JOUR

T1 - General algorithms for testing the ambiguity of finite automata and the double-tape ambiguity of finite-state transducers

AU - Allauzen, Cyril

AU - Mohri, Mehryar

AU - Rastogi, Ashish

PY - 2011/6

Y1 - 2011/6

N2 - We present efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with ε-transitions. We give 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. Additionally, we give an algorithm to determine in time O(|A|E 3) the degree of polynomial ambiguity of a polynomially ambiguous automaton A and present an application of our algorithms to an approximate computation of the entropy of a probabilistic automaton. We also study the double-tape ambiguity of finite-state transducers. We show that the general problem is undecidable and that it is NP-hard for acyclic transducers. We present a specific analysis of the double-tape ambiguity of transducers with bounded delay. In particular, we give a characterization of double-tape ambiguity for synchronized transducers with zero delay that can be tested in quadratic time and give an algorithm for testing the double-tape ambiguity of transducers with bounded delay.

AB - We present efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with ε-transitions. We give 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. Additionally, we give an algorithm to determine in time O(|A|E 3) the degree of polynomial ambiguity of a polynomially ambiguous automaton A and present an application of our algorithms to an approximate computation of the entropy of a probabilistic automaton. We also study the double-tape ambiguity of finite-state transducers. We show that the general problem is undecidable and that it is NP-hard for acyclic transducers. We present a specific analysis of the double-tape ambiguity of transducers with bounded delay. In particular, we give a characterization of double-tape ambiguity for synchronized transducers with zero delay that can be tested in quadratic time and give an algorithm for testing the double-tape ambiguity of transducers with bounded delay.

UR - http://www.scopus.com/inward/record.url?scp=79958815145&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79958815145&partnerID=8YFLogxK

U2 - 10.1142/S0129054111008477

DO - 10.1142/S0129054111008477

M3 - Article

AN - SCOPUS:79958815145

VL - 22

SP - 883

EP - 904

JO - International Journal of Foundations of Computer Science

JF - International Journal of Foundations of Computer Science

SN - 0129-0541

IS - 4

ER -