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LICS

2009

IEEE

2009

IEEE

Weighted automata are nondeterministic automata with numerical weights on transitions. They can deﬁne quantitative languages L that assign to each word w a real number L(w). In the case of inﬁnite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit average, or discounted sum of the transition weights. We study expressiveness and closure questions about these quantitative languages. We ﬁrst show that the set of words with value greater than a threshold can be non-ω-regular for deterministic limit-average and discounted-sum automata, while this set is always ω-regular when the threshold is isolated (i.e., some neighborhood around the threshold contains no word). In the latter case, we prove that the ω-regular language is robust against small perturbations of the transition weights. We next consider automata with transition weights 0 or 1 and show that they are as expressive as general weighted automata in the limit-average case, but not in the ...

Related Content

Added |
24 May 2010 |

Updated |
24 May 2010 |

Type |
Conference |

Year |
2009 |

Where |
LICS |

Authors |
Krishnendu Chatterjee, Laurent Doyen, Thomas A. Henzinger |

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