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2009
IEEE

Expressiveness and Closure Properties for Quantitative Languages

10 years 5 months ago
Expressiveness and Closure Properties for Quantitative Languages
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 ...
Krishnendu Chatterjee, Laurent Doyen, Thomas A. He
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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